Go back to the main page of Sollya

Commands available within Sollya

Help pages

Name:

abs the absolute value.

Library names:

sollya_obj_t sollya_lib_abs(sollya_obj_t) sollya_obj_t sollya_lib_build_function_abs(sollya_obj_t) #define SOLLYA_ABS(x) sollya_lib_build_function_abs(x)

Description:

Go back to the list of commands

Name:

absolute indicates an absolute error for externalplot, fpminimax or supnorm

Library names:

sollya_obj_t sollya_lib_absolute() int sollya_lib_is_absolute(sollya_obj_t)

Usage:

absolute : absolute|relative

Description:

Example 1:

   > bashexecute("gcc -fPIC -c externalplotexample.c");
   > bashexecute("gcc -shared -o externalplotexample externalplotexample.o -lgmp -lmpfr");
   > externalplot("./externalplotexample",absolute,exp(x),[-1/2;1/2],12,perturb);
See also: externalplot, fpminimax, relative, bashexecute, supnorm
Go back to the list of commands

Name:

accurateinfnorm computes a faithful rounding of the infinity norm of a function

Usage:

accurateinfnorm(function,range,constant) : (function, range, constant) -> constant accurateinfnorm(function,range,constant,exclusion range 1,...,exclusion range n) : (function, range, constant, range, ..., range) -> constant

Parameters:

Description:

Example 1:

   > p = remez(exp(x), 5, [-1;1]);
   > accurateinfnorm(p - exp(x), [-1;1], 20);
   4.52055246569216251373291015625e-5
   > accurateinfnorm(p - exp(x), [-1;1], 30);
   4.5205513970358879305422306060791015625e-5
   > accurateinfnorm(p - exp(x), [-1;1], 40);
   4.520551396713923253400935209356248378753662109375e-5

Example 2:

   > p = remez(exp(x), 5, [-1;1]);
   > midpointmode = on!;
   > infnorm(p - exp(x), [-1;1]);
   0.45205~5/7~e-4
   > accurateinfnorm(p - exp(x), [-1;1], 40);
   4.520551396713923253400935209356248378753662109375e-5
See also: infnorm, dirtyinfnorm, supnorm, checkinfnorm, remez, diam
Go back to the list of commands

Name:

acos the arccosine function.

Library names:

sollya_obj_t sollya_lib_acos(sollya_obj_t) sollya_obj_t sollya_lib_build_function_acos(sollya_obj_t) #define SOLLYA_ACOS(x) sollya_lib_build_function_acos(x)

Description:

See also: cos
Go back to the list of commands

Name:

acosh the arg-hyperbolic cosine function.

Library names:

sollya_obj_t sollya_lib_acosh(sollya_obj_t) sollya_obj_t sollya_lib_build_function_acosh(sollya_obj_t) #define SOLLYA_ACOSH(x) sollya_lib_build_function_acosh(x)

Description:

See also: cosh
Go back to the list of commands

Name:

&& boolean AND operator

Library name:

sollya_obj_t sollya_lib_and(sollya_obj_t, sollya_obj_t)

Usage:

expr1 && expr2 : (boolean, boolean) -> boolean

Parameters:

Description:

Example 1:

   > true && false;
   false

Example 2:

   > (1 == exp(0)) && (0 == log(1));
   true
See also: ||, !
Go back to the list of commands

Name:

annotatefunction Annotates a Sollya function object with an approximation that is faster to evaluate

Library names:

sollya_obj_t sollya_lib_annotatefunction(sollya_obj_t, sollya_obj_t,                                          sollya_obj_t, sollya_obj_t, ...); sollya_obj_t sollya_lib_v_annotatefunction(sollya_obj_t, sollya_obj_t,                                            sollya_obj_t, sollya_obj_t,                                            va_list);

Usage:

annotatefunction(f, g, I, d) : (function, function, range, range) -> function annotatefunction(f, g, I, d, x0) : (function, function, range, range, constant) -> function

Parameters:

Description:

Example 1:

   > verbosity=1!;
   > procedure EXP(X,n,p) {
               var res, oldPrec;
               oldPrec = prec;
               prec = p!;
               "Using procedure function exponential with X=" @ X @ ", n=" @ n @ ", and p=" @ p;
               res = exp(X);
               prec = oldPrec!;
               return res;
          };
   > g = function(EXP);
   > p = 46768052394588893382516870161332864698044514954899b-165 + x * (23384026197294446691258465802074096632225783601255b-164 + x * (5846006549323611672948426613035653821819225877423b-163 + x * (3897337699549074448627696490806815137319821946501b-164 + x * (7794675399098148717422744621371434831048848817417b-167 + x * (24942961277114075921122941174178849425809856036737b-171 + x * (8314320425704876115613838900105097456456371179471b-172 + x * (19004160973039701371579356991645932289422670402995b-176 + x * (19004160972669324148912122254449912156003926801563b-179 + x * (33785175062542597526738679493857229456702396042255b-183 + x * (6757035113643674378393625988264926886191860669891b-184 + x * (9828414707511252769908089206114262766633532289937b-188 + x * (26208861108003813314724515233584738706961162212965b-193 + x * (32257064253325954315953742396999456577223350602741b-197 + x * (578429089657689569703509185903214676926704485495b-195 + x * 2467888542176675658523627105540996778984959471957b-201))))))))))))));
   > h = annotatefunction(g, p, [-1/2;1/2], [-475294848522543b-124;475294848522543b-124]);
   > h == g;
   true
   > prec = 24;
   The precision has been set to 24 bits.
   > h(0.25);
   Warning: rounding has happened. The value displayed is a faithful rounding to 24 bits of the true result.
   1.2840254
   > prec = 165;
   The precision has been set to 165 bits.
   > h(0.25);
   Using procedure function exponential with X=[0.25;0.25], n=0, and p=185
   Warning: rounding has happened. The value displayed is a faithful rounding to 165 bits of the true result.
   1.28402541668774148407342056806243645833628086528147
See also: chebyshevform, taylorform, remez, supnorm, infnorm
Go back to the list of commands

Name:

:. add an element at the end of a list.

Library name:

sollya_obj_t sollya_lib_append(sollya_obj_t, sollya_obj_t)

Usage:

L:.x : (list, any type) -> list

Parameters:

Description:

Example 1:

   > [|2,3,4|]:.5;
   [|2, 3, 4, 5|]

Example 2:

   > [|1,2,3|]:.[|4,5,6|];
   [|1, 2, 3, [|4, 5, 6|]|]

Example 3:

   > [||]:.1;
   [|1|]
See also: .:, @
Go back to the list of commands

Name:

~ floating-point evaluation of a constant expression

Library name:

sollya_obj_t sollya_lib_approx(sollya_obj_t)

Usage:

~ expression : function -> constant ~ something : any type -> any type

Parameters:

Description:

Example 1:

   > print(exp(5));
   exp(5)
   > print(~ exp(5));
   148.41315910257660342111558004055227962348766759388

Example 2:

   > autosimplify = off!;

Example 3:

   > print(~sin(5 * pi));
   0

Example 4:

   > print(~exp(x));
   exp(x)
   > print(~ "Hello");
   Hello

Example 5:

   > print(~exp(x*5*Pi));
   exp((pi) * 5 * x)
   > print(exp(x* ~(5*Pi)));
   exp(x * 15.7079632679489661923132169163975144209858469968757)

Example 6:

   > print(~exp(5)*x);
   148.41315910257660342111558004055227962348766759388 * x
   > print( (~exp(5))*x);
   148.41315910257660342111558004055227962348766759388 * x
   > print(~(exp(5)*x));
   exp(5) * x
See also: evaluate, prec, error
Go back to the list of commands

Name:

asciiplot plots a function in a range using ASCII characters

Library name:

void sollya_lib_asciiplot(sollya_obj_t, sollya_obj_t)

Usage:

asciiplot(function, range) : (function, range) -> void

Parameters:

Description:

Example 1:

   > asciiplot(exp(x),[1;2]);
                                                                             xx
                                                                           xx  
                                                                         xx    
                                                                       xx      
                                                                     xx        
                                                                  xxx          
                                                                xx             
                                                             xxx               
                                                           xx                  
                                                        xxx                    
                                                     xxx                       
                                                  xxx                          
                                               xxx                             
                                            xxx                                
                                        xxxx                                   
                                     xxx                                       
                                 xxxx                                          
                             xxxx                                              
                         xxxx                                                  
                     xxxx                                                      
                xxxxx                                                          
           xxxxx                                                               
      xxxxx                                                                    
   xxx                                                                         

Example 2:

   > asciiplot(expm1(x),[-1;2]);
                            |                                                 x
                            |                                                x
                            |                                               x  
                            |                                              x   
                            |                                            xx    
                            |                                           x      
                            |                                          x       
                            |                                        xx        
                            |                                       x          
                            |                                     xx           
                            |                                   xx             
                            |                                 xx               
                            |                               xx                 
                            |                             xx                   
                            |                           xx                     
                            |                        xxx                       
                            |                     xxx                          
                            |                 xxxx                             
                            |             xxxx                                 
                            |         xxxx                                     
                            |   xxxxxx                                         
   ---------------------xxxxxxxx-----------------------------------------------
            xxxxxxxxxxxx    |                                                  
   xxxxxxxxx                |                                                  

Example 3:

   > asciiplot(5,[-1;1]);
   5

Example 4:

   > asciiplot(exp(x),[1;1]);
   2.7182818284590452353602874713526624977572470937
See also: plot, externalplot
Go back to the list of commands

Name:

asin the arcsine function.

Library names:

sollya_obj_t sollya_lib_asin(sollya_obj_t) sollya_obj_t sollya_lib_build_function_asin(sollya_obj_t) #define SOLLYA_ASIN(x) sollya_lib_build_function_asin(x)

Description:

See also: sin
Go back to the list of commands

Name:

asinh the arg-hyperbolic sine function.

Library names:

sollya_obj_t sollya_lib_asinh(sollya_obj_t) sollya_obj_t sollya_lib_build_function_asinh(sollya_obj_t) #define SOLLYA_ASINH(x) sollya_lib_build_function_asinh(x)

Description:

See also: sinh
Go back to the list of commands

Name:

atan the arctangent function.

Library names:

sollya_obj_t sollya_lib_atan(sollya_obj_t) sollya_obj_t sollya_lib_build_function_atan(sollya_obj_t) #define SOLLYA_ATAN(x) sollya_lib_build_function_atan(x)

Description:

See also: tan
Go back to the list of commands

Name:

atanh the hyperbolic arctangent function.

Library names:

sollya_obj_t sollya_lib_atanh(sollya_obj_t) sollya_obj_t sollya_lib_build_function_atanh(sollya_obj_t) #define SOLLYA_ATANH(x) sollya_lib_build_function_atanh(x)

Description:

See also: tanh
Go back to the list of commands

Name:

autodiff Computes the first n derivatives of a function at a point or over an interval.

Library name:

sollya_obj_t sollya_lib_autodiff(sollya_obj_t, sollya_obj_t, sollya_obj_t)

Usage:

autodiff(f, n, x0) : (function, integer, constant) -> list autodiff(f, n, I) : (function, integer, range) -> list

Parameters:

Description:

Example 1:

   > L = autodiff(exp(cos(x))+sin(exp(x)), 5, 0);
   > midpointmode = on!;
   > for f_i in L do f_i;
   0.3559752813266941742012789792982961497379810154498~2/4~e1
   0.5403023058681397174009366074429766037323104206179~0/3~
   -0.3019450507398802024611853185539984893647499733880~6/2~e1
   -0.252441295442368951995750696489089699886768918239~6/4~e1
   0.31227898756481033145214529184139729746320579069~1/3~e1
   -0.16634307959006696033484053579339956883955954978~3/1~e2

Example 2:

   > f = log(cos(x)+x);
   > L = autodiff(log(cos(x)+x), 5, [2,4]);
   > L[0];
   [0;1.27643852425465597132446653114905059102580436018893]
   > evaluate(f, [2,4]);
   [0.45986058925497069206106494332976097408234056912429;1.20787210589964169595901037621103012113048821362855]
   > fprime = diff(f);
   > L[1];
   [2.53086745013099407167484456656211083053393118778677e-2;1.7568024953079282513726390945118290941359128873365]
   > evaluate(fprime,[2,4]);
   [2.71048755415961996452136364304380881763456815673085e-2;1.1091953066394329083739722578862353140555843127995]

Example 3:

   > L = autodiff(sin(x)/x, 0, [-1,1]);
   > L[0];
   [-infty;infty]
   > evaluate(sin(x)/x, [-1,1]);
   [0.5403023058681397174009366074429766037323104206179;1]
See also: diff, evaluate
Go back to the list of commands

Name:

autosimplify activates, deactivates or inspects the value of the automatic simplification state variable

Library names:

void sollya_lib_set_autosimplify_and_print(sollya_obj_t) void sollya_lib_set_autosimplify(sollya_obj_t) sollya_obj_t sollya_lib_get_autosimplify()

Usage:

autosimplify = activation value : on|off -> void autosimplify = activation value ! : on|off -> void autosimplify : on|off

Parameters:

Description:

Example 1:

   > autosimplify = on !;
   > print(x - x);
   0
   > autosimplify = off ;
   Automatic pure tree simplification has been deactivated.
   > print(x - x);
   x - x

Example 2:

   > autosimplify = on !;
   > print(rationalapprox(sin(pi/5.9),7));
   33 / 65
   > autosimplify = off !;
   > print(rationalapprox(sin(pi/5.9),7));
   33 / 65
See also: print, ==, !=, prec, points, diam, display, verbosity, canonical, taylorrecursions, timing, fullparentheses, midpointmode, hopitalrecursions, remez, rationalapprox, taylor
Go back to the list of commands

Name:

bashevaluate executes a shell command and returns its output as a string

Library names:

sollya_obj_t sollya_lib_bashevaluate(sollya_obj_t, ...) sollya_obj_t sollya_lib_v_bashevaluate(sollya_obj_t, va_list)

Usage:

bashevaluate(command) : string -> string bashevaluate(command,input) : (string, string) -> string

Parameters:

Description:

Example 1:

   > bashevaluate("LANG=C date");
   Wed Feb  8 10:46:20 CET 2017

Example 2:

   > [| bashevaluate("echo Hello") |];
   [|"Hello"|]

Example 3:

   > a = bashevaluate("sed -e 's/a/e/g;'", "Hallo");
   > a;
   Hello
See also: bashexecute
Go back to the list of commands

Name:

bashexecute executes a shell command.

Library name:

void sollya_lib_bashexecute(sollya_obj_t)

Usage:

bashexecute(command) : string -> void

Parameters:

Description:

Example 1:

   > bashexecute("LANG=C date");
   Wed Feb  8 10:46:22 CET 2017
See also: execute, readfile, parse, bashevaluate
Go back to the list of commands

Name:

binary special value for global state display

Library names:

sollya_obj_t sollya_lib_binary() int sollya_lib_is_binary(sollya_obj_t)

Description:

See also: decimal, dyadic, powers, hexadecimal, display
Go back to the list of commands

Name:

bind partially applies a procedure to an argument, returning a procedure with one argument less

Usage:

bind(proc, ident, obj) : (procedure, identifier type, any type) -> procedure

Parameters:

Description:

Example 1:

   > procedure add(X,Y) { return X + Y; };
   > succ = bind(add,X,1);
   > succ(5);
   6
   > succ;
   proc(Y)
   {
   nop;
   return (proc(X, Y)
   {
   nop;
   return (X) + (Y);
   })(1, Y);
   }

Example 2:

   > procedure add(X,Y) { return X + Y; };
   > succ = bind(add,X,1);
   > five = bind(succ,Y,4);
   > five();
   5
   > five;
   proc()
   {
   nop;
   return (proc(Y)
   {
   nop;
   return (proc(X, Y)
   {
   nop;
   return (X) + (Y);
   })(1, Y);
   })(4);
   }

Example 3:

   > verbosity = 1!;
   > procedure add(X,Y) { return X + Y; };
   > foo = bind(add,R,1);
   Warning: the given procedure has no argument named "R". The procedure is returned unchanged.
   > foo;
   proc(X, Y)
   {
   nop;
   return (X) + (Y);
   }
See also: procedure, proc, function, @
Go back to the list of commands

Name:

boolean keyword representing a boolean type

Library name:

SOLLYA_EXTERNALPROC_TYPE_BOOLEAN

Usage:

boolean : type type

Description:

See also: externalproc, constant, function, integer, list of, range, string, object
Go back to the list of commands

Name:

canonical brings all polynomial subexpressions of an expression to canonical form or activates, deactivates or checks canonical form printing

Library names:

void sollya_lib_set_canonical_and_print(sollya_obj_t) void sollya_lib_set_canonical(sollya_obj_t) sollya_obj_t sollya_lib_canonical(sollya_obj_t) sollya_obj_t sollya_lib_get_canonical()

Usage:

canonical(function) : function -> function canonical = activation value : on|off -> void canonical = activation value ! : on|off -> void

Parameters:

Description:

Example 1:

   > print(canonical(1 + x * (x + 3 * x^2)));
   1 + x^2 + 3 * x^3
   > print(canonical((x + 1)^7));
   1 + 7 * x + 21 * x^2 + 35 * x^3 + 35 * x^4 + 21 * x^5 + 7 * x^6 + x^7

Example 2:

   > print(canonical(exp((x + 1)^5) - log(asin(((x + 2) + x)^4 * (x + 1)) + x)));
   exp(1 + 5 * x + 10 * x^2 + 10 * x^3 + 5 * x^4 + x^5) - log(asin(16 + 80 * x + 160 * x^2 + 160 * x^3 + 80 * x^4 + 16 * x^5) + x)

Example 3:

   > canonical;
   off
   > (x + 2)^9;
   512 + x * (2304 + x * (4608 + x * (5376 + x * (4032 + x * (2016 + x * (672 + x * (144 + x * (18 + x))))))))
   > canonical = on;
   Canonical automatic printing output has been activated.
   > (x + 2)^9;
   512 + 2304 * x + 4608 * x^2 + 5376 * x^3 + 4032 * x^4 + 2016 * x^5 + 672 * x^6 + 144 * x^7 + 18 * x^8 + x^9
   > canonical;
   on
   > canonical = off!;
   > (x + 2)^9;
   512 + x * (2304 + x * (4608 + x * (5376 + x * (4032 + x * (2016 + x * (672 + x * (144 + x * (18 + x))))))))
See also: horner, print, autosimplify
Go back to the list of commands

Name:

ceil the usual function ceil.

Library names:

sollya_obj_t sollya_lib_ceil(sollya_obj_t) sollya_obj_t sollya_lib_build_function_ceil(sollya_obj_t) #define SOLLYA_CEIL(x) sollya_lib_build_function_ceil(x)

Description:

See also: floor, nearestint, round, RU
Go back to the list of commands

Name:

chebyshevform computes a rigorous polynomial approximation

Library name:

sollya_obj_t sollya_lib_chebyshevform(sollya_obj_t, sollya_obj_t,                                       sollya_obj_t);

Usage:

chebyshevform(f, n, I) : (function, integer, range) -> list

Parameters:

Description:

Example 1:

   > TL=chebyshevform(exp(x), 10, [-1,1]);
   > p=TL[0];
   > Delta=TL[2];
   > p; Delta;
   1.00000000000000000000000000000000000000000000000017 + x * (1.0000000002738981919773953471453626764777115166417 + x * (0.50000000002276754368023326882542097365411870042312 + x * (0.166666661190450656168988993421371510533693281444003 + x * (4.1666666211440433973188799509591566161569698904644e-2 + x * (8.3333639749825520034240517636254576844423981913793e-3 + x * (1.38889143636148090706862105537216777944219976325265e-3 + x * (1.98342776066472142284727329700227389403558111865906e-4 + x * (2.47957727598277888282218067965324267955768146489014e-5 + x * (2.8254033440982477266316370012542019511804700836066e-6 + x * 2.8136983333718843135828091163040197490633045592362e-7)))))))))
   [-2.71406412827174505775085010461449926572460824320373e-11;2.71406412827174505775085010461449926572460824320373e-11]
See also: taylorform, diff, autodiff, taylor, remez
Go back to the list of commands

Name:

checkinfnorm checks whether the infinity norm of a function is bounded by a value

Library name:

sollya_obj_t sollya_lib_checkinfnorm(sollya_obj_t, sollya_obj_t,                                      sollya_obj_t)

Usage:

checkinfnorm(function,range,constant) : (function, range, constant) -> boolean

Parameters:

Description:

Example 1:

   > checkinfnorm(sin(x),[0;1.75], 1);
   true
   > checkinfnorm(sin(x),[0;1.75], 1/2); checkinfnorm(sin(x),[0;20/39],1/2);
   false
   true

Example 2:

   > p = remez(exp(x), 5, [-1;1]);
   > b = dirtyinfnorm(p - exp(x), [-1;1]);
   > checkinfnorm(p - exp(x), [-1;1], b);
   false
   > b1 = round(b, 15, RU);
   > checkinfnorm(p - exp(x), [-1;1], b1);
   true
   > b2 = round(b, 25, RU);
   > checkinfnorm(p - exp(x), [-1;1], b2);
   false
   > diam = 1b-20!;
   > checkinfnorm(p - exp(x), [-1;1], b2);
   true
See also: infnorm, dirtyinfnorm, supnorm, accurateinfnorm, remez, diam
Go back to the list of commands

Name:

coeff gives the coefficient of degree n of a polynomial

Library name:

sollya_obj_t sollya_lib_coeff(sollya_obj_t, sollya_obj_t)

Usage:

coeff(f,n) : (function, integer) -> constant

Parameters:

Description:

Example 1:

   > coeff((1+x)^5,3);
   10

Example 2:

   > coeff(sin(x),0);
   0
See also: degree, roundcoefficients, subpoly
Go back to the list of commands

Name:

composepolynomials computes an approximation to the composition of two polynomials and bounds the error

Library name:

sollya_obj_t sollya_lib_composepolynomials(sollya_obj_t, sollya_obj_t)

Usage:

composepolynomials(p,q) : (function, function) -> structure

Parameters:

Description:

Example 1:

   > composepolynomials(1 + 2 * x + 3 * x^2 + 4 * x^3, 5 + 6 * x + 7 * x^2);
   { .radii = [|[0;0], [0;0], [0;0], [0;0], [0;0], [0;0], [0;0]|], .poly = 586 + x * (1992 + x * (4592 + x * (6156 + x * (6111 + x * (3528 + x * 1372))))) }

Example 2:

   > print(composepolynomials(1/5 * x + exp(17) + log(2) * x^2, x^4 + 1/3 * x^2));
   { .radii = [|[-3.5873240686715317015647477332221852960774705712039e-43;3.5873240686715317015647477332221852960774705712039e-43], [0;0], [-2.67276471009219564614053646715148187881519688010505e-51;2.67276471009219564614053646715148187881519688010505e-51], [0;0], [-1.06910588403687825845621458686059275152607875204202e-50;1.06910588403687825845621458686059275152607875204202e-50], [0;0], [-2.13821176807375651691242917372118550305215750408404e-50;2.13821176807375651691242917372118550305215750408404e-50], [0;0], [-1.06910588403687825845621458686059275152607875204202e-50;1.06910588403687825845621458686059275152607875204202e-50]|], .poly = 2.41549527535752982147754351803858238798675673527228e7 + x^2 * (6.6666666666666666666666666666666666666666666666666e-2 + x^2 * (0.2770163533955494788241369023842418408972777927067 + x^2 * (0.46209812037329687294482141430545104538366675624017 + x^2 * 0.69314718055994530941723212145817656807550013436026))) }

Example 3:

   > composepolynomials(sin(x),x + x^2);
   { .radii = [| |], .poly = sin(x * (1 + x)) }
See also: substitute
Go back to the list of commands

Name:

@ concatenates two lists or strings or applies a list as arguments to a procedure

Library name:

sollya_obj_t sollya_lib_concat(sollya_obj_t, sollya_obj_t)

Usage:

L1@L2 : (list, list) -> list string1@string2 : (string, string) -> string proc@L1 : (procedure, list) -> any type

Parameters:

Description:

Example 1:

   > [|1,...,3|]@[|7,8,9|];
   [|1, 2, 3, 7, 8, 9|]

Example 2:

   > "Hello "@"World!";
   Hello World!

Example 3:

   > procedure cool(a,b,c) {
     write(a,", ", b," and ",c," are cool guys.\n");
     };
   > cool @ [| "Christoph", "Mioara", "Sylvain" |];
   Christoph, Mioara and Sylvain are cool guys.

Example 4:

   > procedure sayhello() {
     "Hello! how are you?";
     };
   > sayhello();
   Hello! how are you?
   > sayhello @ [||];
   Hello! how are you?

Example 5:

   > bashexecute("gcc -fPIC -Wall -c externalprocexample.c");
   > bashexecute("gcc -fPIC -shared -o externalprocexample externalprocexample.o");
   > externalproc(foo, "./externalprocexample", (integer, integer) -> integer);
   > foo;
   foo
   > foo @ [|5, 6|];
   11

Example 6:

   > procedure add(L = ...) {
     var acc, i;
     acc = 0;
     for i in L do acc = i + acc;
     return acc;
     };
   > add(1,2);
   3
   > add(1,2,3);
   6
   > add @ [|1, 2|];
   3
   > add @ [|1, 2, 3|];
   6
   > add @ [||];
   0
See also: .:, :., procedure, externalproc, proc, bind, getbacktrace
Go back to the list of commands

Name:

constant keyword representing a constant type

Library name:

SOLLYA_EXTERNALPROC_TYPE_CONSTANT

Usage:

constant : type type

Description:

See also: externalproc, boolean, function, integer, list of, range, string, object
Go back to the list of commands

Name:

cos the cosine function.

Library names:

sollya_obj_t sollya_lib_cos(sollya_obj_t) sollya_obj_t sollya_lib_build_function_cos(sollya_obj_t) #define SOLLYA_COS(x) sollya_lib_build_function_cos(x)

Description:

See also: acos, sin, tan
Go back to the list of commands

Name:

cosh the hyperbolic cosine function.

Library names:

sollya_obj_t sollya_lib_cosh(sollya_obj_t) sollya_obj_t sollya_lib_build_function_cosh(sollya_obj_t) #define SOLLYA_COSH(x) sollya_lib_build_function_cosh(x)

Description:

See also: acosh, sinh, tanh, exp
Go back to the list of commands

Name:

D short form for double
See also: double
Go back to the list of commands

Name:

DD short form for doubledouble
See also: doubledouble
Go back to the list of commands

Name:

DE short form for doubleextended
See also: doubleextended
Go back to the list of commands

Name:

decimal special value for global state display

Library names:

sollya_obj_t sollya_lib_decimal() int sollya_lib_is_decimal(sollya_obj_t)

Description:

See also: dyadic, powers, hexadecimal, binary, display
Go back to the list of commands

Name:

default default value for some commands.

Library names:

sollya_obj_t sollya_lib_default() int sollya_lib_is_default(sollya_obj_t)

Description:

Example 1:

   > p = remez(exp(x),5,[0;1],default,1e-5);
   > q = remez(exp(x),5,[0;1],1,1e-5);
   > p==q;
   true

Example 2:

   > prec;
   165
   > prec=200;
   The precision has been set to 200 bits.
Go back to the list of commands

Name:

degree gives the degree of a polynomial.

Library name:

sollya_obj_t sollya_lib_degree(sollya_obj_t)

Usage:

degree(f) : function -> integer

Parameters:

Description:

Example 1:

   > degree((1+x)*(2+5*x^2));
   3
   > degree(0);
   0

Example 2:

   > degree(sin(x));
   -1
See also: coeff, subpoly, roundcoefficients
Go back to the list of commands

Name:

denominator gives the denominator of an expression

Library name:

sollya_obj_t sollya_lib_denominator(sollya_obj_t)

Usage:

denominator(expr) : function -> function

Parameters:

Description:

Example 1:

   > denominator(5/3);
   3

Example 2:

   > denominator(exp(x));
   1

Example 3:

   > a = 5/3;
   > b = numerator(a)/denominator(a);
   > print(a);
   5 / 3
   > print(b);
   5 / 3

Example 4:

   > a = exp(x/3);
   > b = numerator(a)/denominator(a);
   > print(a);
   exp(x / 3)
   > print(b);
   exp(x / 3)
See also: numerator, rationalmode
Go back to the list of commands

Name:

diam parameter used in safe algorithms of Sollya and controlling the maximal length of the involved intervals.

Library names:

void sollya_lib_set_diam_and_print(sollya_obj_t) void sollya_lib_set_diam(sollya_obj_t) sollya_obj_t sollya_lib_get_diam()

Usage:

diam = width : constant -> void diam = width ! : constant -> void diam : constant

Parameters:

Description:

See also: infnorm, checkinfnorm, accurateinfnorm, integral, findzeros, supnorm
Go back to the list of commands

Name:

dieonerrormode global variable controlling if Sollya is exited on an error or not.

Library names:

void sollya_lib_set_dieonerrormode_and_print(sollya_obj_t) void sollya_lib_set_dieonerrormode(sollya_obj_t) sollya_obj_t sollya_lib_get_dieonerrormode()

Usage:

dieonerrormode = activation value : on|off -> void dieonerrormode = activation value ! : on|off -> void dieonerrormode : on|off

Parameters:

Description:

Example 1:

   > verbosity = 1!;
   > dieonerrormode = off;
   Die-on-error mode has been deactivated.
   > for i from true to false do i + "Salut";
   Warning: one of the arguments of the for loop does not evaluate to a constant.
   The for loop will not be executed.
   > exp(17);
   Warning: rounding has happened. The value displayed is a faithful rounding to 165 bits of the true result.
   2.41549527535752982147754351803858238798675673527224e7

Example 2:

   > verbosity = 1!;
   > dieonerrormode = off!;
   > 5 */  4;
   Warning: syntax error, unexpected /.
   The last symbol read has been "/".
   Will skip input until next semicolon after the unexpected token. May leak memory.
     exp(17);
   Warning: rounding has happened. The value displayed is a faithful rounding to 165 bits of the true result.
   2.41549527535752982147754351803858238798675673527224e7

Example 3:

   > verbosity = 1!;
   > dieonerrormode;
   off
   > dieonerrormode = on!;
   > dieonerrormode;
   on
   > for i from true to false do i + "Salut";
   Warning: one of the arguments of the for loop does not evaluate to a constant.
   The for loop will not be executed.
   Warning: some syntax, typing or side-effect error has occurred.
   As the die-on-error mode is activated, the tool will be exited.

Example 4:

   > verbosity = 1!;
   > dieonerrormode = on!;
   > 5 */  4;
   Warning: syntax error, unexpected /.
   The last symbol read has been "/".
   Will skip input until next semicolon after the unexpected token. May leak memory.
   Warning: some syntax, typing or side-effect error has occurred.
   As the die-on-error mode is activated, the tool will be exited.

Example 5:

   > verbosity = 0!;
   > dieonerrormode = on!;
   > 5 */  4;
See also: on, off, verbosity, error
Go back to the list of commands

Name:

diff differentiation operator

Library name:

sollya_obj_t sollya_lib_diff(sollya_obj_t)

Usage:

diff(function) : function -> function

Parameters:

Description:

Example 1:

   > diff(sin(x));
   cos(x)

Example 2:

   > diff(x);
   1

Example 3:

   > diff(x^x);
   x^x * (1 + log(x))
See also: library, autodiff, taylor, taylorform
Go back to the list of commands

Name:

dirtyfindzeros gives a list of numerical values listing the zeros of a function on an interval.

Library name:

sollya_obj_t sollya_lib_dirtyfindzeros(sollya_obj_t, sollya_obj_t)

Usage:

dirtyfindzeros(f,I) : (function, range) -> list

Parameters:

Description:

Example 1:

   > dirtyfindzeros(sin(x),[-5;5]);
   [|-3.1415926535897932384626433832795028841971693993751, 0, 3.1415926535897932384626433832795028841971693993751|]

Example 2:

   > L1=dirtyfindzeros(x^2*sin(1/x),[0;1]);
   > points=1000!;
   > L2=dirtyfindzeros(x^2*sin(1/x),[0;1]);
   > length(L1); length(L2);
   18
   25
See also: prec, points, findzeros, dirtyinfnorm, numberroots
Go back to the list of commands

Name:

dirtyinfnorm computes a numerical approximation of the infinity norm of a function on an interval.

Library name:

sollya_obj_t sollya_lib_dirtyinfnorm(sollya_obj_t, sollya_obj_t)

Usage:

dirtyinfnorm(f,I) : (function, range) -> constant

Parameters:

Description:

Example 1:

   > dirtyinfnorm(sin(x),[-10;10]);
   1

Example 2:

   > prec=15!;
   > dirtyinfnorm(exp(cos(x))*sin(x),[0;5]);
   1.45856
   > prec=40!;
   > dirtyinfnorm(exp(cos(x))*sin(x),[0;5]);
   1.458528537136
   > prec=100!;
   > dirtyinfnorm(exp(cos(x))*sin(x),[0;5]);
   1.458528537136237644438147455025
   > prec=200!;
   > dirtyinfnorm(exp(cos(x))*sin(x),[0;5]);
   1.458528537136237644438147455023841718299214087993682374094153

Example 3:

   > dirtyinfnorm(x^2, [log(0);log(1)]);
   NaN
See also: prec, points, infnorm, checkinfnorm, supnorm
Go back to the list of commands

Name:

dirtyintegral computes a numerical approximation of the integral of a function on an interval.

Library name:

sollya_obj_t sollya_lib_dirtyintegral(sollya_obj_t, sollya_obj_t)

Usage:

dirtyintegral(f,I) : (function, range) -> constant

Parameters:

Description:

Example 1:

   > sin(10);
   -0.54402111088936981340474766185137728168364301291622
   > dirtyintegral(cos(x),[0;10]);
   -0.54400304905152629822448058882475382036536298356282
   > points=2000!;
   > dirtyintegral(cos(x),[0;10]);
   -0.54401997751158321972222697312583199035995837926893
See also: prec, points, integral
Go back to the list of commands

Name:

dirtysimplify simplifies an expression representing a function

Library name:

sollya_obj_t sollya_lib_dirtysimplify(sollya_obj_t)

Usage:

dirtysimplify(function) : function -> function

Parameters:

Description:

Example 1:

   > print(dirtysimplify(sin(pi * x)));
   sin(3.1415926535897932384626433832795028841971693993751 * x)
   > print(dirtysimplify(erf(exp(3) + x * log(4))));
   erf(20.0855369231876677409285296545817178969879078385544 + x * 1.3862943611198906188344642429163531361510002687205)

Example 2:

   > prec = 20!;
   > t = erf(0.5);
   > s = dirtysimplify(erf(0.5));
   > prec = 200!;
   > t;
   0.520499877813046537682746653891964528736451575757963700058806
   > s;
   0.52050018310546875
See also: simplify, autosimplify, prec, evaluate, horner, rationalmode
Go back to the list of commands

Name:

display sets or inspects the global variable specifying number notation

Library names:

void sollya_lib_set_display_and_print(sollya_obj_t) void sollya_lib_set_display(sollya_obj_t) sollya_obj_t sollya_lib_get_display()

Usage:

display = notation value : decimal|binary|dyadic|powers|hexadecimal -> void display = notation value ! : decimal|binary|dyadic|powers|hexadecimal -> void display : decimal|binary|dyadic|powers|hexadecimal

Parameters:

Description:

Example 1:

   > display = decimal;
   Display mode is decimal numbers.
   > a = evaluate(sin(pi * x), 0.25);
   > a;
   0.70710678118654752440084436210484903928483593768847
   > display = binary;
   Display mode is binary numbers.
   > a;
   1.01101010000010011110011001100111111100111011110011001001000010001011001011111011000100110110011011101010100101010111110100111110001110101101111011000001011101010001_2 * 2^(-1)
   > display = hexadecimal;
   Display mode is hexadecimal numbers.
   > a;
   0x1.6a09e667f3bcc908b2fb1366ea957d3e3adec1751p-1
   > display = dyadic;
   Display mode is dyadic numbers.
   > a;
   33070006991101558613323983488220944360067107133265b-165
   > display = powers;
   Display mode is dyadic numbers in integer-power-of-2 notation.
   > a;
   33070006991101558613323983488220944360067107133265 * 2^(-165)
See also: print, write, decimal, dyadic, powers, binary, hexadecimal, prec
Go back to the list of commands

Name:

/ division function

Library names:

sollya_obj_t sollya_lib_div(sollya_obj_t, sollya_obj_t) sollya_obj_t sollya_lib_build_function_div(sollya_obj_t, sollya_obj_t) #define SOLLYA_DIV(x,y) sollya_lib_build_function_div((x), (y))

Usage:

function1 / function2 : (function, function) -> function interval1 / interval2 : (range, range) -> range interval1 / constant : (range, constant) -> range interval1 / constant : (constant, range) -> range

Parameters:

Description:

Example 1:

   > 5 / 2;
   2.5

Example 2:

   > x / 2;
   x * 0.5

Example 3:

   > x / x;
   1

Example 4:

   > 3 / 0;
   NaN

Example 5:

   > diff(sin(x) / exp(x));
   (exp(x) * cos(x) - sin(x) * exp(x)) / exp(x)^2

Example 6:

   > [1;2] / [3;4];
   [0.25;0.66666666666666666666666666666666666666666666666668]
   > [1;2] / 17;
   [5.8823529411764705882352941176470588235294117647059e-2;0.11764705882352941176470588235294117647058823529412]
   > -13 / [4;17];
   [-3.25;-0.76470588235294117647058823529411764705882352941175]
See also: +, -, *, ^
Go back to the list of commands

Names:

double, D rounding to the nearest IEEE 754 double (binary64).

Library names:

sollya_obj_t sollya_lib_double(sollya_obj_t) sollya_obj_t sollya_lib_double_obj() int sollya_lib_is_double_obj(sollya_obj_t) sollya_obj_t sollya_lib_build_function_double(sollya_obj_t) #define SOLLYA_D(x) sollya_lib_build_function_double(x)

Description:

Example 1:

   > display=binary!;
   > D(0.1);
   1.100110011001100110011001100110011001100110011001101_2 * 2^(-4)
   > D(4.17);
   1.000010101110000101000111101011100001010001111010111_2 * 2^(2)
   > D(1.011_2 * 2^(-1073));
   1.1_2 * 2^(-1073)
See also: halfprecision, single, doubleextended, doubledouble, quad, tripledouble, roundcoefficients, implementpoly, round, printdouble
Go back to the list of commands

Names:

doubledouble, DD represents a number as the sum of two IEEE doubles.

Library names:

sollya_obj_t sollya_lib_double_double(sollya_obj_t) sollya_obj_t sollya_lib_double_double_obj() int sollya_lib_is_double_double_obj(sollya_obj_t) sollya_obj_t sollya_lib_build_function_double_double(sollya_obj_t) #define SOLLYA_DD(x) sollya_lib_build_function_double_double(x)

Description:

Example 1:

   > verbosity=1!;
   > a = 1+ 2^(-100);
   > DD(a);
   1.0000000000000000000000000000007888609052210118054
   > prec=50!;
   > DD(a);
   1.000000000000000000000000000000788860905
See also: halfprecision, single, double, doubleextended, quad, tripledouble, roundcoefficients, implementpoly, round
Go back to the list of commands

Names:

doubleextended, DE computes the nearest number with 64 bits of mantissa.

Library names:

sollya_obj_t sollya_lib_doubleextended(sollya_obj_t) sollya_obj_t sollya_lib_doubleextended_obj() int sollya_lib_is_doubleextended_obj(sollya_obj_t) sollya_obj_t sollya_lib_build_function_doubleextended(sollya_obj_t) #define SOLLYA_DE(x) sollya_lib_build_function_doubleextended(x)

Description:

Example 1:

   > display=binary!;
   > DE(0.1);
   1.100110011001100110011001100110011001100110011001100110011001101_2 * 2^(-4)
   > round(0.1,64,RN);
   1.100110011001100110011001100110011001100110011001100110011001101_2 * 2^(-4)

Example 2:

   > D(2^(-2000));
   0
   > DE(2^(-20000));
   0

Example 3:

   > verbosity=1!;
   > f = sin(DE(x));
   > f(pi);
   Warning: rounding has happened. The value displayed is a faithful rounding to 165 bits of the true result.
   -5.016557612668332023557327080330757013831561670255e-20
   > g = sin(round(x,64,RN));
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
See also: roundcoefficients, halfprecision, single, double, doubledouble, quad, tripledouble, round
Go back to the list of commands

Name:

dyadic special value for global state display

Library names:

sollya_obj_t sollya_lib_dyadic() int sollya_lib_is_dyadic(sollya_obj_t)

Description:

See also: decimal, powers, hexadecimal, binary, display
Go back to the list of commands

Name:

== equality test operator

Library name:

sollya_obj_t sollya_lib_cmp_equal(sollya_obj_t, sollya_obj_t)

Usage:

expr1 == expr2 : (any type, any type) -> boolean

Parameters:

Description:

Example 1:

   > "Hello" == "Hello";
   true
   > "Hello" == "Salut";
   false
   > "Hello" == 5;
   false
   > 5 + x == 5 + x;
   true

Example 2:

   > verbosity = 1!;
   > asin(1) * 2 == pi;
   true
   > cos(3)^2 == 1 - sin(3)^2;
   Warning: the tool is unable to decide an equality test by evaluation even though faithful evaluation of the terms has been possible. The terms will be considered to be equal.
   true
   > exp(5) == log(4);
   false

Example 3:

   > autosimplify=off;
   Automatic pure tree simplification has been deactivated.
   > exp(1+x) == exp(x+1);
   false
   > autosimplify=on;
   Automatic pure tree simplification has been activated.
   > exp(1+x) == exp(x+1);
   false
   > (1/3+x)^2 == x^2 + 1/9 + (5-3)*x/3;
   true
   > log(x)/log(10) == log10(x);
   false

Example 4:

   > prec = 12;
   The precision has been set to 12 bits.
   > verbosity = 1!;
   > 16384.1 == 16385.1;
   Warning: Rounding occurred when converting the constant "16384.1" to floating-point with 12 bits.
   If safe computation is needed, try to increase the precision.
   Warning: Rounding occurred when converting the constant "16385.1" to floating-point with 12 bits.
   If safe computation is needed, try to increase the precision.
   true
   > 16384 == 16384.25;
   false
   > 0.1 == 1/10;
   Warning: Rounding occurred when converting the constant "0.1" to floating-point with 12 bits.
   If safe computation is needed, try to increase the precision.
   false
   > 0.1 == round(1/10, prec, RN);
   Warning: Rounding occurred when converting the constant "0.1" to floating-point with 12 bits.
   If safe computation is needed, try to increase the precision.
   true

Example 5:

   > error == error;
   false
   > error != error;
   false
   > @NaN@ == @NaN@;
   false
   > @NaN@ != @NaN@;
   false
   > error == @NaN@;
   false
   > error != @NaN@;
   false
   > a = error;
   > match a with
     @NaN@ : ("a contains @NaN@")
     default:("a contains something else");
   error
   > a = @NaN@;
   > match a with
     @NaN@ : ("a contains @NaN@")
     default:("a contains something else");
   a contains @NaN@
See also: !=, >, >=, <=, <, in, !, &&, ||, error, prec, autosimplify
Go back to the list of commands

Name:

erfc the complementary error function.

Library names:

sollya_obj_t sollya_lib_erfc(sollya_obj_t) sollya_obj_t sollya_lib_build_function_erfc(sollya_obj_t) #define SOLLYA_ERFC(x) sollya_lib_build_function_erfc(x)

Description:

See also: erf
Go back to the list of commands

Name:

erf the error function.

Library names:

sollya_obj_t sollya_lib_erf(sollya_obj_t) sollya_obj_t sollya_lib_build_function_erf(sollya_obj_t) #define SOLLYA_ERF(x) sollya_lib_build_function_erf(x)

Description:

See also: erfc, exp
Go back to the list of commands

Name:

error expression representing an input that is wrongly typed or that cannot be executed

Library names:

sollya_obj_t sollya_lib_error() int sollya_lib_obj_is_error(sollya_obj_t)

Usage:

error : error

Description:

Example 1:

   > print(5 + "foo");
   error

Example 2:

   > error;
   error

Example 3:

   > error == error;
   false
   > error != error;
   false

Example 4:

   > correct = 5 + 6;
   > incorrect = 5 + "foo";
   > correct == correct;
   true
   > incorrect == incorrect;
   false
   > errorhappened = !(incorrect == incorrect);
   > errorhappened;
   true
See also: void, parse, ==, !=
Go back to the list of commands

Name:

div Computes the euclidian division of polynomials or numbers and returns the quotient

Library name:

sollya_obj_t sollya_lib_euclidian_div(sollya_obj_t, sollya_obj_t)

Usage:

div(a, b) : (function, function) -> function

Parameters:

Description:

Example 1:

   > div(1001, 231);
   4
   > div(13, 17);
   0
   > div(-14, 15);
   -1
   > div(-213, -5);
   42
   > div(23/13, 11/17);
   2
   > div(exp(13),-sin(17));
   460177

Example 2:

   > div(24 + 68 * x + 74 * x^2 + 39 * x^3 + 10 * x^4 + x^5, 4 + 4 * x + x^2);
   6 + x * (11 + x * (6 + x))
   > div(24 + 68 * x + 74 * x^2 + 39 * x^3 + 10 * x^4 + x^5, 2 * x^3);
   19.5 + x * (5 + x * 0.5)
   > div(x^2, x^3);
   0

Example 3:

   > div(exp(x), x^2);
   0
See also: gcd, mod, numberroots
Go back to the list of commands

Name:

mod Computes the euclidian division of polynomials or numbers and returns the rest

Library name:

sollya_obj_t sollya_lib_euclidian_mod(sollya_obj_t, sollya_obj_t)

Usage:

mod(p, q) : (function, function) -> function

Parameters:

Description:

Example 1:

   > mod(1001, 231);
   77
   > mod(13, 17);
   13
   > mod(-14, 15);
   1
   > mod(-213, -5);
   -3
   > print(mod(23/13, 11/17));
   105 / 221
   > print(mod(exp(13),-sin(17)));
   exp(13) + 460177 * sin(17)

Example 2:

   > mod(24 + 68 * x + 74 * x^2 + 39 * x^3 + 10 * x^4 + x^5, 4 + 4 * x + x^2);
   0
   > mod(24 + 68 * x + 74 * x^2 + 39 * x^3 + 10 * x^4 + x^5, 2 * x^3);
   24 + x * (68 + x * 74)
   > mod(x^2, x^3);
   x^2

Example 3:

   > mod(exp(x), x^2);
   exp(x)
   > mod(x^3, sin(x));
   x^3
See also: gcd, div, numberroots
Go back to the list of commands

Name:

evaluate evaluates a function at a constant point or in a range

Library name:

sollya_obj_t sollya_lib_evaluate(sollya_obj_t, sollya_obj_t)

Usage:

evaluate(function, constant) : (function, constant) -> constant | range evaluate(function, range) : (function, range) -> range evaluate(function, function2) : (function, function) -> function

Parameters:

Description:

Example 1:

   > midpointmode=on!;
   > print(evaluate(sin(pi * x), 2.25));
   0.70710678118654752440084436210484903928483593768847
   > print(evaluate(sin(pi * x), [2.25; 2.25]));
   0.707106781186547524400844362104849039284835937688~4/5~

Example 2:

   > print(evaluate(sin(pi * x), 2));
   [-1.7298645251438126951650861503109812954283676799168e-12715;7.5941198201187963145069564314525661706039084390068e-12716]

Example 3:

   > print(evaluate(sin(pi * x), [2, 2.25]));
   [-5.143390272677254630046998919961912407349224165421e-50;0.70710678118654752440084436210484903928483593768866]

Example 4:

   > print(evaluate(sin(pi * x), 2 + 0.25 * x));
   sin((pi) * 2 + x * (pi) * 0.25)

Example 5:

   > print(evaluate(sin(pi * 1/x), 0));
   [-1;1]
See also: isevaluable
Go back to the list of commands

Name:

execute executes the content of a file

Library name:

void sollya_lib_execute(sollya_obj_t)

Usage:

execute(filename) : string -> void

Parameters:

Description:

Example 1:

   > a=2;
   > a;
   2
   > print("a=1;") > "example.sollya";
   > execute("example.sollya");
   > a;
   1

Example 2:

   > verbosity=1!;
   > print("a=1; restart; a=2;") > "example.sollya";
   > execute("example.sollya");
   Warning: a restart command has been used in a file read into another.
   This restart command will be neglected.
   > a;
   2

Example 3:

   > verbosity=1!;
   > print("a=1; quit; a=2;") > "example.sollya";
   > execute("example.sollya");
   Warning: the execution of a file read by execute demanded stopping the interpretation but it is not stopped.
   > a;
   1
See also: parse, readfile, write, print, bashexecute, quit, restart
Go back to the list of commands

Name:

expand expands polynomial subexpressions

Library name:

sollya_obj_t sollya_lib_expand(sollya_obj_t)

Usage:

expand(function) : function -> function

Parameters:

Description:

Example 1:

   > print(expand(x^3));
   x * x * x

Example 2:

   > print(expand((x + 2)^3 + 2 * x));
   8 + 12 * x + 6 * x * x + x * x * x + 2 * x

Example 3:

   > print(expand(exp((x + (x + 3))^5)));
   exp(243 + 405 * x + 270 * x * x + 90 * x * x * x + 15 * x * x * x * x + x * x * x * x * x + x * 405 + 108 * x * 5 * x + 54 * x * x * 5 * x + 12 * x * x * x * 5 * x + x * x * x * x * 5 * x + x * x * 270 + 27 * x * x * x * 10 + 9 * x * x * x * x * 10 + x * x * x * x * x * 10 + x * x * x * 90 + 6 * x * x * x * x * 10 + x * x * x * x * x * 10 + x * x * x * x * 5 * x + 15 * x * x * x * x + x * x * x * x * x)
See also: dirtysimplify, simplify, horner, coeff, degree
Go back to the list of commands

Name:

exp the exponential function.

Library names:

sollya_obj_t sollya_lib_exp(sollya_obj_t) sollya_obj_t sollya_lib_build_function_exp(sollya_obj_t) #define SOLLYA_EXP(x) sollya_lib_build_function_exp(x)

Description:

See also: exp, log
Go back to the list of commands

Name:

expm1 shifted exponential function.

Library names:

sollya_obj_t sollya_lib_expm1(sollya_obj_t) sollya_obj_t sollya_lib_build_function_expm1(sollya_obj_t) #define SOLLYA_EXPM1(x) sollya_lib_build_function_expm1(x)

Description:

See also: exp
Go back to the list of commands

Name:

exponent returns the scaled binary exponent of a number.

Library name:

sollya_obj_t sollya_lib_exponent(sollya_obj_t)

Usage:

exponent(x) : constant -> integer

Parameters:

Description:

Example 1:

   > a=round(Pi,20,RN);
   > e=exponent(a);
   > e;
   -17
   > m=mantissa(a);
   > a-m*2^e;
   0
See also: mantissa, precision
Go back to the list of commands

Name:

externalplot plots the error of an external code with regard to a function

Library names:

void sollya_lib_externalplot(sollya_obj_t, sollya_obj_t, sollya_obj_t,                              sollya_obj_t, sollya_obj_t, ...) void sollya_lib_v_externalplot(sollya_obj_t, sollya_obj_t, sollya_obj_t,                                sollya_obj_t, sollya_obj_t, va_list)

Usage:

externalplot(filename, mode, function, range, precision) : (string, absolute|relative, function, range, integer) -> void externalplot(filename, mode, function, range, precision, perturb) : (string, absolute|relative, function, range, integer, perturb) -> void externalplot(filename, mode, function, range, precision, plot mode, result filename) : (string, absolute|relative, function, range, integer, file|postscript|postscriptfile, string) -> void externalplot(filename, mode, function, range, precision, perturb, plot mode, result filename) : (string, absolute|relative, function, range, integer, perturb, file|postscript|postscriptfile, string) -> void

Description:

Example 1:

   > bashexecute("gcc -fPIC -c externalplotexample.c");
   > bashexecute("gcc -shared -o externalplotexample externalplotexample.o -lgmp -lmpfr");
   > externalplot("./externalplotexample",relative,exp(x),[-1/2;1/2],12,perturb);
See also: plot, asciiplot, perturb, absolute, relative, file, postscript, postscriptfile, bashexecute, externalproc, library
Go back to the list of commands

Name:

externalproc binds an external code to a Sollya procedure

Library names:

  sollya_obj_t sollya_lib_externalprocedure(sollya_externalprocedure_type_t,                                             sollya_externalprocedure_type_t *,                                             int, char *, void *);   sollya_obj_t sollya_lib_externalprocedure_with_data(                                             sollya_externalprocedure_type_t,                                             sollya_externalprocedure_type_t *,                                             int, char *, void *, void *,                                             void (*)(void *));

Usage:

externalproc(identifier, filename, argumenttype -> resulttype) : (identifier type, string, type type, type type) -> void

Parameters:

Description:

Example 1:

   > bashexecute("gcc -fPIC -Wall -c externalprocexample.c");
   > bashexecute("gcc -fPIC -shared -o externalprocexample externalprocexample.o");
   > externalproc(foo, "./externalprocexample", (integer, integer) -> integer);
   > foo;
   foo
   > foo(5, 6);
   11
   > verbosity = 1!;
   > foo();
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
   error
   > a = foo;
   > a(5,6);
   11
See also: library, libraryconstant, externalplot, bashexecute, void, constant, function, range, integer, string, boolean, list of
Go back to the list of commands

Name:

false the boolean value representing the false.

Library names:

sollya_obj_t sollya_lib_false() int sollya_lib_is_false(sollya_obj_t)

Description:

Example 1:

   > true && false;
   false
   > 2<1;
   false
See also: true, &&, ||
Go back to the list of commands

Name:

file special value for commands plot and externalplot

Library names:

sollya_obj_t sollya_lib_file() int sollya_lib_is_file(sollya_obj_t)

Description:

Example 1:

   > savemode=file;
   > name="plotSinCos";
   > plot(sin(x),0,cos(x),[-Pi,Pi],savemode, name);
See also: externalplot, plot, postscript, postscriptfile
Go back to the list of commands

Name:

findzeros gives a list of intervals containing all zeros of a function on an interval.

Library name:

sollya_obj_t sollya_lib_findzeros(sollya_obj_t, sollya_obj_t)

Usage:

findzeros(f,I) : (function, range) -> list

Parameters:

Description:

Example 1:

   > findzeros(sin(x),[-5;5]);
   [|[-3.14208984375;-3.140869140625], [-1.220703125e-3;1.220703125e-3], [3.140869140625;3.14208984375]|]
   > diam=1e-10!;
   > findzeros(sin(x),[-5;5]);
   [|[-3.14159265370108187198638916015625;-3.141592652536928653717041015625], [-1.16415321826934814453125e-9;1.16415321826934814453125e-9], [3.141592652536928653717041015625;3.14159265370108187198638916015625]|]
See also: dirtyfindzeros, infnorm, prec, diam, taylorrecursions, hopitalrecursions, numberroots
Go back to the list of commands

Name:

fixed indicates that fixed-point formats should be used for fpminimax

Library names:

sollya_obj_t sollya_lib_fixed() int sollya_lib_is_fixed(sollya_obj_t)

Usage:

fixed : fixed|floating

Description:

Example 1:

   > fpminimax(cos(x),6,[|32,32,32,32,32,32,32|],[-1;1],fixed);
   0.9999997480772435665130615234375 + x^2 * (-0.4999928693287074565887451171875 + x^2 * (4.163351492024958133697509765625e-2 + x^2 * (-1.338223926723003387451171875e-3)))
See also: fpminimax, floating
Go back to the list of commands

Name:

floating indicates that floating-point formats should be used for fpminimax

Library names:

sollya_obj_t sollya_lib_floating() int sollya_lib_is_floating(sollya_obj_t)

Usage:

floating : fixed|floating

Description:

Example 1:

   > fpminimax(cos(x),6,[|D...|],[-1;1],floating);
   0.99999974816012215939053930924274027347564697265625 + x * (-2.795931796958502334440230695107655659202089892465e-15 + x * (-0.49999286980201401719980935922649223357439041137695 + x * (4.0484539189054105169841244454207387920433372507922e-14 + x * (4.1633515528919168291466235132247675210237503051758e-2 + x * (-4.015858818743733758578949218474363725507386355118e-14 + x * (-1.3382240885483781024645200119493892998434603214264e-3))))))
See also: fpminimax, fixed
Go back to the list of commands

Name:

floor the usual function floor.

Library names:

sollya_obj_t sollya_lib_floor(sollya_obj_t) sollya_obj_t sollya_lib_build_function_floor(sollya_obj_t) #define SOLLYA_FLOOR(x) sollya_lib_build_function_floor(x)

Description:

See also: ceil, nearestint, round, RD
Go back to the list of commands

Name:

fpminimax computes a good polynomial approximation with fixed-point or floating-point coefficients

Library names:

sollya_obj_t sollya_lib_fpminimax(sollya_obj_t, sollya_obj_t, sollya_obj_t,                                   sollya_obj_t, ...) sollya_obj_t sollya_lib_v_fpminimax(sollya_obj_t, sollya_obj_t,                                     sollya_obj_t, sollya_obj_t, va_list)

Usage:

fpminimax(f, n, formats, range, indic1, indic2, indic3, P) : (function, integer, list, range, absolute|relative | fixed|floating | function, absolute|relative | fixed|floating | function, absolute|relative | fixed|floating | function, function) -> function fpminimax(f, monomials, formats, range, indic1, indic2, indic3, P) : (function, list, list, range, absolute|relative | fixed|floating | function, absolute|relative | fixed|floating | function, absolute|relative | fixed|floating | function, function) -> function fpminimax(f, n, formats, L, indic1, indic2, indic3, P) : (function, integer, list, list, absolute|relative | fixed|floating | function, absolute|relative | fixed|floating | function, absolute|relative | fixed|floating | function, function) -> function fpminimax(f, monomials, formats, L, indic1, indic2, indic3, P) : (function, list, list, list, absolute|relative | fixed|floating | function, absolute|relative | fixed|floating | function, absolute|relative | fixed|floating | function, function) -> function

Parameters:

Description:

Example 1:

   > P = fpminimax(cos(x),6,[|DD, DD, D...|],[-1b-5;1b-5]);
   > printexpansion(P);
   (0x3ff0000000000000 + 0xbc09fda15e029b00) + x * ((0x3af9eb57163024a8 + 0x37942c2f3f3e3839) + x * (0xbfdfffffffffff98 + x * (0xbbd1693f9c028849 + x * (0x3fa5555555145337 + x * (0x3c7a25f610ad9ebc + x * 0xbf56c138142da5b0)))))

Example 2:

   > P = fpminimax(sin(x),6,[|32...|],[-1b-5;1b-5], fixed, absolute);
   > display = powers!;
   > P;
   x * (1 + x^2 * (-357913941 * 2^(-31) + x^2 * (35789873 * 2^(-32))))

Example 3:

   > P = fpminimax(exp(x), [|3,4|], [|D,24|], [-1/256; 1/246], 1+x+x^2/2);
   > display = powers!;
   > P;
   1 + x * (1 + x * (1 * 2^(-1) + x * (375300225001191 * 2^(-51) + x * (5592621 * 2^(-27)))))

Example 4:

   > f = cos(exp(x));
   > pstar = remez(f, 5, [-1b-7;1b-7]);
   > listpoints = dirtyfindzeros(f-pstar, [-1b-7; 1b-7]);
   > P1 = fpminimax(f, 5, [|DD...|], listpoints, absolute, default, default, pstar);
   > P2 = fpminimax(f, 5, [|D...|], listpoints, absolute, default, default, pstar);
   > P3 = fpminimax(f, 5, [|D, D, D, 24...|], listpoints, absolute, default, default, pstar);
   > print("Error of pstar: ", dirtyinfnorm(f-pstar, [-1b-7; 1b-7]));
   Error of pstar:  7.9048441259903026332577436001060063099817726177425e-16
   > print("Error of P1:    ", dirtyinfnorm(f-P1, [-1b-7; 1b-7]));
   Error of P1:     7.9048441259903026580081299123420463921479618202064e-16
   > print("Error of P2:    ", dirtyinfnorm(f-P2, [-1b-7; 1b-7]));
   Error of P2:     8.2477144579950871737109573536791331686347620955985e-16
   > print("Error of P3:    ", dirtyinfnorm(f-P3, [-1b-7; 1b-7]));
   Error of P3:     1.08454277156993282593701156841863009789063333951055e-15

Example 5:

   > L = [|exp(x), sin(x), cos(x)-1, sin(x^3)|];
   > g = (2^x-1)/x;
   > p = fpminimax(g, L, [|D...|], [-1/16;1/16],absolute);
   > display = powers!;
   > p;
   -3267884797436153 * 2^(-54) * sin(x^3) + 5247089102535885 * 2^(-53) * (cos(x) - 1) + -8159095033730771 * 2^(-54) * sin(x) + 6243315658446641 * 2^(-53) * exp(x)

Example 6:

   > n = 9;
   > T = [|1, x|];
   > for i from 2 to n do T[i] = canonical(2*x*T[i-1]-T[i-2]);
   > g = (2^x-1)/x;
   > PCheb = fpminimax(g, T, [|DD,DE...|], [-1/16;1/16],absolute);
   > display = dyadic!;
   > print(PCheb);
   8733930098894247371b-98 * (9 * x + -120 * x^3 + 432 * x^5 + -576 * x^7 + 256 * x^9) + 15750497046710770365b-94 * (1 + -32 * x^2 + 160 * x^4 + -256 * x^6 + 128 * x^8) + 6467380330985872933b-88 * (-7 * x + 56 * x^3 + -112 * x^5 + 64 * x^7) + 9342762606926218927b-84 * (-1 + 18 * x^2 + -48 * x^4 + 32 * x^6) + 11814521367456461131b-80 * (5 * x + -20 * x^3 + 16 * x^5) + 6405479474328570593b-75 * (1 + -8 * x^2 + 8 * x^4) + 11584457324781949889b-72 * (-3 * x + 4 * x^3) + 16779705312447201161b-69 * (-1 + 2 * x^2) + 18265014280997359319b-66 * x + 117054497448175143902009975397253b-107
See also: remez, dirtyfindzeros, absolute, relative, fixed, floating, default, halfprecision, single, double, doubleextended, doubledouble, quad, tripledouble, implementpoly, coeff, degree, roundcoefficients, guessdegree
Go back to the list of commands

Name:

fullparentheses activates, deactivates or inspects the state variable controlling output with full parenthesising

Library names:

void sollya_lib_set_fullparentheses_and_print(sollya_obj_t); void sollya_lib_set_fullparentheses(sollya_obj_t); sollya_obj_t sollya_lib_get_fullparentheses();

Usage:

fullparentheses = activation value : on|off -> void fullparentheses = activation value ! : on|off -> void

Parameters:

Description:

Example 1:

   > autosimplify = off!;
   > fullparentheses = off;
   Full parentheses mode has been deactivated.
   > print(1 + 2 + 3);
   1 + 2 + 3
   > fullparentheses = on;
   Full parentheses mode has been activated.
   > print(1 + 2 + 3);
   (1 + 2) + 3
See also: print, write, autosimplify
Go back to the list of commands

Name:

function keyword for declaring a procedure-based function or a keyword representing a function type

Library names:

sollya_obj_t sollya_lib_procedurefunction(sollya_obj_t, sollya_obj_t) sollya_obj_t sollya_lib_build_function_procedurefunction(sollya_obj_t,                                                          sollya_obj_t) SOLLYA_EXTERNALPROC_TYPE_FUNCTION

Usage:

function(procedure) : procedure -> function function : type type

Parameters:

Description:

Example 1:

   > procedure EXP(X,n,p) {
       var res, oldPrec;
       oldPrec = prec;
       prec = p!;
       
       res = exp(X);
       
       prec = oldPrec!;
       return res;
     };
   > f = function(EXP);
   > f(1);
   2.7182818284590452353602874713526624977572470937
   > exp(1);
   2.7182818284590452353602874713526624977572470937
   > f(x + 3);
   (function(proc(X, n, p)
   {
   var res, oldPrec;
   oldPrec = prec;
   prec = p!;
   res = exp(X);
   prec = oldPrec!;
   return res;
   }))(3 + x)
   > diff(f);
   diff(function(proc(X, n, p)
   {
   var res, oldPrec;
   oldPrec = prec;
   prec = p!;
   res = exp(X);
   prec = oldPrec!;
   return res;
   }))
   > (diff(f))(0);
   1
   > g = f(sin(x));
   > g(17);
   0.38235816999386683402690554641655641359573458342088
   > diff(g);
   (diff(function(proc(X, n, p)
   {
   var res, oldPrec;
   oldPrec = prec;
   prec = p!;
   res = exp(X);
   prec = oldPrec!;
   return res;
   })))(sin(x)) * cos(x)
   > (diff(g))(1);
   1.25338076749344683697237458088447611474812675164344
   > p = remez(f,3,[-1/2;1/2]);
   > p;
   0.99967120901420646830315493949039176881764871951833 + x * (0.99973702983571140134762682913614052309208076875596 + x * (0.510497293602826249216227216546435103583073053437 + x * 0.169814324607133287588897694747370380479108785868016))
See also: proc, library, procedure, externalproc, boolean, constant, integer, list of, range, string, object
Go back to the list of commands

Name:

gcd Computes the greatest common divisor of polynomials or numbers.

Library name:

sollya_obj_t sollya_lib_gcd(sollya_obj_t, sollya_obj_t)

Usage:

gcd(p, q) : (function, function) -> function

Parameters:

Description:

Example 1:

   > gcd(1001, 231);
   77
   > gcd(13, 17);
   1
   > gcd(-210, 462);
   42

Example 2:

   > rationalmode = on!;
   > gcd(6/7, 33/13);
   3 / 91

Example 3:

   > gcd(exp(13),sin(17));
   1

Example 4:

   > gcd(24 + 68 * x + 74 * x^2 + 39 * x^3 + 10 * x^4 + x^5, 480 + 776 * x + 476 * x^2 + 138 * x^3 + 19 * x^4 + x^5);
   4 + x * (4 + x)
   > gcd(1001 * x^2, 231 * x);
   x * 77

Example 5:

   > gcd(exp(x), x^2);
   1
See also: div, mod, numberroots
Go back to the list of commands

Name:

>= greater-than-or-equal-to operator

Library name:

sollya_obj_t sollya_lib_cmp_greater_equal(sollya_obj_t, sollya_obj_t)

Usage:

expr1 >= expr2 : (constant, constant) -> boolean

Parameters:

Description:

Example 1:

   > 5 >= 4;
   true
   > 5 >= 5;
   true
   > 5 >= 6;
   false
   > exp(2) >= exp(1);
   true
   > log(1) >= exp(2);
   false

Example 2:

   > prec = 12;
   The precision has been set to 12 bits.
   > 16384.1 >= 16385.1;
   true
See also: ==, !=, >, <=, <, in, !, &&, ||, prec, max, min
Go back to the list of commands

Name:

getbacktrace returns the list of Sollya procedures currently run

Library name:

sollya_obj_t sollya_lib_getbacktrace();

Usage:

getbacktrace() : void -> list

Description:

Example 1:

   > procedure testA() {
       "Current backtrace:";
       getbacktrace();
     };
   > procedure testB(X) {
       "X = ", X;
       testA();
     };
   > procedure testC(X, Y) {
       "X = ", X, ", Y = ", Y;
       testB(Y);
     };
   > testC(17, 42);
   X = 17, Y = 42
   X = 42
   Current backtrace:
   [|{ .passed_args = [| |], .called_proc = proc()
   {
   "Current backtrace:";
   getbacktrace();
   return void;
   } }, { .passed_args = [|42|], .called_proc = proc(X)
   {
   "X = ", X;
   testA();
   return void;
   } }, { .passed_args = [|17, 42|], .called_proc = proc(X, Y)
   {
   "X = ", X, ", Y = ", Y;
   testB(Y);
   return void;
   } }|]

Example 2:

   > getbacktrace();
   [| |]

Example 3:

   > procedure printnumargs(X) {
       var L, t;
       "number of arguments: ", X;
       L = getbacktrace();
       "Backtrace:";
       for t in L do {
         "  " @ objectname(t.called_proc) @ ", ", t.passed_args;
       };
     };
   > procedure numargs(l = ...) {
       "l[17] = ", l[17];
       printnumargs(length(l));
     };
   > procedure test() {
       numargs @ [|25, 26, 27 ...|];
     };
   > test();
   l[17] = 42
   number of arguments: infty
   Backtrace:
     printnumargs, [|infty|]
     numargs, [|25, 26, 27...|]
     test, [| |]
See also: proc, procedure, objectname, bind, @
Go back to the list of commands

Name:

getsuppressedmessages returns a list of numbers of messages that have been suppressed from message output

Library name:

sollya_obj_t sollya_lib_getsuppressedmessages();

Usage:

getsuppressedmessages() : void -> list

Description:

Example 1:

   > verbosity = 1;
   The verbosity level has been set to 1.
   > 0.1;
   Warning: Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   0.1
   > suppressmessage(174);
   > 0.1;
   0.1
   > suppressmessage(407);
   > 0.1;
   0.1
   > getsuppressedmessages();
   [|174, 407|]
   > suppressmessage(207, 196);
   > getsuppressedmessages();
   [|174, 196, 207, 407|]

Example 2:

   > suppressmessage(174, 209, 13, 24, 196);
   > suppressmessage([| 16, 17 |]);
   > suppressmessage(19);
   > unsuppressmessage([| 13, 17 |]);
   > getsuppressedmessages();
   [|16, 19, 24, 174, 196, 209|]
   > unsuppressmessage(getsuppressedmessages());
   > getsuppressedmessages();
   [| |]

Example 3:

   > verbosity = 12;
   The verbosity level has been set to 12.
   > suppressmessage(174);
   > exp(x * 0.1);
   Information: no Horner simplification will be performed because the given tree is already in Horner form.
   exp(x * 0.1)
   > getsuppressedmessages();
   [|174|]
   > verbosity = 0;
   The verbosity level has been set to 0.
   > exp(x * 0.1);
   exp(x * 0.1)
   > getsuppressedmessages();
   [|174|]
See also: getsuppressedmessages, suppressmessage, unsuppressmessage, verbosity, roundingwarnings
Go back to the list of commands

Name:

> greater-than operator

Library name:

sollya_obj_t sollya_lib_cmp_greater(sollya_obj_t, sollya_obj_t)

Usage:

expr1 > expr2 : (constant, constant) -> boolean

Parameters:

Description:

Example 1:

   > 5 > 4;
   true
   > 5 > 5;
   false
   > 5 > 6;
   false
   > exp(2) > exp(1);
   true
   > log(1) > exp(2);
   false

Example 2:

   > prec = 12;
   The precision has been set to 12 bits.
   > 16385.1 > 16384.1;
   false
See also: ==, !=, >=, <=, <, in, !, &&, ||, prec, max, min
Go back to the list of commands

Name:

guessdegree returns the minimal degree needed for a polynomial to approximate a function with a certain error on an interval.

Library names:

sollya_obj_t sollya_lib_guessdegree(sollya_obj_t, sollya_obj_t,                                     sollya_obj_t, ...) sollya_obj_t sollya_lib_v_guessdegree(sollya_obj_t, sollya_obj_t,                                       sollya_obj_t, va_list)

Usage:

guessdegree(f,I,eps,w,bound) : (function, range, constant, function, constant) -> range

Parameters:

Description:

Example 1:

   > guessdegree(exp(x),[-1;1],1e-10);
   [10;10]

Example 2:

   > guessdegree(exp(x),[-1;1],1e-10,default, 9);
   [10;infty]

Example 3:

   > guessdegree(1, [-1;1], 1e-8, 1/exp(x));
   [8;9]
See also: dirtyinfnorm, remez, fpminimax, degree
Go back to the list of commands

Names:

halfprecision, HP rounding to the nearest IEEE 754 half-precision number (binary16).

Library names:

sollya_obj_t sollya_lib_halfprecision(sollya_obj_t) sollya_obj_t sollya_lib_halfprecision_obj() int sollya_lib_is_halfprecision_obj(sollya_obj_t) sollya_obj_t sollya_lib_build_function_halfprecision(sollya_obj_t) #define SOLLYA_HP(x) sollya_lib_build_function_halfprecision(x)

Description:

Example 1:

   > display=binary!;
   > HP(0.1);
   1.100110011_2 * 2^(-4)
   > HP(4.17);
   1.00001011_2 * 2^(2)
   > HP(1.011_2 * 2^(-23));
   1.1_2 * 2^(-23)
See also: single, double, doubleextended, doubledouble, quad, tripledouble, roundcoefficients, fpminimax, implementpoly, round, printsingle
Go back to the list of commands

Name:

hexadecimal special value for global state display

Library names:

sollya_obj_t sollya_lib_hexadecimal() int sollya_lib_is_hexadecimal(sollya_obj_t)

Description:

See also: decimal, dyadic, powers, binary, display
Go back to the list of commands

Name:

honorcoeffprec indicates the (forced) honoring the precision of the coefficients in implementpoly

Library names:

sollya_obj_t sollya_lib_honorcoeffprec() int sollya_lib_is_honorcoeffprec(sollya_obj_t)

Usage:

honorcoeffprec : honorcoeffprec

Description:

Example 1:

   > verbosity = 1!;
   > q = implementpoly(1 - dirtysimplify(TD(1/6)) * x^2,[-1b-10;1b-10],1b-60,DD,"p","implementation.c");
   Warning: at least one of the coefficients of the given polynomial has been rounded in a way
   that the target precision can be achieved at lower cost. Nevertheless, the implemented polynomial
   is different from the given one.
   > printexpansion(q);
   0x3ff0000000000000 + x^2 * 0xbfc5555555555555
   > r = implementpoly(1 - dirtysimplify(TD(1/6)) * x^2,[-1b-10;1b-10],1b-60,DD,"p","implementation.c",honorcoeffprec);
   Warning: the inferred precision of the 2th coefficient of the polynomial is greater than
   the necessary precision computed for this step. This may make the automatic determination
   of precisions useless.
   > printexpansion(r);
   0x3ff0000000000000 + x^2 * (0xbfc5555555555555 + 0xbc65555555555555 + 0xb905555555555555)
See also: implementpoly, printexpansion, fpminimax
Go back to the list of commands

Name:

hopitalrecursions controls the number of recursion steps when applying L'Hopital's rule.

Library names:

void sollya_lib_set_hopitalrecursions_and_print(sollya_obj_t) void sollya_lib_set_hopitalrecursions(sollya_obj_t) sollya_obj_t sollya_lib_get_hopitalrecursions()

Usage:

hopitalrecursions = n : integer -> void hopitalrecursions = n ! : integer -> void hopitalrecursions : integer

Parameters:

Description:

Example 1:

   > hopitalrecursions=0;
   The number of recursions for Hopital's rule has been set to 0.
   > evaluate(log(1+x)^2/x^2,[-1/2; 1]);
   [-infty;infty]
   > hopitalrecursions=1;
   The number of recursions for Hopital's rule has been set to 1.
   > evaluate(log(1+x)^2/x^2,[-1/2; 1]);
   [-2.5225887222397812376689284858327062723020005374411;6.7725887222397812376689284858327062723020005374412]
See also: taylorrecursions, infnorm, findzeros, evaluate
Go back to the list of commands

Name:

horner brings all polynomial subexpressions of an expression to Horner form

Library name:

sollya_obj_t sollya_lib_horner(sollya_obj_t)

Usage:

horner(function) : function -> function

Parameters:

Description:

Example 1:

   > print(horner(1 + 2 * x + 3 * x^2));
   1 + x * (2 + x * 3)
   > print(horner((x + 1)^7));
   1 + x * (7 + x * (21 + x * (35 + x * (35 + x * (21 + x * (7 + x))))))

Example 2:

   > print(horner(exp((x + 1)^5) - log(asin(x + x^3) + x)));
   exp(1 + x * (5 + x * (10 + x * (10 + x * (5 + x))))) - log(asin(x * (1 + x^2)) + x)
See also: canonical, print, coeff, degree, autosimplify, simplify
Go back to the list of commands

Name:

HP short form for halfprecision
See also: halfprecision
Go back to the list of commands

Name:

implementconstant implements a constant in arbitrary precision

Library names:

void sollya_lib_implementconstant(sollya_obj_t, ...); void sollya_lib_v_implementconstant(sollya_obj_t, va_list);

Usage:

implementconstant(expr) : constant -> void implementconstant(expr,filename) : (constant, string) -> void implementconstant(expr,filename,functionname) : (constant, string, string) -> void

Description:

Example 1:

   > implementconstant(exp(1)+log(2)/sqrt(1/10));
                   [ The first 100 lines of the output have been removed ]
   #include <mpfr.h>
   
   void
   const_something (mpfr_ptr y, mp_prec_t prec)
   {
     /* Declarations */
     mpfr_t tmp1;
     mpfr_t tmp2;
     mpfr_t tmp3;
     mpfr_t tmp4;
     mpfr_t tmp5;
     mpfr_t tmp6;
     mpfr_t tmp7;
   
     /* Initializations */
     mpfr_init2 (tmp2, prec+5);
     mpfr_init2 (tmp1, prec+3);
     mpfr_init2 (tmp4, prec+8);
     mpfr_init2 (tmp3, prec+7);
     mpfr_init2 (tmp6, prec+11);
     mpfr_init2 (tmp7, prec+11);
     mpfr_init2 (tmp5, prec+11);
   
     /* Core */
     mpfr_set_prec (tmp2, prec+4);
     mpfr_set_ui (tmp2, 1, MPFR_RNDN);
     mpfr_set_prec (tmp1, prec+3);
     mpfr_exp (tmp1, tmp2, MPFR_RNDN);
     mpfr_set_prec (tmp4, prec+8);
     mpfr_set_ui (tmp4, 2, MPFR_RNDN);
     mpfr_set_prec (tmp3, prec+7);
     mpfr_log (tmp3, tmp4, MPFR_RNDN);
     mpfr_set_prec (tmp6, prec+11);
     mpfr_set_ui (tmp6, 1, MPFR_RNDN);
     mpfr_set_prec (tmp7, prec+11);
     mpfr_set_ui (tmp7, 10, MPFR_RNDN);
     mpfr_set_prec (tmp5, prec+11);
     mpfr_div (tmp5, tmp6, tmp7, MPFR_RNDN);
     mpfr_set_prec (tmp4, prec+7);
     mpfr_sqrt (tmp4, tmp5, MPFR_RNDN);
     mpfr_set_prec (tmp2, prec+5);
     mpfr_div (tmp2, tmp3, tmp4, MPFR_RNDN);
     mpfr_set_prec (y, prec+3);
     mpfr_add (y, tmp1, tmp2, MPFR_RNDN);
   
     /* Cleaning stuff */
     mpfr_clear(tmp1);
     mpfr_clear(tmp2);
     mpfr_clear(tmp3);
     mpfr_clear(tmp4);
     mpfr_clear(tmp5);
     mpfr_clear(tmp6);
     mpfr_clear(tmp7);
   }

Example 2:

   > implementconstant(sin(13/17),"sine_of_thirteen_seventeenth.c");
   > bashevaluate("tail -n 30 sine_of_thirteen_seventeenth.c");
   #include <mpfr.h>
   
   void
   const_something (mpfr_ptr y, mp_prec_t prec)
   {
     /* Declarations */
     mpfr_t tmp1;
     mpfr_t tmp2;
     mpfr_t tmp3;
   
     /* Initializations */
     mpfr_init2 (tmp2, prec+6);
     mpfr_init2 (tmp3, prec+6);
     mpfr_init2 (tmp1, prec+6);
   
     /* Core */
     mpfr_set_prec (tmp2, prec+6);
     mpfr_set_ui (tmp2, 13, MPFR_RNDN);
     mpfr_set_prec (tmp3, prec+6);
     mpfr_set_ui (tmp3, 17, MPFR_RNDN);
     mpfr_set_prec (tmp1, prec+6);
     mpfr_div (tmp1, tmp2, tmp3, MPFR_RNDN);
     mpfr_set_prec (y, prec+2);
     mpfr_sin (y, tmp1, MPFR_RNDN);
   
     /* Cleaning stuff */
     mpfr_clear(tmp1);
     mpfr_clear(tmp2);
     mpfr_clear(tmp3);
   }

Example 3:

   > implementconstant(asin(1/3 * pi),default,"arcsin_of_one_third_pi");
                   [ The first 100 lines of the output have been removed ]
   #include <mpfr.h>
   
   void
   arcsin_of_one_third_pi (mpfr_ptr y, mp_prec_t prec)
   {
     /* Declarations */
     mpfr_t tmp1;
     mpfr_t tmp2;
     mpfr_t tmp3;
   
     /* Initializations */
     mpfr_init2 (tmp2, prec+8);
     mpfr_init2 (tmp3, prec+8);
     mpfr_init2 (tmp1, prec+8);
   
     /* Core */
     mpfr_set_prec (tmp2, prec+8);
     mpfr_const_pi (tmp2, MPFR_RNDN);
     mpfr_set_prec (tmp3, prec+8);
     mpfr_set_ui (tmp3, 3, MPFR_RNDN);
     mpfr_set_prec (tmp1, prec+8);
     mpfr_div (tmp1, tmp2, tmp3, MPFR_RNDN);
     mpfr_set_prec (y, prec+2);
     mpfr_asin (y, tmp1, MPFR_RNDN);
   
     /* Cleaning stuff */
     mpfr_clear(tmp1);
     mpfr_clear(tmp2);
     mpfr_clear(tmp3);
   }

Example 4:

   > implementconstant(ceil(log(19 + 1/3)),"constant_code.c","magic_constant");
   > bashevaluate("tail -n -9 constant_code.c");
   void
   magic_constant (mpfr_ptr y, mp_prec_t prec)
   {
     /* Initializations */
   
     /* Core */
     mpfr_set_prec (y, prec);
     mpfr_set_ui (y, 3, MPFR_RNDN);
   }

Example 5:

   > bashexecute("gcc -fPIC -Wall -c libraryconstantexample.c -I$HOME/.local/include");
   > bashexecute("gcc -shared -o libraryconstantexample libraryconstantexample.o -lgmp -lmpfr");
   > euler_gamma = libraryconstant("./libraryconstantexample");
   > implementconstant(euler_gamma^(1/3), "euler.c");
   > bashevaluate("tail -n -17 euler.c");
   void
   const_something (mpfr_ptr y, mp_prec_t prec)
   {
     /* Declarations */
     mpfr_t tmp1;
   
     /* Initializations */
     mpfr_init2 (tmp1, prec+1);
   
     /* Core */
     euler_gamma (tmp1, prec+1);
     mpfr_set_prec (y, prec+2);
     mpfr_root (y, tmp1, 3, MPFR_RNDN);
   
     /* Cleaning stuff */
     mpfr_clear(tmp1);
   }
See also: implementpoly, libraryconstant, library, function, bashevaluate
Go back to the list of commands

Name:

implementpoly implements a polynomial using double, double-double and triple-double arithmetic and generates a Gappa proof

Library names:

sollya_obj_t sollya_lib_implementpoly(sollya_obj_t, sollya_obj_t,                                       sollya_obj_t, sollya_obj_t,                                       sollya_obj_t, sollya_obj_t, ...) sollya_obj_t sollya_lib_v_implementpoly(sollya_obj_t, sollya_obj_t,                                         sollya_obj_t, sollya_obj_t,                                         sollya_obj_t, sollya_obj_t, va_list)

Usage:

implementpoly(polynomial, range, error bound, format, functionname, filename) : (function, range, constant, D|double|DD|doubledouble|TD|tripledouble, string, string) -> function implementpoly(polynomial, range, error bound, format, functionname, filename, honor coefficient precisions) : (function, range, constant, D|double|DD|doubledouble|TD|tripledouble, string, string, honorcoeffprec) -> function implementpoly(polynomial, range, error bound, format, functionname, filename, proof filename) : (function, range, constant, D|double|DD|doubledouble|TD|tripledouble, string, string, string) -> function implementpoly(polynomial, range, error bound, format, functionname, filename, honor coefficient precisions, proof filename) : (function, range, constant, D|double|DD|doubledouble|TD|tripledouble, string, string, honorcoeffprec, string) -> function

Description:

Example 1:

   > implementpoly(1 - 1/6 * x^2 + 1/120 * x^4, [-1b-10;1b-10], 1b-30, D, "p","implementation.c");
   1 + x^2 * (-0.166666666666666657414808128123695496469736099243164 + x^2 * 8.3333333333333332176851016015461937058717012405396e-3)
   > bashevaluate("tail -n -29 implementation.c");
   #define p_coeff_0h 1.00000000000000000000000000000000000000000000000000000000000000000000000000000000e+00
   #define p_coeff_2h -1.66666666666666657414808128123695496469736099243164062500000000000000000000000000e-01
   #define p_coeff_4h 8.33333333333333321768510160154619370587170124053955078125000000000000000000000000e-03
   
   
   void p(double *p_resh, double x) {
   double p_x_0_pow2h;
   
   
   p_x_0_pow2h = x * x;
   
   
   double p_t_1_0h;
   double p_t_2_0h;
   double p_t_3_0h;
   double p_t_4_0h;
   double p_t_5_0h;
    
   
   
   p_t_1_0h = p_coeff_4h;
   p_t_2_0h = p_t_1_0h * p_x_0_pow2h;
   p_t_3_0h = p_coeff_2h + p_t_2_0h;
   p_t_4_0h = p_t_3_0h * p_x_0_pow2h;
   p_t_5_0h = p_coeff_0h + p_t_4_0h;
   *p_resh = p_t_5_0h;
   
   
   }

Example 2:

   > implementpoly(1 - 1/6 * x^2 + 1/120 * x^4, [-1b-10;1b-10], 1b-30, D, "p","implementation.c","implementation.gappa");
   1 + x^2 * (-0.166666666666666657414808128123695496469736099243164 + x^2 * 8.3333333333333332176851016015461937058717012405396e-3)

Example 3:

   > verbosity = 1!;
   > q = implementpoly(1 - dirtysimplify(TD(1/6)) * x^2,[-1b-10;1b-10],1b-60,DD,"p","implementation.c");
   Warning: at least one of the coefficients of the given polynomial has been rounded in a way
   that the target precision can be achieved at lower cost. Nevertheless, the implemented polynomial
   is different from the given one.
   > printexpansion(q);
   0x3ff0000000000000 + x^2 * 0xbfc5555555555555
   > r = implementpoly(1 - dirtysimplify(TD(1/6)) * x^2,[-1b-10;1b-10],1b-60,DD,"p","implementation.c",honorcoeffprec);
   Warning: the inferred precision of the 2th coefficient of the polynomial is greater than
   the necessary precision computed for this step. This may make the automatic determination
   of precisions useless.
   > printexpansion(r);
   0x3ff0000000000000 + x^2 * (0xbfc5555555555555 + 0xbc65555555555555 + 0xb905555555555555)

Example 4:

   > p = 0x3ff0000000000000 + x * (0x3ff0000000000000 + x * (0x3fe0000000000000 + x * (0x3fc5555555555559 + x * (0x3fa55555555555bd + x * (0x3f811111111106e2 + x * (0x3f56c16c16bf5eb7 + x * (0x3f2a01a01a292dcd + x * (0x3efa01a0218a016a + x * (0x3ec71de360331aad + x * (0x3e927e42e3823bf3 + x * (0x3e5ae6b2710c2c9a + x * (0x3e2203730c0a7c1d + x * 0x3de5da557e0781df))))))))))));
   > q = implementpoly(p,[-1/2;1/2],1b-60,D,"p","implementation.c",honorcoeffprec,"implementation.gappa");
   > if (q != p) then print("During implementation, rounding has happened.") else print("Polynomial implemented as given.");
   Polynomial implemented as given.
See also: honorcoeffprec, roundcoefficients, double, doubledouble, tripledouble, bashevaluate, printexpansion, error, remez, fpminimax, taylor, implementconstant
Go back to the list of commands

Name:

inf gives the lower bound of an interval.

Library name:

sollya_obj_t sollya_lib_inf(sollya_obj_t)

Usage:

inf(I) : range -> constant inf(x) : constant -> constant

Parameters:

Description:

Example 1:

   > inf([1;3]);
   1
   > inf(0);
   0

Example 2:

   > display=binary!;
   > I=[0.111110000011111_2; 1];
   > inf(I);
   1.11110000011111_2 * 2^(-1)
   > prec=12!;
   > inf(I);
   1.11110000011111_2 * 2^(-1)
See also: mid, sup, max, min
Go back to the list of commands

Name:

infnorm computes an interval bounding the infinity norm of a function on an interval.

Library names:

sollya_obj_t sollya_lib_infnorm(sollya_obj_t, sollya_obj_t, ...) sollya_obj_t sollya_lib_v_infnorm(sollya_obj_t, sollya_obj_t, va_list)

Usage:

infnorm(f,I,filename,Ilist) : (function, range, string, list) -> range

Parameters:

Description:

Example 1:

   > infnorm(exp(x),[-2;3]);
   [20.085536923187667740928529654581717896987907838554;20.0855369231876677409285296545817178969879078385544]

Example 2:

   > infnorm(exp(x),[-2;3],"proof.txt");
   [20.085536923187667740928529654581717896987907838554;20.0855369231876677409285296545817178969879078385544]

Example 3:

   > infnorm(exp(x),[-2;3],[| [0;1], [2;2.5] |]);
   [20.085536923187667740928529654581717896987907838554;20.0855369231876677409285296545817178969879078385544]

Example 4:

   > infnorm(exp(x),[-2;3],"proof.txt", [| [0;1], [2;2.5] |]);
   [20.085536923187667740928529654581717896987907838554;20.0855369231876677409285296545817178969879078385544]

Example 5:

   > infnorm(exp(x),[1;1]);
   [2.7182818284590452353602874713526624977572470936999;2.7182818284590452353602874713526624977572470937]

Example 6:

   > infnorm(exp(x), [log(0);log(1)]);
   [0;infty]
See also: prec, diam, hopitalrecursions, taylorrecursions, dirtyinfnorm, checkinfnorm, supnorm, findzeros, diff, taylorrecursions, autodiff, numberroots, taylorform
Go back to the list of commands

Name:

in containment test operator

Library name:

sollya_obj_t sollya_lib_cmp_in(sollya_obj_t, sollya_obj_t)

Usage:

expr in range1 : (constant, range) -> boolean range1 in range2 : (range, range) -> boolean

Parameters:

Description:

Example 1:

   > 5 in [-4;7];
   true
   > 4 in [-1;1];
   false
   > 0 in sin([-17;17]);
   true

Example 2:

   > [5;7] in [2;8];
   true
   > [2;3] in [4;5];
   false
   > [2;3] in [2.5;5];
   false

Example 3:

   > for i in [|1,...,5|] do print(i);
   1
   2
   3
   4
   5
See also: ==, !=, >=, >, <=, <, !, &&, ||, prec, print
Go back to the list of commands

Name:

integer keyword representing a machine integer type

Library name:

SOLLYA_EXTERNALPROC_TYPE_INTEGER

Usage:

integer : type type

Description:

See also: externalproc, boolean, constant, function, list of, range, string, object
Go back to the list of commands

Name:

integral computes an interval bounding the integral of a function on an interval.

Library name:

sollya_obj_t sollya_lib_integral(sollya_obj_t, sollya_obj_t)

Usage:

integral(f,I) : (function, range) -> range

Parameters:

Description:

Example 1:

   > sin(10);
   -0.54402111088936981340474766185137728168364301291622
   > integral(cos(x),[0;10]);
   [-0.54710197983579690224097637163525943075698599257333;-0.54094015130013183848150540881373370744053741191729]
   > diam=1e-5!;
   > integral(cos(x),[0;10]);
   [-0.54432915685955427101857780295936956775293876382777;-0.54371306401249969508039644221927489010425803173555]
See also: diam, dirtyintegral, prec
Go back to the list of commands

Name:

isbound indicates whether a variable is bound or not.

Usage:

isbound(ident) : boolean

Parameters:

Description:

Example 1:

   > isbound(x);
   false
   > isbound(f);
   false
   > isbound(g);
   false
   > f=sin(x);
   > isbound(x);
   true
   > isbound(f);
   true
   > isbound(g);
   false

Example 2:

   > isbound(a);
   false
   > { var a; isbound(a); };
   true
   > isbound(a);
   false

Example 3:

   > f=sin(x);
   > isbound(x);
   true
   > rename(x,y);
   > isbound(x);
   false

Example 4:

   > x=1;
   > f=sin(y);
   > rename(y,x);
   > f;
   sin(x)
   > x;
   x
   > isbound(x);
   true
   > rename(x,y);
   > isbound(x);
   true
   > x;
   1
See also: rename
Go back to the list of commands

Name:

isevaluable tests whether a function can be evaluated at a point

Usage:

isevaluable(function, constant) : (function, constant) -> boolean

Parameters:

Description:

Example 1:

   > isevaluable(sin(pi * 1/x), 0.75);
   true
   > print(evaluate(sin(pi * 1/x), 0.75));
   -0.86602540378443864676372317075293618347140262690519

Example 2:

   > isevaluable(sin(pi * 1/x), 0.5);
   true
   > print(evaluate(sin(pi * 1/x), 0.5));
   [-1.7298645251438126951650861503109812954283676799168e-12715;7.5941198201187963145069564314525661706039084390068e-12716]

Example 3:

   > isevaluable(sin(pi * 1/x), 0);
   true
   > print(evaluate(sin(pi * 1/x), 0));
   [-1;1]

Example 4:

   > procedure isEvaluableEmulation(f, c) {
       return match evaluate(f, c) with
               NaN : (false)
            [NaN;NaN] : (false)
            default : (true);
     };
   > isEvaluableEmulation(sin(pi * 1/x), 0.75);
   true
   > isEvaluableEmulation(sin(pi * 1/x), 0.5);
   true
   > isEvaluableEmulation(sin(pi * 1/x), 0);
   true
See also: evaluate
Go back to the list of commands

Name:

<= less-than-or-equal-to operator

Library name:

sollya_obj_t sollya_lib_cmp_less_equal(sollya_obj_t, sollya_obj_t)

Usage:

expr1 <= expr2 : (constant, constant) -> boolean

Parameters:

Description:

Example 1:

   > 5 <= 4;
   false
   > 5 <= 5;
   true
   > 5 <= 6;
   true
   > exp(2) <= exp(1);
   false
   > log(1) <= exp(2);
   true

Example 2:

   > prec = 12;
   The precision has been set to 12 bits.
   > 16385.1 <= 16384.1;
   true
See also: ==, !=, >=, >, <, in, !, &&, ||, prec, max, min
Go back to the list of commands

Name:

length computes the length of a list or string.

Library name:

sollya_obj_t sollya_lib_length(sollya_obj_t)

Usage:

length(L) : list -> integer length(s) : string -> integer

Parameters:

Description:

Example 1:

   > length("Hello World!");
   12

Example 2:

   > length([|1,...,5|]);
   5

Example 3:

   > length([| |]);
   0

Example 4:

   > length([|1,2...|]);
   infty
Go back to the list of commands

Name:

libraryconstant binds an external mathematical constant to a variable in Sollya

Library names:

sollya_obj_t sollya_lib_libraryconstant(char *, void (*)(mpfr_t, mp_prec_t)) sollya_obj_t sollya_lib_build_function_libraryconstant(char *,                                                        void (*)(mpfr_t,                                                                 mp_prec_t)) sollya_obj_t sollya_lib_libraryconstant_with_data(char *,                                                   void (*)(mpfr_t,                                                            mp_prec_t,                                                            void *),                                                   void *,                                                   void (*)(void *)) sollya_obj_t sollya_lib_build_function_libraryconstant_with_data(                                                   char *,                                                   void (*)(mpfr_t,                                                            mp_prec_t,                                                            void *),                                                   void *,                                                   void (*)(void *))

Usage:

libraryconstant(path) : string -> function

Description:

Example 1:

   > bashexecute("gcc -fPIC -Wall -c libraryconstantexample.c -I$HOME/.local/include");
   > bashexecute("gcc -shared -o libraryconstantexample libraryconstantexample.o -lgmp -lmpfr");
   > euler_gamma = libraryconstant("./libraryconstantexample");
   > prec = 20!;
   > euler_gamma;
   0.577215
   > prec = 100!;
   > euler_gamma;
   0.577215664901532860606512090082
   > midpointmode = on;
   Midpoint mode has been activated.
   > [euler_gamma];
   0.57721566490153286060651209008~2/4~
See also: bashexecute, externalproc, externalplot, pi, library, evaluate
Go back to the list of commands

Name:

library binds an external mathematical function to a variable in Sollya

Library names:

sollya_obj_t sollya_lib_libraryfunction(sollya_obj_t, char *,                                         int (*)(mpfi_t, mpfi_t, int)) sollya_obj_t sollya_lib_build_function_libraryfunction(sollya_obj_t, char *,                                                        int (*)(mpfi_t,                                                                mpfi_t, int)) sollya_obj_t sollya_lib_libraryfunction_with_data(                                         sollya_obj_t, char *,                                         int (*)(mpfi_t, mpfi_t, int, void *),                                         void *, void (*)(void *)) sollya_obj_t sollya_lib_build_function_libraryfunction_with_data(                                         sollya_obj_t, char *,                                         int (*)(mpfi_t,                                                 mpfi_t, int, void *),                                         void *, void (*)(void *))

Usage:

library(path) : string -> function

Description:

Example 1:

   > bashexecute("gcc -fPIC -Wall -c libraryexample.c -I$HOME/.local/include");
   > bashexecute("gcc -shared -o libraryexample libraryexample.o -lgmp -lmpfr");
   > myownlog = library("./libraryexample");
   > evaluate(log(x), 2);
   0.69314718055994530941723212145817656807550013436025
   > evaluate(myownlog(x), 2);
   0.69314718055994530941723212145817656807550013436025
See also: function, bashexecute, externalproc, externalplot, diff, evaluate, libraryconstant
Go back to the list of commands

Name:

list of keyword used in combination with a type keyword

Library names:

SOLLYA_EXTERNALPROC_TYPE_CONSTANT_LIST SOLLYA_EXTERNALPROC_TYPE_FUNCTION_LIST SOLLYA_EXTERNALPROC_TYPE_RANGE_LIST SOLLYA_EXTERNALPROC_TYPE_INTEGER_LIST SOLLYA_EXTERNALPROC_TYPE_STRING_LIST SOLLYA_EXTERNALPROC_TYPE_BOOLEAN_LIST SOLLYA_EXTERNALPROC_TYPE_OBJECT_LIST

Description:

See also: externalproc, boolean, constant, function, integer, range, string, object
Go back to the list of commands

Name:

log10 decimal logarithm.

Library names:

sollya_obj_t sollya_lib_log10(sollya_obj_t) sollya_obj_t sollya_lib_build_function_log10(sollya_obj_t) #define SOLLYA_LOG10(x) sollya_lib_build_function_log10(x)

Description:

See also: log, log2
Go back to the list of commands

Name:

log1p translated logarithm.

Library names:

sollya_obj_t sollya_lib_log1p(sollya_obj_t) sollya_obj_t sollya_lib_build_function_log1p(sollya_obj_t) #define SOLLYA_LOG1P(x) sollya_lib_build_function_log1p(x)

Description:

See also: log
Go back to the list of commands

Name:

log2 binary logarithm.

Library names:

sollya_obj_t sollya_lib_log2(sollya_obj_t) sollya_obj_t sollya_lib_build_function_log2(sollya_obj_t) #define SOLLYA_LOG2(x) sollya_lib_build_function_log2(x)

Description:

See also: log, log10
Go back to the list of commands

Name:

log natural logarithm.

Library names:

sollya_obj_t sollya_lib_log(sollya_obj_t) sollya_obj_t sollya_lib_build_function_log(sollya_obj_t) #define SOLLYA_LOG(x) sollya_lib_build_function_log(x)

Description:

See also: exp, log2, log10
Go back to the list of commands

Name:

< less-than operator

Library name:

sollya_obj_t sollya_lib_cmp_less(sollya_obj_t, sollya_obj_t)

Usage:

expr1 < expr2 : (constant, constant) -> boolean

Parameters:

Description:

Example 1:

   > 5 < 4;
   false
   > 5 < 5;
   false
   > 5 < 6;
   true
   > exp(2) < exp(1);
   false
   > log(1) < exp(2);
   true

Example 2:

   > prec = 12;
   The precision has been set to 12 bits.
   > 16384.1 < 16385.1;
   false
See also: ==, !=, >=, >, <=, in, !, &&, ||, prec, max, min
Go back to the list of commands

Name:

mantissa returns the integer mantissa of a number.

Library name:

sollya_obj_t sollya_lib_mantissa(sollya_obj_t)

Usage:

mantissa(x) : constant -> integer

Parameters:

Description:

Example 1:

   > a=round(Pi,20,RN);
   > e=exponent(a);
   > m=mantissa(a);
   > m;
   411775
   > a-m*2^e;
   0
See also: exponent, precision
Go back to the list of commands

Name:

max determines which of given constant expressions has maximum value

Library names:

sollya_obj_t sollya_lib_max(sollya_obj_t, ...) sollya_obj_t sollya_lib_v_max(sollya_obj_t, va_list)

Usage:

max(expr1,expr2,...,exprn) : (constant, constant, ..., constant) -> constant max(l) : list -> constant

Parameters:

Description:

Example 1:

   > max(1,2,3,exp(5),log(0.25));
   148.41315910257660342111558004055227962348766759388
   > max(17);
   17

Example 2:

   > l = [|1,2,3,exp(5),log(0.25)|];
   > max(l);
   148.41315910257660342111558004055227962348766759388

Example 3:

   > print(max(exp(17),sin(62)));
   exp(17)

Example 4:

   > verbosity = 1!;
   > print(max(17 + log2(13)/log2(9),17 + log(13)/log(9)));
   Warning: the tool is unable to decide a maximum computation by evaluation even though faithful evaluation of the terms has been possible. The terms will be considered to be equal.
   17 + log2(13) / log2(9)
See also: min, ==, !=, >=, >, <, <=, in, inf, sup
Go back to the list of commands

Name:

mid gives the middle of an interval.

Library name:

sollya_obj_t sollya_lib_mid(sollya_obj_t)

Usage:

mid(I) : range -> constant mid(x) : constant -> constant

Parameters:

Description:

Example 1:

   > mid([1;3]);
   2
   > mid(17);
   17
See also: inf, sup
Go back to the list of commands

Name:

midpointmode global variable controlling the way intervals are displayed.

Library names:

void sollya_lib_set_midpointmode_and_print(sollya_obj_t) void sollya_lib_set_midpointmode(sollya_obj_t) sollya_obj_t sollya_lib_get_midpointmode()

Usage:

midpointmode = activation value : on|off -> void midpointmode = activation value ! : on|off -> void midpointmode : on|off

Parameters:

Description:

Example 1:

   > a = round(Pi,30,RD);
   > b = round(Pi,30,RU);
   > d = [a,b];
   > d;
   [3.1415926516056060791015625;3.1415926553308963775634765625]
   > midpointmode=on!;
   > d;
   0.314159265~1/6~e1
See also: on, off, roundingwarnings, display, decimal
Go back to the list of commands

Name:

min determines which of given constant expressions has minimum value

Library names:

sollya_obj_t sollya_lib_min(sollya_obj_t, ...) sollya_obj_t sollya_lib_v_min(sollya_obj_t, va_list)

Usage:

min(expr1,expr2,...,exprn) : (constant, constant, ..., constant) -> constant min(l) : list -> constant

Parameters:

Description:

Example 1:

   > min(1,2,3,exp(5),log(0.25));
   -1.3862943611198906188344642429163531361510002687205
   > min(17);
   17

Example 2:

   > l = [|1,2,3,exp(5),log(0.25)|];
   > min(l);
   -1.3862943611198906188344642429163531361510002687205

Example 3:

   > print(min(exp(17),sin(62)));
   sin(62)

Example 4:

   > verbosity = 1!;
   > print(min(17 + log2(13)/log2(9),17 + log(13)/log(9)));
   Warning: the tool is unable to decide a minimum computation by evaluation even though faithful evaluation of the terms has been possible. The terms will be considered to be equal.
   17 + log(13) / log(9)
See also: max, ==, !=, >=, >, <, <=, in, inf, sup
Go back to the list of commands

Name:

- subtraction function

Library names:

sollya_obj_t sollya_lib_sub(sollya_obj_t, sollya_obj_t) sollya_obj_t sollya_lib_build_function_sub(sollya_obj_t, sollya_obj_t) #define SOLLYA_SUB(x,y) sollya_lib_build_function_sub((x), (y)) sollya_obj_t sollya_lib_neg(sollya_obj_t) sollya_obj_t sollya_lib_build_function_neg(sollya_obj_t) #define SOLLYA_NEG(x) sollya_lib_build_function_neg(x)

Usage:

function1 - function2 : (function, function) -> function interval1 - interval2 : (range, range) -> range interval1 - constant : (range, constant) -> range interval1 - constant : (constant, range) -> range - function1 : function -> function - interval1 : range -> range

Parameters:

Description:

Example 1:

   > 5 - 2;
   3

Example 2:

   > x - 2;
   -2 + x

Example 3:

   > x - x;
   0

Example 4:

   > diff(sin(x) - exp(x));
   cos(x) - exp(x)

Example 5:

   > [1;2] - [3;4];
   [-3;-1]
   > [1;2] - 17;
   [-16;-15]
   > 13 - [-4;17];
   [-4;17]

Example 6:

   > -exp(x);
   -exp(x)
   > -13;
   -13
   > -[13;17];
   [-17;-13]
See also: +, *, /, ^
Go back to the list of commands

Name:

* multiplication function

Library names:

sollya_obj_t sollya_lib_mul(sollya_obj_t, sollya_obj_t) sollya_obj_t sollya_lib_build_function_mul(sollya_obj_t, sollya_obj_t) #define SOLLYA_MUL(x,y) sollya_lib_build_function_mul((x), (y))

Usage:

function1 * function2 : (function, function) -> function interval1 * interval2 : (range, range) -> range interval1 * constant : (range, constant) -> range interval1 * constant : (constant, range) -> range

Parameters:

Description:

Example 1:

   > 5 * 2;
   10

Example 2:

   > x * 2;
   x * 2

Example 3:

   > x * x;
   x^2

Example 4:

   > diff(sin(x) * exp(x));
   sin(x) * exp(x) + exp(x) * cos(x)

Example 5:

   > [1;2] * [3;4];
   [3;8]
   > [1;2] * 17;
   [17;34]
   > 13 * [-4;17];
   [-52;221]
See also: +, -, /, ^
Go back to the list of commands

Name:

nearestint the function mapping the reals to the integers nearest to them.

Library names:

sollya_obj_t sollya_lib_nearestint(sollya_obj_t) sollya_obj_t sollya_lib_build_function_nearestint(sollya_obj_t) #define SOLLYA_NEARESTINT(x) sollya_lib_build_function_nearestint(x)

Description:

See also: ceil, floor, round, RN
Go back to the list of commands

Name:

!= negated equality test operator

Library name:

sollya_obj_t sollya_lib_cmp_not_equal(sollya_obj_t, sollya_obj_t)

Usage:

expr1 != expr2 : (any type, any type) -> boolean

Parameters:

Description:

Example 1:

   > "Hello" != "Hello";
   false
   > "Hello" != "Salut";
   true
   > "Hello" != 5;
   true
   > 5 + x != 5 + x;
   false

Example 2:

   > 1 != exp(0);
   false
   > asin(1) * 2 != pi;
   false
   > exp(5) != log(4);
   true

Example 3:

   > sin(pi/6) != 1/2 * sqrt(3);
   true

Example 4:

   > prec = 12;
   The precision has been set to 12 bits.
   > 16384.1 != 16385.1;
   false

Example 5:

   > error != error;
   false

Example 6:

   > p = x + x^2;
   > q = x * (1 + x);
   > autosimplify = on;
   Automatic pure tree simplification has been activated.
   > p != q;
   false
   > autosimplify = off;
   Automatic pure tree simplification has been deactivated.
   > p != q;
   true
See also: ==, >, >=, <=, <, in, !, &&, ||, error, prec, autosimplify
Go back to the list of commands

Name:

nop no operation

Usage:

nop : void -> void nop() : void -> void nop(n) : integer -> void

Description:

Example 1:

   > nop;

Example 2:

   > nop(100);

Example 3:

   > succ = proc(n) { return n + 1; };
   > succ;
   proc(n)
   {
   nop;
   return (n) + (1);
   }
   > succ(5);
   6
See also: proc, time
Go back to the list of commands

Name:

! boolean NOT operator

Library name:

sollya_obj_t sollya_lib_negate(sollya_obj_t)

Usage:

! expr : boolean -> boolean

Parameters:

Description:

Example 1:

   > ! false;
   true

Example 2:

   > ! (1 == exp(0));
   false
See also: &&, ||
Go back to the list of commands

Name:

numberroots Computes the number of roots of a polynomial in a given range.

Library name:

sollya_obj_t sollya_lib_numberroots(sollya_obj_t, sollya_obj_t)

Usage:

numberroots(p, I) : (function, range) -> integer

Parameters:

Description:

Example 1:

   > numberroots(1+x-x^2, [1,2]);
   1
   > findzeros(1+x-x^2, [1,2]);
   [|[1.617919921875;1.6180419921875]|]

Example 2:

   > numberroots((1+x)*(1-x), [-1,1]);
   2
   > numberroots(x^2, [-1,1]);
   1

Example 3:

   > verbosity = 1!;
   > numberroots(x-pi, [0,4]);
   Warning: the 0th coefficient of the polynomial is neither a floating point
   constant nor can be evaluated without rounding to a floating point constant.
   Will faithfully evaluate it with the current precision (165 bits)
   1

Example 4:

   > verbosity = 1!;
   > numberroots(1+x-x^2, [0, @Inf@]);
   Warning: the given interval must have finite bounds.
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
   error
   > numberroots(exp(x), [0, 1]);
   Warning: the given function must be a polynomial in this context.
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
   error
See also: dirtyfindzeros, findzeros, gcd
Go back to the list of commands

Name:

numerator gives the numerator of an expression

Library name:

sollya_obj_t sollya_lib_numerator(sollya_obj_t)

Usage:

numerator(expr) : function -> function

Parameters:

Description:

Example 1:

   > numerator(5/3);
   5

Example 2:

   > numerator(exp(x));
   exp(x)

Example 3:

   > a = 5/3;
   > b = numerator(a)/denominator(a);
   > print(a);
   5 / 3
   > print(b);
   5 / 3

Example 4:

   > a = exp(x/3);
   > b = numerator(a)/denominator(a);
   > print(a);
   exp(x / 3)
   > print(b);
   exp(x / 3)
See also: denominator, rationalmode
Go back to the list of commands

Name:

objectname returns, given a Sollya object, a string that can be reparsed to the object

Library name:

sollya_obj_t sollya_lib_objectname(sollya_obj_t);

Usage:

objectname(obj) : any type -> string

Description:

Example 1:

   > s = "Hello";
   > objectname("Hello");
   s

Example 2:

   > f = exp(x);
   > g = sin(x);
   > [| objectname(exp(x)), objectname(sin(x)), objectname(cos(x)) |];
   [|"f", "g", "cos(x)"|]

Example 3:

   > o = { .f = exp(x), .I = [-1;1] };
   > s1 = o@""; s1;
   { .f = exp(x), .I = [-1;1] }
   > s2 = objectname({ .I = [-1;1], .f = exp(x)}); s2;
   o
   > parse(s1) == parse(s2);
   true
   > write("s2 = \"", s2, "\" parses to ", parse(s2), "\n");
   s2 = "o" parses to { .f = exp(x), .I = [-1;1] }

Example 4:

   > n = 1664;
   > objectname(n);
   n

Example 5:

   > f = exp(x);
   > g = sin(x);
   > procedure test() {
         var f;
         var h;
         f = tan(x);
         h = cos(x);
         [| objectname(exp(x)), objectname(sin(x)), objectname(cos(x)), objectname(tan(x)) |];
     };
   > test();
   [|"exp(x)", "g", "h", "f"|]

Example 6:

   > procedure apply_proc(p, a, b) {
         return p(a, b);
     };
   > procedure show_trace_and_add(n, m) {
         var i, bt;
         bt = getbacktrace();
         write("Procedure stack:\n");
         for i from 0 to length(bt) - 1 do {
          write("   Procedure ", objectname((bt[i]).called_proc), " called with ", length((bt[i]).passed_args), " arguments\n");
         };
         write("\n");
         return n + m;
     };
   > procedure show_and_succ(u) {
       return apply_proc(show_trace_and_add, u, 1);
     };
   > show_and_succ(16);
   Procedure stack:
      Procedure show_trace_and_add called with 2 arguments
      Procedure apply_proc called with 3 arguments
      Procedure show_and_succ called with 1 arguments
   
   17

Example 7:

   > f = exp(three_decker_sauerkraut_and_toadstool_sandwich_with_arsenic_sauce);
   > g = sin(_x_);
   > h = f(g);
   > h;
   exp(sin(three_decker_sauerkraut_and_toadstool_sandwich_with_arsenic_sauce))
   > objectname(_x_);
   three_decker_sauerkraut_and_toadstool_sandwich_with_arsenic_sauce
See also: parse, var, getbacktrace, proc, procedure, @
Go back to the list of commands

Name:

object keyword representing a Sollya object type

Library name:

SOLLYA_EXTERNALPROC_TYPE_OBJECT

Usage:

object : type type

Description:

See also: externalproc, boolean, constant, function, list of, range, string, integer
Go back to the list of commands

Name:

off special value for certain global variables.

Library names:

sollya_obj_t sollya_lib_off() int sollya_lib_is_off(sollya_obj_t)

Description:

Example 1:

   > canonical=on;
   Canonical automatic printing output has been activated.
   > p=1+x+x^2;
   > mode=off;
   > p;
   1 + x + x^2
   > canonical=mode;
   Canonical automatic printing output has been deactivated.
   > p;
   1 + x * (1 + x)
See also: on, autosimplify, canonical, timing, fullparentheses, midpointmode, rationalmode, roundingwarnings, timing, dieonerrormode
Go back to the list of commands

Name:

on special value for certain global variables.

Library names:

sollya_obj_t sollya_lib_on() int sollya_lib_is_on(sollya_obj_t)

Description:

Example 1:

   > p=1+x+x^2;
   > mode=on;
   > p;
   1 + x * (1 + x)
   > canonical=mode;
   Canonical automatic printing output has been activated.
   > p;
   1 + x + x^2
See also: off, autosimplify, canonical, timing, fullparentheses, midpointmode, rationalmode, roundingwarnings, timing, dieonerrormode
Go back to the list of commands

Name:

|| boolean OR operator

Library name:

sollya_obj_t sollya_lib_or(sollya_obj_t, sollya_obj_t)

Usage:

expr1 || expr2 : (boolean, boolean) -> boolean

Parameters:

Description:

Example 1:

   > false || false;
   false

Example 2:

   > (1 == exp(0)) || (0 == log(1));
   true
See also: &&, !
Go back to the list of commands

Name:

parse parses an expression contained in a string

Library name:

sollya_obj_t sollya_lib_parse(sollya_obj_t)

Usage:

parse(string) : string -> function | error

Parameters:

Description:

Example 1:

   > parse("exp(x)");
   exp(x)

Example 2:

   > text = "remez(exp(x),5,[-1;1])";
   > print("The string", text, "gives", parse(text));
   The string remez(exp(x),5,[-1;1]) gives 8.7381909882756203676868315731687604903964388498642e-3 * x^5 + 4.3793696379596015478233171265365272893795005588381e-2 * x^4 + 0.16642465614952768185129433844012193925654065755905 * x^3 + 0.49919698262963614991826575452094101562044819693772 * x^2 + 1.00003834650599815466340068058231011540878088492516 * x + 1.00004475029559502606203712816558243384077522932213

Example 3:

   > verbosity = 1!;
   > parse("5 + * 3");
   Warning: syntax error, unexpected *. Will try to continue parsing (expecting ";"). May leak memory.
   Warning: the string "5 + * 3" could not be parsed by the miniparser.
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
   error
See also: execute, readfile, print, error, dieonerrormode
Go back to the list of commands

Name:

perturb indicates random perturbation of sampling points for externalplot

Library names:

sollya_obj_t sollya_lib_perturb() int sollya_lib_is_perturb(sollya_obj_t)

Usage:

perturb : perturb

Description:

Example 1:

   > bashexecute("gcc -fPIC -c externalplotexample.c");
   > bashexecute("gcc -shared -o externalplotexample externalplotexample.o -lgmp -lmpfr");
   > externalplot("./externalplotexample",relative,exp(x),[-1/2;1/2],12,perturb);
See also: externalplot, absolute, relative, bashexecute
Go back to the list of commands

Name:

pi the constant Pi.

Library names:

sollya_obj_t sollya_lib_pi() int sollya_lib_is_pi(sollya_obj_t) sollya_obj_t sollya_lib_build_function_pi() #define SOLLYA_PI (sollya_lib_build_function_pi())

Description:

Example 1:

   > verbosity=1!; prec=12!;
   > a = 2*pi;
   > a;
   Warning: rounding has happened. The value displayed is a faithful rounding to 12 bits of the true result.
   6.283
   > prec=20!;
   > a;
   Warning: rounding has happened. The value displayed is a faithful rounding to 20 bits of the true result.
   6.28319

Example 2:

   > display=binary;
   Display mode is binary numbers.
   > prec=12!;
   > d = [pi; 5];
   > d;
   [1.1001001_2 * 2^(1);1.01_2 * 2^(2)]
   > prec=20!;
   > d;
   [1.1001001_2 * 2^(1);1.01_2 * 2^(2)]
See also: cos, sin, tan, asin, acos, atan, evaluate, prec, libraryconstant
Go back to the list of commands

Name:

plot plots one or several functions

Library names:

void sollya_lib_plot(sollya_obj_t, sollya_obj_t, ...) void sollya_lib_v_plot(sollya_obj_t, sollya_obj_t, va_list)

Usage:

plot(f1, ... ,fn, I) : (function, ... ,function, range) -> void plot(f1, ... ,fn, I, file, name) : (function, ... ,function, range, file, string) -> void plot(f1, ... ,fn, I, postscript, name) : (function, ... ,function, range, postscript, string) -> void plot(f1, ... ,fn, I, postscriptfile, name) : (function, ... ,function, range, postscriptfile, string) -> void plot(L, I) : (list, range) -> void plot(L, I, file, name) : (list, range, file, string) -> void plot(L, I, postscript, name) : (list, range, postscript, string) -> void plot(L, I, postscriptfile, name) : (list, range, postscriptfile, string) -> void

Parameters:

Description:

Example 1:

   > plot(sin(x),0,cos(x),[-Pi,Pi]);

Example 2:

   > plot(sin(x),0,cos(x),[-Pi,Pi],postscriptfile,"plotSinCos");

Example 3:

   > plot(exp(0), sin(1), [0;1]);
   1
   0.84147098480789650665250232163029899962256306079837

Example 4:

   > plot(sin(x), cos(x), [1;1]);
   0.84147098480789650665250232163029899962256306079837
   0.54030230586813971740093660744297660373231042061792
See also: externalplot, asciiplot, file, postscript, postscriptfile, points
Go back to the list of commands

Name:

+ addition function

Library names:

sollya_obj_t sollya_lib_add(sollya_obj_t, sollya_obj_t) sollya_obj_t sollya_lib_build_function_add(sollya_obj_t, sollya_obj_t) #define SOLLYA_ADD(x,y) sollya_lib_build_function_add((x), (y))

Usage:

function1 + function2 : (function, function) -> function interval1 + interval2 : (range, range) -> range interval1 + constant : (range, constant) -> range interval1 + constant : (constant, range) -> range

Parameters:

Description:

Example 1:

   > 1 + 2;
   3

Example 2:

   > x + 2;
   2 + x

Example 3:

   > x + x;
   x * 2

Example 4:

   > diff(sin(x) + exp(x));
   cos(x) + exp(x)

Example 5:

   > [1;2] + [3;4];
   [4;6]
   > [1;2] + 17;
   [18;19]
   > 13 + [-4;17];
   [9;30]
See also: -, *, /, ^
Go back to the list of commands

Name:

points controls the number of points chosen by Sollya in certain commands.

Library names:

void sollya_lib_set_points_and_print(sollya_obj_t) void sollya_lib_set_points(sollya_obj_t) sollya_obj_t sollya_lib_get_points()

Usage:

points = n : integer -> void points = n ! : integer -> void points : constant

Parameters:

Description:

Example 1:

   > f=x^2*sin(1/x);
   > points=10;
   The number of points has been set to 10.
   > dirtyfindzeros(f, [0;1]);
   [|0, 0.31830988618379067153776752674502872406891929148092|]
   > points=100;
   The number of points has been set to 100.
   > dirtyfindzeros(f, [0;1]);
   [|0, 2.4485375860291590118289809749617594159147637806224e-2, 3.9788735772973833942220940843128590508614911435115e-2, 4.5472840883398667362538218106432674866988470211559e-2, 5.3051647697298445256294587790838120678153215246819e-2, 6.3661977236758134307553505349005744813783858296184e-2, 7.957747154594766788444188168625718101722982287023e-2, 0.106103295394596890512589175581676241356306430493638, 0.15915494309189533576888376337251436203445964574046, 0.31830988618379067153776752674502872406891929148092|]
See also: dirtyinfnorm, dirtyintegral, dirtyfindzeros, plot, diam, prec
Go back to the list of commands

Name:

postscriptfile special value for commands plot and externalplot

Library names:

sollya_obj_t sollya_lib_postscriptfile() int sollya_lib_is_postscriptfile(sollya_obj_t)

Description:

Example 1:

   > savemode=postscriptfile;
   > name="plotSinCos";
   > plot(sin(x),0,cos(x),[-Pi,Pi],savemode, name);
See also: externalplot, plot, file, postscript
Go back to the list of commands

Name:

postscript special value for commands plot and externalplot

Library names:

sollya_obj_t sollya_lib_postscript() int sollya_lib_is_postscript(sollya_obj_t)

Description:

Example 1:

   > savemode=postscript;
   > name="plotSinCos";
   > plot(sin(x),0,cos(x),[-Pi,Pi],savemode, name);
See also: externalplot, plot, file, postscriptfile
Go back to the list of commands

Name:

^ power function

Library names:

sollya_obj_t sollya_lib_pow(sollya_obj_t, sollya_obj_t) sollya_obj_t sollya_lib_build_function_pow(sollya_obj_t, sollya_obj_t) #define SOLLYA_POW(x,y) sollya_lib_build_function_pow((x), (y))

Usage:

function1 ^ function2 : (function, function) -> function interval1 ^ interval2 : (range, range) -> range interval1 ^ constant : (range, constant) -> range interval1 ^ constant : (constant, range) -> range

Parameters:

Description:

Example 1:

   > 5 ^ 2;
   25

Example 2:

   > x ^ 2;
   x^2

Example 3:

   > 3 ^ (-5);
   4.1152263374485596707818930041152263374485596707819e-3

Example 4:

   > (-3) ^ (-2.5);
   NaN

Example 5:

   > diff(sin(x) ^ exp(x));
   sin(x)^exp(x) * ((cos(x) * exp(x)) / sin(x) + exp(x) * log(sin(x)))

Example 6:

   > 2^3^5;
   1.4134776518227074636666380005943348126619871175005e73
   > (2^3)^5;
   32768
   > 2^(3^5);
   1.4134776518227074636666380005943348126619871175005e73

Example 7:

   > [1;2] ^ [3;4];
   [1;16.000000000000000000000000000000000000000000000001]
   > [1;2] ^ 17;
   [1;131072]
   > 13 ^ [-4;17];
   [3.501277966457757081334687160813696999404782745702e-5;8650415919381337933]
See also: +, -, *, /
Go back to the list of commands

Name:

powers special value for global state display

Library names:

sollya_obj_t sollya_lib_powers() int sollya_lib_is_powers(sollya_obj_t)

Description:

See also: decimal, dyadic, hexadecimal, binary, display
Go back to the list of commands

Name:

precision returns the precision necessary to represent a number.

Library name:

sollya_obj_t sollya_lib_precision(sollya_obj_t)

Usage:

precision(x) : constant -> integer

Parameters:

Description:

Example 1:

   > a=round(Pi,20,RN);
   > precision(a);
   19
   > m=mantissa(a);
   > 1+floor(log2(m));
   19

Example 2:

   > a=255;
   > precision(a);
   8
   > m=mantissa(a);
   > 1+floor(log2(m));
   8

Example 3:

   > a=256;
   > precision(a);
   1
   > m=mantissa(a);
   > 1+floor(log2(m));
   1
See also: mantissa, exponent, round
Go back to the list of commands

Name:

prec controls the precision used in numerical computations.

Library names:

void sollya_lib_set_prec_and_print(sollya_obj_t) void sollya_lib_set_prec(sollya_obj_t) sollya_obj_t sollya_lib_get_prec()

Description:

Example 1:

   > display=binary!;
   > prec=50;
   The precision has been set to 50 bits.
   > dirtyinfnorm(exp(x),[1;2]);
   1.110110001110011001001011100011010100110111011011_2 * 2^(2)
   > prec=100;
   The precision has been set to 100 bits.
   > dirtyinfnorm(exp(x),[1;2]);
   1.11011000111001100100101110001101010011011101101011011100110000110011101000111011101000100000011011_2 * 2^(2)
See also: evaluate, diam
Go back to the list of commands

Name:

.: add an element at the beginning of a list.

Library name:

sollya_obj_t sollya_lib_prepend(sollya_obj_t, sollya_obj_t)

Usage:

x.:L : (any type, list) -> list

Parameters:

Description:

Example 1:

   > 1.:[|2,3,4|];
   [|1, 2, 3, 4|]

Example 2:

   > [|1,2,3|].:[|4,5,6|];
   [|[|1, 2, 3|], 4, 5, 6|]

Example 3:

   > 1.:[||];
   [|1|]
See also: :., @
Go back to the list of commands

Name:

printdouble prints a constant value as a hexadecimal double precision number

Library name:

void sollya_lib_printdouble(sollya_obj_t)

Usage:

printdouble(constant) : constant -> void

Parameters:

Description:

Example 1:

   > printdouble(3);
   0x4008000000000000

Example 2:

   > prec=100!;
   > verbosity = 1!;
   > printdouble(exp(5));
   Warning: the given expression is not a constant but an expression to evaluate. A faithful evaluation to 100 bits will be used.
   Warning: rounding down occurred before printing a value as a double.
   0x40628d389970338f
See also: printsingle, printexpansion, double
Go back to the list of commands

Name:

printexpansion prints a polynomial in Horner form with its coefficients written as a expansions of double precision numbers

Library name:

void sollya_lib_printexpansion(sollya_obj_t)

Usage:

printexpansion(polynomial) : function -> void

Parameters:

Description:

Example 1:

   > printexpansion(roundcoefficients(taylor(exp(x),5,0),[|DD...|]));
   0x3ff0000000000000 + x * (0x3ff0000000000000 + x * (0x3fe0000000000000 + x * ((0x3fc5555555555555 + 0x3c65555555555555) + x * ((0x3fa5555555555555 + 0x3c45555555555555) + x * (0x3f81111111111111 + 0x3c01111111111111)))))

Example 2:

   > printexpansion(remez(exp(x),5,[-1;1]));
   (0x3ff0002eec90e5a6 + 0x3c9ea6a6a0087757 + 0xb8eb3e644ef44998) + x * ((0x3ff00028358fd3ac + 0x3c8ffa7d96c95f7a + 0xb91da9809b13dd54 + 0x35c0000000000000) + x * ((0x3fdff2d7e6a9fea5 + 0x3c74460e4c0e4fe2 + 0x38fcd1b6b4e85bb0 + 0x3590000000000000) + x * ((0x3fc54d6733b4839e + 0x3c6654e4d8614a44 + 0xb905c7a26b66ea92 + 0xb598000000000000) + x * ((0x3fa66c209b7150a8 + 0x3c34b1bba8f78092 + 0xb8c75f6eb90dae02 + 0x3560000000000000) + x * (0x3f81e554242ab128 + 0xbc23e920a76e760c + 0x38c0589c2cae6caf + 0x3564000000000000)))))

Example 3:

   > verbosity = 1!;
   > prec = 3500!;
   > printexpansion(pi);
   (0x400921fb54442d18 + 0x3ca1a62633145c07 + 0xb92f1976b7ed8fbc + 0x35c4cf98e804177d + 0x32631d89cd9128a5 + 0x2ec0f31c6809bbdf + 0x2b5519b3cd3a431b + 0x27e8158536f92f8a + 0x246ba7f09ab6b6a9 + 0xa0eedd0dbd2544cf + 0x1d779fb1bd1310ba + 0x1a1a637ed6b0bff6 + 0x96aa485fca40908e + 0x933e501295d98169 + 0x8fd160dbee83b4e0 + 0x8c59b6d799ae131c + 0x08f6cf70801f2e28 + 0x05963bf0598da483 + 0x023871574e69a459 + 0x8000000005702db3 + 0x8000000000000000)
   Warning: the expansion is not complete because of the limited exponent range of double precision.
   Warning: rounding occurred while printing.
See also: printdouble, horner, print, prec, remez, taylor, roundcoefficients, fpminimax, implementpoly
Go back to the list of commands

Name:

print prints an expression

Usage:

print(expr1,...,exprn) : (any type,..., any type) -> void print(expr1,...,exprn) > filename : (any type,..., any type, string) -> void print(expr1,...,exprn) >> filename : (any type,...,any type, string) -> void

Parameters:

Description:

Example 1:

   > print(x + 2 + exp(sin(x)));
   x + 2 + exp(sin(x))
   > print("Hello","world");
   Hello world
   > print("Hello","you", 4 + 3, "other persons.");
   Hello you 7 other persons.

Example 2:

   > print("Hello");
   Hello
   > print([|"Hello"|]);
   [|"Hello"|]
   > s = "Hello";
   > print(s,[|s|]);
   Hello [|"Hello"|]
   > t = "Hello\tyou";
   > print(t,[|t|]);
   Hello you [|"Hello\tyou"|]

Example 3:

   > print(x + 2 + exp(sin(x))) > "foo.sol";
   > readfile("foo.sol");
   x + 2 + exp(sin(x))
   

Example 4:

   > print(x + 2 + exp(sin(x))) >> "foo.sol";

Example 5:

   > display = decimal;
   Display mode is decimal numbers.
   > a = evaluate(sin(pi * x), 0.25);
   > b = evaluate(sin(pi * x), [0.25; 0.25 + 1b-50]);
   > print(a);
   0.70710678118654752440084436210484903928483593768847
   > display = binary;
   Display mode is binary numbers.
   > print(a);
   1.01101010000010011110011001100111111100111011110011001001000010001011001011111011000100110110011011101010100101010111110100111110001110101101111011000001011101010001_2 * 2^(-1)
   > display = hexadecimal;
   Display mode is hexadecimal numbers.
   > print(a);
   0x1.6a09e667f3bcc908b2fb1366ea957d3e3adec1751p-1
   > display = dyadic;
   Display mode is dyadic numbers.
   > print(a);
   33070006991101558613323983488220944360067107133265b-165
   > display = powers;
   Display mode is dyadic numbers in integer-power-of-2 notation.
   > print(a);
   33070006991101558613323983488220944360067107133265 * 2^(-165)
   > display = decimal;
   Display mode is decimal numbers.
   > midpointmode = off;
   Midpoint mode has been deactivated.
   > print(b);
   [0.70710678118654752440084436210484903928483593768845;0.70710678118654949743721782517557347782646274417049]
   > midpointmode = on;
   Midpoint mode has been activated.
   > print(b);
   0.7071067811865~4/5~
   > display = dyadic;
   Display mode is dyadic numbers.
   > print(b);
   [2066875436943847413332748968013809022504194195829b-161;16535003495550825444196237019385936414432675156571b-164]
   > display = decimal;
   Display mode is decimal numbers.
   > autosimplify = off;
   Automatic pure tree simplification has been deactivated.
   > fullparentheses = off;
   Full parentheses mode has been deactivated.
   > print(x + x * ((x + 1) + 1));
   x + x * (x + 1 + 1)
   > fullparentheses = on;
   Full parentheses mode has been activated.
   > print(x + x * ((x + 1) + 1));
   x + (x * ((x + 1) + 1))
See also: write, printexpansion, printdouble, printsingle, printxml, readfile, autosimplify, display, midpointmode, fullparentheses, evaluate, rationalmode
Go back to the list of commands

Name:

printsingle prints a constant value as a hexadecimal single precision number

Library name:

void sollya_lib_printsingle(sollya_obj_t)

Usage:

printsingle(constant) : constant -> void

Parameters:

Description:

Example 1:

   > printsingle(3);
   0x40400000

Example 2:

   > prec=100!;
   > verbosity = 1!;
   > printsingle(exp(5));
   Warning: the given expression is not a constant but an expression to evaluate. A faithful evaluation to 100 bits will be used.
   Warning: rounding up occurred before printing a value as a single.
   0x431469c5
See also: printdouble, single
Go back to the list of commands

Name:

printxml prints an expression as an MathML-Content-Tree

Library names:

void sollya_lib_printxml(sollya_obj_t) void sollya_lib_printxml_newfile(sollya_obj_t, sollya_obj_t) void sollya_lib_printxml_appendfile(sollya_obj_t, sollya_obj_t)

Usage:

printxml(expr) : function -> void printxml(expr) > filename : (function, string) -> void printxml(expr) > > filename : (function, string) -> void

Parameters:

Description:

Example 1:

   > printxml(x + 2 + exp(sin(x)));
   
   <?xml version="1.0" encoding="UTF-8"?>
   <!-- generated by sollya: http://sollya.gforge.inria.fr/ -->
   <!-- syntax: printxml(...);   example: printxml(x^2-2*x+5); -->
   <?xml-stylesheet type="text/xsl" href="http://sollya.gforge.inria.fr/mathmlc2p-web.xsl"?>
   <?xml-stylesheet type="text/xsl" href="mathmlc2p-web.xsl"?>
   <!-- This stylesheet allows direct web browsing of MathML-c XML files (http:// or file://) -->
   
   <math xmlns="http://www.w3.org/1998/Math/MathML">
   <semantics>
   <annotation-xml encoding="MathML-Content">
   <lambda>
   <bvar><ci> x </ci></bvar>
   <apply>
   <apply>
   <plus/>
   <apply>
   <plus/>
   <ci> x </ci>
   <cn type="integer" base="10"> 2 </cn>
   </apply>
   <apply>
   <exp/>
   <apply>
   <sin/>
   <ci> x </ci>
   </apply>
   </apply>
   </apply>
   </apply>
   </lambda>
   </annotation-xml>
   <annotation encoding="sollya/text">(x + 1b1) + exp(sin(x))</annotation>
   </semantics>
   </math>
   

Example 2:

   > printxml(x + 2 + exp(sin(x))) > "foo.xml";

Example 3:

   > printxml(x + 2 + exp(sin(x))) >> "foo.xml";
See also: readxml, print, write
Go back to the list of commands

Name:

procedure defines and assigns a Sollya procedure

Usage:

procedure identifier(formal parameter1, formal parameter2,..., formal parameter n) { procedure body } : void -> void procedure identifier(formal parameter1, formal parameter2,..., formal parameter n) { procedure body return expression; } : void -> void procedure identifier(formal list parameter = ...) { procedure body } : void -> void procedure identifier(formal list parameter = ...) { procedure body return expression; } : void -> void

Parameters:

Description:

Example 1:

   > procedure succ(n) { return n + 1; };
   > succ(5);
   6
   > 3 + succ(0);
   4
   > succ;
   proc(n)
   {
   nop;
   return (n) + (1);
   }

Example 2:

   > procedure myprint(L = ...) { var i; for i in L do i; };
   > myprint("Lyon","Nancy","Beaverton","Coye-la-Foret","Amberg","Nizhny Novgorod","Cluj-Napoca");
   Lyon
   Nancy
   Beaverton
   Coye-la-Foret
   Amberg
   Nizhny Novgorod
   Cluj-Napoca
See also: proc, var, bind
Go back to the list of commands

Name:

proc defines a Sollya procedure

Usage:

proc(formal parameter1, formal parameter2,..., formal parameter n) { procedure body } : void -> procedure proc(formal parameter1, formal parameter2,..., formal parameter n) { procedure body return expression; } : void -> procedure proc(formal list parameter = ...) { procedure body } : void -> procedure proc(formal list parameter = ...) { procedure body return expression; } : void -> procedure

Parameters:

Description:

Example 1:

   > succ = proc(n) { return n + 1; };
   > succ(5);
   6
   > 3 + succ(0);
   4
   > succ;
   proc(n)
   {
   nop;
   return (n) + (1);
   }

Example 2:

   > add = proc(m,n) { var res; res := m + n; return res; };
   > add(5,6);
   11
   > add;
   proc(m, n)
   {
   var res;
   res := (m) + (n);
   return res;
   }
   > verbosity = 1!;
   > add(3);
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
   error
   > add(true,false);
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
   Warning: the given expression or command could not be handled.
   error

Example 3:

   > succ = proc(n) { return n + 1; };
   > succ(5);
   6
   > succ(x);
   1 + x

Example 4:

   > hey = proc() { print("Hello world."); };
   > hey();
   Hello world.
   > print(hey());
   Hello world.
   void
   > hey;
   proc()
   {
   print("Hello world.");
   return void;
   }

Example 5:

   > fac = proc(n) { var res; if (n == 0) then res := 1 else res := n * fac(n - 1); return res; };
   > fac(5);
   120
   > fac(11);
   39916800
   > fac;
   proc(n)
   {
   var res;
   if (n) == (0) then
   res := 1
   else
   res := (n) * (fac((n) - (1)));
   return res;
   }

Example 6:

   > myprocs = [| proc(m,n) { return m + n; }, proc(m,n) { return m - n; } |];
   > (myprocs[0])(5,6);
   11
   > (myprocs[1])(5,6);
   -1
   > succ = proc(n) { return n + 1; };
   > pred = proc(n) { return n - 1; };
   > applier = proc(p,n) { return p(n); };
   > applier(succ,5);
   6
   > applier(pred,5);
   4

Example 7:

   > verbosity = 1!;
   > myquit = proc(n) { print(n); quit; };
   > myquit;
   proc(n)
   {
   print(n);
   quit;
   return void;
   }
   > myquit(5);
   Warning: a quit or restart command may not be part of a procedure body.
   The procedure will not be executed.
   Warning: an error occurred while executing a procedure.
   Warning: the given expression or command could not be handled.
   error

Example 8:

   > printsucc = proc(n) { var succ; succ = proc(n) { return n + 1; }; print("Successor of",n,"is",succ(n)); };
   > printsucc(5);
   Successor of 5 is 6

Example 9:

   > makeadd = proc(n) { var add; print("n =",n); add = proc(m,n) { return n + m; }; return add; };
   > makeadd(4);
   n = 4
   proc(m, n)
   {
   nop;
   return (n) + (m);
   }
   > (makeadd(4))(5,6);
   n = 4
   11

Example 10:

   > sumall = proc(L = ...) { var acc, i; acc = 0; for i in L do acc = acc + i; return acc; };
   > sumall;
   proc(L = ...)
   {
   var acc, i;
   acc = 0;
   for i in L do
   acc = (acc) + (i);
   return acc;
   }
   > sumall();
   0
   > sumall(2);
   2
   > sumall(2,5);
   7
   > sumall(2,5,7,9,16);
   39
   > sumall @ [|1,...,10|];
   55
See also: return, externalproc, void, quit, restart, var, @, bind, getbacktrace, error
Go back to the list of commands

Name:

QD short form for quad
See also: quad
Go back to the list of commands

Names:

quad, QD rounding to the nearest IEEE 754 quad (binary128).

Library names:

sollya_obj_t sollya_lib_quad(sollya_obj_t) sollya_obj_t sollya_lib_quad_obj() int sollya_lib_is_quad_obj(sollya_obj_t) sollya_obj_t sollya_lib_build_function_quad(sollya_obj_t) #define SOLLYA_QD(x) sollya_lib_build_function_quad(x)

Description:

Example 1:

   > display=binary!;
   > QD(0.1);
   1.100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001101_2 * 2^(-4)
   > QD(4.17);
   1.000010101110000101000111101011100001010001111010111000010100011110101110000101000111101011100001010001111010111_2 * 2^(2)
   > QD(1.011_2 * 2^(-16493));
   1.1_2 * 2^(-16493)
See also: halfprecision, single, double, doubleextended, doubledouble, tripledouble, roundcoefficients, implementpoly, fpminimax, round, printsingle
Go back to the list of commands

Name:

quit quits Sollya

Usage:

quit : void -> void

Description:

Example 1:

   > quit;
See also: restart, execute, plot, externalplot, return
Go back to the list of commands

Name:

range keyword representing a range type

Library name:

SOLLYA_EXTERNALPROC_TYPE_RANGE

Usage:

range : type type

Description:

See also: externalproc, boolean, constant, function, integer, list of, string, object
Go back to the list of commands

Name:

rationalapprox returns a fraction close to a given number.

Library name:

sollya_obj_t sollya_lib_rationalapprox(sollya_obj_t, sollya_obj_t)

Usage:

rationalapprox(x,n) : (constant, integer) -> function

Parameters:

Description:

Example 1:

   > pi10 = rationalapprox(Pi,10);
   > pi50 = rationalapprox(Pi,50);
   > pi100 = rationalapprox(Pi,100);
   > print( pi10, ": ", dirtysimplify(floor(-log2(abs(pi10-Pi)/Pi))), "bits." );
   3.140625 :  11 bits.
   > print( pi50, ": ", dirtysimplify(floor(-log2(abs(pi50-Pi)/Pi))), "bits." );
   85563208 / 27235615 :  51 bits.
   > print( pi100, ": ", dirtysimplify(floor(-log2(abs(pi100-Pi)/Pi))), "bits." );
   4422001152019829 / 1407566683404023 :  100 bits.

Example 2:

   > a=0.1;
   > b=rationalapprox(a,4);
   > numerator(b); denominator(b);
   1
   10
   > print(dirtysimplify(floor(-log2(abs((b-a)/a)))), "bits.");
   166 bits.
See also: print, numerator, denominator, rationalmode
Go back to the list of commands

Name:

rationalmode global variable controlling if rational arithmetic is used or not.

Library names:

void sollya_lib_set_rationalmode_and_print(sollya_obj_t) void sollya_lib_set_rationalmode(sollya_obj_t) sollya_obj_t sollya_lib_get_rationalmode()

Usage:

rationalmode = activation value : on|off -> void rationalmode = activation value ! : on|off -> void rationalmode : on|off

Parameters:

Description:

Example 1:

   > rationalmode=off!;
   > 19/17 + 3/94;
   1.1495619524405506883604505632040050062578222778473
   > rationalmode=on!;
   > 19/17 + 3/94;
   1837 / 1598

Example 2:

   > rationalmode=off!;
   > exp(19/17 + 3/94);
   3.1568097739551413675470920894482427634032816281442
   > rationalmode=on!;
   > exp(19/17 + 3/94);
   3.1568097739551413675470920894482427634032816281442
See also: on, off, numerator, denominator, simplify, rationalapprox, autosimplify
Go back to the list of commands

Name:

RD constant representing rounding-downwards mode.

Library names:

sollya_obj_t sollya_lib_round_down() int sollya_lib_is_round_down(sollya_obj_t)

Description:

Example 1:

   > display=binary!;
   > round(Pi,20,RD);
   1.1001001000011111101_2 * 2^(1)
See also: RZ, RU, RN, round, floor
Go back to the list of commands

Name:

readfile reads the content of a file into a string variable

Usage:

readfile(filename) : string -> string

Parameters:

Description:

Example 1:

   > print("Hello world") > "myfile.txt";
   > t = readfile("myfile.txt");
   > t;
   Hello world
   

Example 2:

   > verbosity=1!;
   > readfile("afile.txt");
   Warning: the file "afile.txt" could not be opened for reading.
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
   error
See also: parse, execute, write, print, bashexecute, error
Go back to the list of commands

Name:

readxml reads an expression written as a MathML-Content-Tree in a file

Library name:

sollya_obj_t sollya_lib_readxml(sollya_obj_t)

Usage:

readxml(filename) : string -> function | error

Parameters:

Description:

Example 1:

   > readxml("readxmlexample.xml");
   2 + _x_ + exp(sin(_x_))
See also: printxml, readfile, parse, error
Go back to the list of commands

Name:

relative indicates a relative error for externalplot, fpminimax or supnorm

Library names:

sollya_obj_t sollya_lib_relative() int sollya_lib_is_relative(sollya_obj_t)

Usage:

relative : absolute|relative

Description:

Example 1:

   > bashexecute("gcc -fPIC -c externalplotexample.c");
   > bashexecute("gcc -shared -o externalplotexample externalplotexample.o -lgmp -lmpfr");
   > externalplot("./externalplotexample",absolute,exp(x),[-1/2;1/2],12,perturb);
See also: externalplot, fpminimax, absolute, bashexecute, supnorm
Go back to the list of commands

Name:

remez computes the minimax of a function on an interval.

Library names:

sollya_obj_t sollya_lib_remez(sollya_obj_t, sollya_obj_t, sollya_obj_t, ...) sollya_obj_t sollya_lib_v_remez(sollya_obj_t, sollya_obj_t, sollya_obj_t,                                 va_list)

Usage:

remez(f, n, range, w, quality, bounds) : (function, integer, range, function, constant, range) -> function remez(f, L, range, w, quality, bounds) : (function, list, range, function, constant, range) -> function

Parameters:

Description:

Example 1:

   > p = remez(exp(x),5,[0;1]);
   > degree(p);
   5
   > dirtyinfnorm(p-exp(x),[0;1]);
   1.1295698151096148707171193829266077607222634589363e-6

Example 2:

   > p = remez(1,[|0,2,4,6,8|],[0,Pi/4],1/cos(x));
   > canonical=on!;
   > p;
   0.99999999994393732180959690352543887130348096061124 + -0.49999999571556857768772053063721544670949467222259 * x^2 + 4.1666613233473633009941059480570275870113220089059e-2 * x^4 + -1.3886529147145693651355523880319714051047635695061e-3 * x^6 + 2.4372679177224179934800328511009205218114284220126e-5 * x^8

Example 3:

   > p1 = remez(exp(x),5,[0;1],default,1e-5);
   > p2 = remez(exp(x),5,[0;1],default,1e-10);
   > p3 = remez(exp(x),5,[0;1],default,1e-15);
   > dirtyinfnorm(p1-exp(x),[0;1]);
   1.1295698151096148707171193829266077607222634589363e-6
   > dirtyinfnorm(p2-exp(x),[0;1]);
   1.12956980227478675612619255125474525171079325793124e-6
   > dirtyinfnorm(p3-exp(x),[0;1]);
   1.12956980227478675612619255125474525171079325793124e-6

Example 4:

   > L = [|exp(x), sin(x), cos(x)-1, sin(x^3)|];
   > g = (2^x-1)/x;
   > p1 = remez(g, L, [-1/16;1/16]);
   > p2 = remez(g, 3, [-1/16;1/16]);
   > dirtyinfnorm(p1 - g, [-1/16;1/16]);
   9.8841323829271038137685646777951687620288462194746e-8
   > dirtyinfnorm(p2 - g, [-1/16;1/16]);
   2.54337800593461418356437401152248866818783932027105e-9

Example 5:

   > f = sin(x);
   > I = [-3b-5;-1b-1074];
   > time(popt = remez(1, [|1, 3, 4, 5, 7, 8, 9|], I, 1/f));
   0.15019228700000000000000000000000000001035540031029
   > time(p1 = remez(1, [|1, 3, 4, 5, 7, 8, 9|], I, 1/f, default, [0, 1b-73]));
   0.11643645700000000000000000000000000000245839540723
   > time(p2 = remez(1, [|1, 3, 4, 5, 7, 8, 9|], I, 1/f, default, [3b-72, +@Inf@]));
   0.11916222900000000000000000000000000001046103154921
   > dirtyinfnorm(popt/f-1, I);
   2.06750931454112835098093903810531156576504665659064e-22
   > dirtyinfnorm(p1/f-1, I);
   2.49711266837493110470637913808914046704452778960875e-22
   > dirtyinfnorm(p2/f-1, I);
   5.4567247553615435246376977231253834265248756996947e-22
   > 1b-73;
   1.05879118406787542383540312584955245256423950195312e-22
   > 3b-72;
   6.3527471044072525430124187550973147153854370117187e-22
See also: dirtyinfnorm, infnorm, fpminimax, guessdegree, taylorform, taylor
Go back to the list of commands

Name:

rename rename the free variable.

Library name:

void sollya_lib_name_free_variable(const char *)

Usage:

rename(ident1,ident2) : void

Parameters:

Description:

Example 1:

   > f=sin(x);
   > f;
   sin(x)
   > rename(x,y);
   > f;
   sin(y)

Example 2:

   > a=1;
   > f=sin(x);
   > rename(x,a);
   > a;
   a
   > f;
   sin(a)

Example 3:

   > verbosity=1!;
   > f=sin(x);
   > rename(y, z);
   Warning: the current free variable is named "x" and not "y". Can only rename the free variable.
   The last command will have no effect.
   > rename(_x_, z);
   Information: the free variable has been renamed from "x" to "z".

Example 4:

   > verbosity=1!;
   > rename(x,y);
   Information: the free variable has been named "y".
   > isbound(x);
   false
   > isbound(y);
   true
See also: isbound
Go back to the list of commands

Name:

restart brings Sollya back to its initial state

Usage:

restart : void -> void

Description:

Example 1:

   > print(exp(x));
   exp(x)
   > a = 3;
   > restart;
   The tool has been restarted.
   > print(x);
   x
   > a;
   Warning: the identifier "a" is neither assigned to, nor bound to a library function nor external procedure, nor equal to the current free variable.
   Will interpret "a" as "x".
   x

Example 2:

   > print(exp(x));
   exp(x)
   > for i from 1 to 10 do {
     print(i);
     if (i == 5) then restart;
     };
   1
   2
   3
   4
   5
   The tool has been restarted.
   Warning: the tool has been restarted inside a for loop.
   The for loop will no longer be executed.

Example 3:

   > print(exp(x));
   exp(x)
   > a = 3;
   > for i from 1 to 10 do {
     print(i);
     if (i == 5) then {
     restart;
     i = 7;
     };
     };
   1
   2
   3
   4
   5
   The tool has been restarted.
   8
   9
   10
   > print(x);
   x
   > a;
   Warning: the identifier "a" is neither assigned to, nor bound to a library function nor external procedure, nor equal to the current free variable.
   Will interpret "a" as "x".
   x
See also: quit, execute
Go back to the list of commands

Name:

return indicates an expression to be returned in a procedure

Usage:

return expression : void

Parameters:

Description:

Example 1:

   > succ = proc(n) { var res; res := n + 1; return res; };
   > succ(5);
   6
   > succ;
   proc(n)
   {
   var res;
   res := (n) + (1);
   return res;
   }

Example 2:

   > hey = proc(s) { print("Hello",s); };
   > hey("world");
   Hello world
   > hey;
   proc(s)
   {
   print("Hello", s);
   return void;
   }
See also: proc, void
Go back to the list of commands

Name:

revert reverts a list.

Library name:

sollya_obj_t sollya_lib_revert(sollya_obj_t)

Usage:

revert(L) : list -> list

Parameters:

Description:

Example 1:

   > revert([| |]);
   [| |]

Example 2:

   > revert([|2,3,5,2,1,4|]);
   [|4, 1, 2, 5, 3, 2|]
See also: sort, head
Go back to the list of commands

Name:

RN constant representing rounding-to-nearest mode.

Library names:

sollya_obj_t sollya_lib_round_to_nearest() int sollya_lib_is_round_to_nearest(sollya_obj_t)

Description:

Example 1:

   > display=binary!;
   > round(Pi,20,RN);
   1.100100100001111111_2 * 2^(1)
See also: RD, RU, RZ, round, nearestint
Go back to the list of commands

Name:

roundcoefficients rounds the coefficients of a polynomial to classical formats.

Library name:

sollya_obj_t sollya_lib_roundcoefficients(sollya_obj_t, sollya_obj_t)

Usage:

roundcoefficients(p,L) : (function, list) -> function

Parameters:

Description:

Example 1:

   > p=exp(1) + x*(exp(2) + x*exp(3));
   > display=binary!;
   > roundcoefficients(p,[|DD,D,D|]);
   1.010110111111000010101000101100010100010101110110100101010011010101011111101110001010110001000000010011101_2 * 2^(1) + x * (1.110110001110011001001011100011010100110111011010111_2 * 2^(2) + x * (1.010000010101111001011011111101101111101100010000011_2 * 2^(4)))
   > roundcoefficients(p,[|DD,D...|]);
   1.010110111111000010101000101100010100010101110110100101010011010101011111101110001010110001000000010011101_2 * 2^(1) + x * (1.110110001110011001001011100011010100110111011010111_2 * 2^(2) + x * (1.010000010101111001011011111101101111101100010000011_2 * 2^(4)))

Example 2:

   > f=sin(exp(1)*x);
   > display=binary!;
   > f;
   sin(x * (1.0101101111110000101010001011000101000101011101101001010100110101010111111011100010101100010000000100111001111010011110011110001110110001011100111000101100000111101_2 * 2^(1)))
   > roundcoefficients(f,[|D...|]);
   sin(x * (1.0101101111110000101010001011000101000101011101101001010100110101010111111011100010101100010000000100111001111010011110011110001110110001011100111000101100000111101_2 * 2^(1)))

Example 3:

   > p=exp(1) + x*(exp(2) + x*exp(3));
   > verbosity=1!;
   > display=binary!;
   > roundcoefficients(p,[|DD,D|]);
   Warning: the number of the given formats does not correspond to the degree of the given polynomial.
   Warning: the 0th coefficient of the given polynomial does not evaluate to a floating-point constant without any rounding.
   Will evaluate the coefficient in the current precision in floating-point before rounding to the target format.
   Warning: the 1th coefficient of the given polynomial does not evaluate to a floating-point constant without any rounding.
   Will evaluate the coefficient in the current precision in floating-point before rounding to the target format.
   Warning: rounding may have happened.
   1.010110111111000010101000101100010100010101110110100101010011010101011111101110001010110001000000010011101_2 * 2^(1) + x * (1.110110001110011001001011100011010100110111011010111_2 * 2^(2) + x * (1.01000001010111100101101111110110111110110001000001011111001011010100101111011111110001010011011101000100110000111010001110010000010110000101100000111001011100101001_2 * 2^(4)))
See also: halfprecision, single, double, doubleextended, doubledouble, quad, tripledouble, fpminimax, remez, implementpoly, subpoly
Go back to the list of commands

Name:

roundcorrectly rounds an approximation range correctly to some precision

Library name:

sollya_obj_t sollya_lib_roundcorrectly(sollya_obj_t)

Usage:

roundcorrectly(range) : range -> constant

Parameters:

Description:

Example 1:

   > printbinary(roundcorrectly([1.010001_2; 1.0101_2]));
   1.01_2
   > printbinary(roundcorrectly([1.00001_2; 1.001_2]));
   1_2

Example 2:

   > roundcorrectly([-1; 1]);
   NaN
See also: round, mantissa, exponent, precision
Go back to the list of commands

Name:

roundingwarnings global variable controlling whether or not a warning is displayed when roundings occur.

Library names:

void sollya_lib_set_roundingwarnings_and_print(sollya_obj_t) void sollya_lib_set_roundingwarnings(sollya_obj_t) sollya_obj_t sollya_lib_get_roundingwarnings()

Usage:

roundingwarnings = activation value : on|off -> void roundingwarnings = activation value ! : on|off -> void roundingwarnings : on|off

Parameters:

Description:

Example 1:

   > verbosity=1!;
   > roundingwarnings = on;
   Rounding warning mode has been activated.
   > exp(0.1);
   Warning: Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   Warning: rounding has happened. The value displayed is a faithful rounding to 165 bits of the true result.
   1.1051709180756476248117078264902466682245471947375
   > roundingwarnings = off;
   Rounding warning mode has been deactivated.
   > exp(0.1);
   1.1051709180756476248117078264902466682245471947375
See also: on, off, verbosity, midpointmode, rationalmode, suppressmessage, unsuppressmessage, showmessagenumbers, getsuppressedmessages
Go back to the list of commands

Name:

round rounds a number to a floating-point format.

Library name:

sollya_obj_t sollya_lib_round(sollya_obj_t, sollya_obj_t, sollya_obj_t)

Usage:

round(x,n,mode) : (constant, integer, RN|RZ|RU|RD) -> constant round(x,format,mode) : (constant, HP|halfprecision|SG|single|D|double|DE|doubleextended|DD|doubledouble|QD|quad|TD|tripledouble, RN|RZ|RU|RD) -> constant

Parameters:

Description:

Example 1:

   > display=binary!;
   > round(Pi,20,RN);
   1.100100100001111111_2 * 2^(1)

Example 2:

   > printdouble(round(exp(17),53,RU));
   0x417709348c0ea4f9
   > printdouble(D(exp(17)));
   0x417709348c0ea4f9

Example 3:

   > display=binary!;
   > a=2^(-1100);
   > round(a,53,RN);
   1_2 * 2^(-1100)
   > round(a,D,RN);
   0
   > double(a);
   0
See also: RN, RD, RU, RZ, halfprecision, single, double, doubleextended, doubledouble, quad, tripledouble, roundcoefficients, roundcorrectly, printdouble, printsingle, ceil, floor, nearestint
Go back to the list of commands

Name:

RU constant representing rounding-upwards mode.

Library names:

sollya_obj_t sollya_lib_round_up() int sollya_lib_is_round_up(sollya_obj_t)

Description:

Example 1:

   > display=binary!;
   > round(Pi,20,RU);
   1.100100100001111111_2 * 2^(1)
See also: RZ, RD, RN, round, ceil
Go back to the list of commands

Name:

RZ constant representing rounding-to-zero mode.

Library names:

sollya_obj_t sollya_lib_round_towards_zero() int sollya_lib_is_round_towards_zero(sollya_obj_t)

Description:

Example 1:

   > display=binary!;
   > round(Pi,20,RZ);
   1.1001001000011111101_2 * 2^(1)
See also: RD, RU, RN, round, floor, ceil
Go back to the list of commands

Name:

searchgal searches for a preimage of a function such that the rounding the image yields an error smaller than a constant

Library name:

sollya_obj_t sollya_lib_searchgal(sollya_obj_t, sollya_obj_t, sollya_obj_t,                                   sollya_obj_t, sollya_obj_t, sollya_obj_t)

Usage:

searchgal(function, start, preimage precision, steps, format, error bound) : (function, constant, integer, integer, HP|halfprecision|SG|single|D|double|DE|doubleextended|DD|doubledouble|QD|quad|TD|tripledouble, constant) -> list searchgal(list of functions, start, preimage precision, steps, list of format, list of error bounds) : (list, constant, integer, integer, list, list) -> list

Parameters:

Description:

Example 1:

   > searchgal(log(x),2,53,15,DD,1b-112);
   [| |]
   > searchgal(log(x),2,53,18,DD,1b-112);
   [|2.0000000000384972054234822280704975128173828125|]

Example 2:

   > f = exp(x);
   > s = searchgal(f,2,53,18,DD,1b-112);
   > if (s != [||]) then {
        v = s[0];
        print("The rounding error is 2^(",evaluate(log2(abs(DD(f)/f - 1)),v),")");
     } else print("No value found");
   The rounding error is 2^( -112.106878438809380148206984258358542322113874177832 )

Example 3:

   > searchgal([|sin(x),cos(x)|],1,53,15,[|D,D|],[|1b-62,1b-60|]);
   [|1.00000000000159494639717649988597258925437927246094|]
See also: round, double, doubledouble, tripledouble, evaluate, worstcase
Go back to the list of commands

Name:

SG short form for single
See also: single
Go back to the list of commands

Name:

showmessagenumbers activates, deactivates or inspects the state variable controlling the displaying of numbers for messages

Library names:

void sollya_lib_set_showmessagenumbers_and_print(sollya_obj_t) void sollya_lib_set_showmessagenumbers(sollya_obj_t) sollya_obj_t sollya_lib_get_showmessagenumbers()

Usage:

showmessagenumbers = activation value : on|off -> void showmessagenumbers = activation value ! : on|off -> void showmessagenumbers : on|off

Parameters:

Description:

Example 1:

   > verbosity = 1;
   The verbosity level has been set to 1.
   > 0.1;
   Warning: Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   0.1
   > showmessagenumbers = on;
   Displaying of message numbers has been activated.
   > 0.1;
   Warning (174): Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   0.1
   > showmessagenumbers;
   on
   > showmessagenumbers = off!;
   > 0.1;
   Warning: Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   0.1

Example 2:

   > showmessagenumbers = on;
   Displaying of message numbers has been activated.
   > verbosity = 1;
   The verbosity level has been set to 1.
   > diff(0.1 * x + 1.5 * x^2);
   Warning (174): Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   0.1 + x * 3
   > verbosity = 0;
   The verbosity level has been set to 0.
   > diff(0.1 * x + 1.5 * x^2);
   0.1 + x * 3
   > verbosity = 12;
   The verbosity level has been set to 12.
   > diff(0.1 * x + 1.5 * x^2);
   Warning (174): Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   Information (196): formally differentiating a function.
   Information (197): differentiating the expression '0.1 * x + 1.5 * x^2'
   Information (195): expression '0.1 + 2 * 1.5 * x' has been simplified to expression '0.1 + 3 * x'.
   0.1 + x * 3
See also: getsuppressedmessages, suppressmessage, unsuppressmessage, verbosity, roundingwarnings
Go back to the list of commands

Name:

simplify simplifies an expression representing a function

Library name:

sollya_obj_t sollya_lib_simplify(sollya_obj_t)

Usage:

simplify(function) : function -> function

Parameters:

Description:

Example 1:

   > print(simplify((6 + 2) + (5 + exp(0)) * x));
   8 + 6 * x

Example 2:

   > print(simplify((log(x - x + 1) + asin(1))));
   (pi) / 2

Example 3:

   > print(simplify((log(x - x + 1) + asin(1)) - (atan(1) * 2)));
   (pi) / 2 - (pi) / 4 * 2
See also: dirtysimplify, autosimplify, rationalmode, horner
Go back to the list of commands

Names:

single, SG rounding to the nearest IEEE 754 single (binary32).

Library names:

sollya_obj_t sollya_lib_single(sollya_obj_t) sollya_obj_t sollya_lib_single_obj() int sollya_lib_is_single_obj(sollya_obj_t) sollya_obj_t sollya_lib_build_function_single(sollya_obj_t) #define SOLLYA_SG(x) sollya_lib_build_function_single(x)

Description:

Example 1:

   > display=binary!;
   > SG(0.1);
   1.10011001100110011001101_2 * 2^(-4)
   > SG(4.17);
   1.000010101110000101001_2 * 2^(2)
   > SG(1.011_2 * 2^(-1073));
   0
See also: halfprecision, double, doubleextended, doubledouble, quad, tripledouble, roundcoefficients, implementpoly, round, printsingle
Go back to the list of commands

Name:

sinh the hyperbolic sine function.

Library names:

sollya_obj_t sollya_lib_sinh(sollya_obj_t) sollya_obj_t sollya_lib_build_function_sinh(sollya_obj_t) #define SOLLYA_SINH(x) sollya_lib_build_function_sinh(x)

Description:

See also: asinh, cosh, tanh
Go back to the list of commands

Name:

sin the sine function.

Library names:

sollya_obj_t sollya_lib_sin(sollya_obj_t) sollya_obj_t sollya_lib_build_function_sin(sollya_obj_t) #define SOLLYA_SIN(x) sollya_lib_build_function_sin(x)

Description:

See also: asin, cos, tan
Go back to the list of commands

Name:

sort sorts a list of real numbers.

Library name:

sollya_obj_t sollya_lib_sort(sollya_obj_t)

Usage:

sort(L) : list -> list

Parameters:

Description:

Example 1:

   > sort([| |]);
   [| |]
   > sort([|2,3,5,2,1,4|]);
   [|1, 2, 2, 3, 4, 5|]
Go back to the list of commands

Name:

sqrt square root.

Library names:

sollya_obj_t sollya_lib_sqrt(sollya_obj_t) sollya_obj_t sollya_lib_build_function_sqrt(sollya_obj_t) #define SOLLYA_SQRT(x) sollya_lib_build_function_sqrt(x)

Description:

Go back to the list of commands

Name:

string keyword representing a string type

Library name:

SOLLYA_EXTERNALPROC_TYPE_STRING

Usage:

string : type type

Description:

See also: externalproc, boolean, constant, function, integer, list of, range, object
Go back to the list of commands

Name:

subpoly restricts the monomial basis of a polynomial to a list of monomials

Library name:

sollya_obj_t sollya_lib_subpoly(sollya_obj_t, sollya_obj_t)

Usage:

subpoly(polynomial, list) : (function, list) -> function

Parameters:

Description:

Example 1:

   > p = taylor(exp(x),5,0);
   > s = subpoly(p,[|1,3,5|]);
   > print(p);
   1 + x * (1 + x * (0.5 + x * (1 / 6 + x * (1 / 24 + x / 120))))
   > print(s);
   x * (1 + x^2 * (1 / 6 + x^2 / 120))

Example 2:

   > p = remez(atan(x),10,[-1,1]);
   > subpoly(p,[|1,3,5...|]);
   x * (0.99986632941452949026018468446163586361700915018232 + x^2 * (-0.33030478502455936362667794059988443130926433421739 + x^2 * (0.18015929317818756462894237037824735129130095574422 + x * (2.2845584115424788285112501565358576642429856963072e-9 + x * (-8.5156349064111377895500552996061844977507560037485e-2 + x * (-2.717563409627750199168187692393409435243830189218e-9 + x * (2.08451134307114729373239910549169872454686955895e-2 + x * 1.10889861181129057657199664386826630081793400489512e-9)))))))

Example 3:

   > subpoly(exp(x),[|1,2,3|]);
   0
See also: roundcoefficients, taylor, remez, fpminimax, implementpoly
Go back to the list of commands

Name:

substitute replace the occurrences of the free variable in an expression.

Library name:

sollya_obj_t sollya_lib_substitute(sollya_obj_t, sollya_obj_t)

Usage:

substitute(f,g) : (function, function) -> function substitute(f,t) : (function, constant) -> constant

Parameters:

Description:

Example 1:

   > f=sin(x);
   > g=cos(x);
   > substitute(f,g);
   sin(cos(x))
   > f(g);
   sin(cos(x))

Example 2:

   > a=1;
   > f=sin(x);
   > substitute(f,a);
   0.84147098480789650665250232163029899962256306079837
   > f(a);
   0.84147098480789650665250232163029899962256306079837
See also: evaluate, composepolynomials
Go back to the list of commands

Name:

supnorm computes an interval bounding the supremum norm of an approximation error (absolute or relative) between a given polynomial and a function.

Library name:

sollya_obj_t sollya_lib_supnorm(sollya_obj_t, sollya_obj_t, sollya_obj_t,                                 sollya_obj_t, sollya_obj_t)

Usage:

supnorm(p, f, I, errorType, accuracy) : (function, function, range, absolute|relative, constant) -> range

Parameters:

Description:

Example 1:

   > p = remez(exp(x), 5, [-1;1]);
   > midpointmode=on!;
   > supnorm(p, exp(x), [-1;1], absolute, 2^(-40));
   0.45205513967~0/2~e-4

Example 2:

   > prec=200!;
   > midpointmode=on!;
   > d = [1;2];
   > f = exp(cos(x)^2 + 1);
   > p = remez(1,15,d,1/f,1e-40);
   > theta=1b-60;
   > prec=default!;
   > mode=relative;
   > supnorm(p,f,d,mode,theta);
   0.30893006200251428~5/6~e-13

Example 3:

   > midpointmode=on!;
   > mode=relative;
   > theta=1b-135;
   > d = [-1b-2;1b-2];
   > f = expm1(x);
   > p = x * (1 +  x * ( 2097145 * 2^(-22) + x * ( 349527 * 2^(-21) + x * (87609 * 2^(-21) + x * 4369 * 2^(-19)))));
   > theta=1b-40;
   > supnorm(p,f,d,mode,theta);
   0.98349131972~2/3~e-7
See also: dirtyinfnorm, infnorm, checkinfnorm, absolute, relative, taylorform, autodiff, numberroots, diam
Go back to the list of commands

Name:

suppressmessage suppresses the displaying of messages with a certain number

Library names:

void sollya_lib_suppressmessage(sollya_obj_t, ...); void sollya_lib_v_suppressmessage(sollya_obj_t, va_list);

Usage:

suppressmessage(msg num 1, ..., msg num n) : (integer, ..., integer) -> void suppressmessage(msg list) : list -> void

Parameters:

Description:

Example 1:

   > verbosity = 1;
   The verbosity level has been set to 1.
   > 0.1;
   Warning: Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   0.1
   > suppressmessage(174);
   > 0.1;
   0.1
   > suppressmessage(407);
   > 0.1;
   0.1
   > verbosity = 12;
   The verbosity level has been set to 12.
   > showmessagenumbers = on;
   Displaying of message numbers has been activated.
   > diff(exp(x * 0.1));
   Information (196): formally differentiating a function.
   Information (197): differentiating the expression 'exp(x * 0.1)'
   Information (207): no Horner simplification will be performed because the given tree is already in Horner form.
   exp(x * 0.1) * 0.1
   > suppressmessage(207, 196);
   > diff(exp(x * 0.1));
   Information (197): differentiating the expression 'exp(x * 0.1)'
   exp(x * 0.1) * 0.1
   > unsuppressmessage(174);
   > 0.1;
   Warning (174): Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   0.1

Example 2:

   > verbosity = 12;
   The verbosity level has been set to 12.
   > showmessagenumbers = on;
   Displaying of message numbers has been activated.
   > diff(exp(x * 0.1));
   Warning (174): Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   Information (196): formally differentiating a function.
   Information (197): differentiating the expression 'exp(x * 0.1)'
   Information (207): no Horner simplification will be performed because the given tree is already in Horner form.
   exp(x * 0.1) * 0.1
   > suppressmessage([| 174, 207, 196 |]);
   > diff(exp(x * 0.1));
   Information (197): differentiating the expression 'exp(x * 0.1)'
   exp(x * 0.1) * 0.1
See also: getsuppressedmessages, suppressmessage, unsuppressmessage, verbosity, roundingwarnings
Go back to the list of commands

Name:

sup gives the upper bound of an interval.

Library name:

sollya_obj_t sollya_lib_sup(sollya_obj_t)

Usage:

sup(I) : range -> constant sup(x) : constant -> constant

Parameters:

Description:

Example 1:

   > sup([1;3]);
   3
   > sup(5);
   5

Example 2:

   > display=binary!;
   > I=[0; 0.111110000011111_2];
   > sup(I);
   1.11110000011111_2 * 2^(-1)
   > prec=12!;
   > sup(I);
   1.11110000011111_2 * 2^(-1)
See also: inf, mid, max, min
Go back to the list of commands

Name:

tail gives the tail of a list.

Library name:

sollya_obj_t sollya_lib_tail(sollya_obj_t)

Usage:

tail(L) : list -> list

Parameters:

Description:

Example 1:

   > tail([|1,2,3|]);
   [|2, 3|]
   > tail([|1,2...|]);
   [|2...|]
See also: head, revert
Go back to the list of commands

Name:

tanh the hyperbolic tangent function.

Library names:

sollya_obj_t sollya_lib_tanh(sollya_obj_t) sollya_obj_t sollya_lib_build_function_tanh(sollya_obj_t) #define SOLLYA_TANH(x) sollya_lib_build_function_tanh(x)

Description:

See also: atanh, cosh, sinh
Go back to the list of commands

Name:

tan the tangent function.

Library names:

sollya_obj_t sollya_lib_tan(sollya_obj_t) sollya_obj_t sollya_lib_build_function_tan(sollya_obj_t) #define SOLLYA_TAN(x) sollya_lib_build_function_tan(x)

Description:

See also: atan, cos, sin
Go back to the list of commands

Name:

taylorform computes a rigorous polynomial approximation (polynomial, interval error bound) for a function, based on Taylor expansions.

Library names:

sollya_obj_t sollya_lib_taylorform(sollya_obj_t, sollya_obj_t,                                    sollya_obj_t, ...) sollya_obj_t sollya_lib_v_taylorform(sollya_obj_t, sollya_obj_t,                                      sollya_obj_t, va_list)

Usage:

taylorform(f, n, x0, I, errorType) : (function, integer, constant, range, absolute|relative) -> list taylorform(f, n, x0, I, errorType) : (function, integer, range, range, absolute|relative) -> list taylorform(f, n, x0, errorType) : (function, integer, constant, absolute|relative) -> list taylorform(f, n, x0, errorType) : (function, integer, range, absolute|relative) -> list

Parameters:

Description:

Example 1:

   > TL=taylorform(sin(x)/x, 10, 0, [-1,1], relative);
   > p=TL[0];
   > Delta=TL[2];
   > errors=TL[1];
   > for epsi in errors do epsi;
   [0;0]
   [0;0]
   [0;5.3455294201843912922810729343029637576303937602101e-51]
   [0;0]
   [-3.3409558876152445576756705839393523485189961001313e-52;3.3409558876152445576756705839393523485189961001313e-52]
   [0;0]
   [-1.04404871487976392427364705748104760891218628129103e-53;1.04404871487976392427364705748104760891218628129103e-53]
   [0;0]
   [-1.63132611699963113167757352731413688892529106451724e-55;1.63132611699963113167757352731413688892529106451724e-55]
   [0;0]
   [-1.91171029335894273243465647732125416670932546623114e-57;1.91171029335894273243465647732125416670932546623114e-57]
   > p; Delta;
   1 + x^2 * (-0.16666666666666666666666666666666666666666666666667 + x^2 * (8.3333333333333333333333333333333333333333333333333e-3 + x^2 * (-1.984126984126984126984126984126984126984126984127e-4 + x^2 * (2.7557319223985890652557319223985890652557319223986e-6 + x^2 * (-2.5052108385441718775052108385441718775052108385442e-8)))))
   [-1.6135797443886066084999806203254010793747502812764e-10;1.6135797443886066084999806203254010793747502812764e-10]

Example 2:

   > TL=taylorform(exp(x), 10, 0, [-1,1], absolute);
   > p=TL[0];
   > Delta=TL[2];
   > p; Delta;
   1 + x * (1 + x * (0.5 + x * (0.16666666666666666666666666666666666666666666666667 + x * (4.1666666666666666666666666666666666666666666666668e-2 + x * (8.3333333333333333333333333333333333333333333333333e-3 + x * (1.3888888888888888888888888888888888888888888888889e-3 + x * (1.984126984126984126984126984126984126984126984127e-4 + x * (2.4801587301587301587301587301587301587301587301587e-5 + x * (2.7557319223985890652557319223985890652557319223986e-6 + x * 2.7557319223985890652557319223985890652557319223986e-7)))))))))
   [-2.3114271964118761944124253418268474583253955510297e-8;2.7312660755642474420206278018039434042553645532164e-8]

Example 3:

   > TL1 = taylorform(exp(x), 10, log2(10), [-1,1], absolute);
   > TL2 = taylorform(exp(x), 10, [log2(10)], [-1,1], absolute);
   > TL1==TL2;
   false

Example 4:

   > TL1 = taylorform(exp(x), 3, 0, [0,1], relative);
   > TL2 = taylorform(exp(x), 3, 0, relative);
   > TL1[0]==TL2[0];
   true
   > TL1[1]==TL2[1];
   true
   > length(TL1);
   3
   > length(TL2);
   2

Example 5:

   > f = exp(cos(x)); x0 = 0;
   > TL = taylorform(f, 3, x0);
   > T1 = TL[0];
   > T2 = taylor(f, 3, x0);
   > print(coeff(T1, 2));
   -1.35914091422952261768014373567633124887862354685
   > print(coeff(T2, 2));
   -(0.5 * exp(1))
See also: diff, autodiff, taylor, remez, chebyshevform
Go back to the list of commands

Name:

taylorrecursions controls the number of recursion steps when applying Taylor's rule.

Library names:

void sollya_lib_set_taylorrecursions_and_print(sollya_obj_t) void sollya_lib_set_taylorrecursions(sollya_obj_t) sollya_obj_t sollya_lib_get_taylorrecursions()

Usage:

taylorrecursions = n : integer -> void taylorrecursions = n ! : integer -> void taylorrecursions : integer

Parameters:

Description:

Example 1:

   > f=exp(x);
   > p=remez(f,3,[0;1]);
   > taylorrecursions=0;
   The number of recursions for Taylor evaluation has been set to 0.
   > evaluate(f-p, [0;1]);
   [-0.46839364816268368775174657814112460243249079671039;0.46947781754646820647293019728402934746974652584671]
   > taylorrecursions=1;
   The number of recursions for Taylor evaluation has been set to 1.
   > evaluate(f-p, [0;1]);
   [-0.138131114954063839905475752120786856031651747712954;0.13921528433784835862665937126369160106890747684927]
See also: hopitalrecursions, evaluate, infnorm
Go back to the list of commands

Name:

taylor computes a Taylor expansion of a function in a point

Library name:

sollya_obj_t sollya_lib_taylor(sollya_obj_t, sollya_obj_t, sollya_obj_t)

Usage:

taylor(function, degree, point) : (function, integer, constant) -> function

Parameters:

Description:

Example 1:

   > print(taylor(exp(x),3,1));
   exp(1) + x * (exp(1) + x * (0.5 * exp(1) + x * exp(1) / 6))

Example 2:

   > print(taylor(asin(x),7,0));
   x * (1 + x^2 * (1 / 6 + x^2 * (3 / 40 + x^2 * 5 / 112)))

Example 3:

   > print(taylor(erf(x),6,0));
   x * (1 / sqrt((pi) / 4) + x^2 * ((sqrt((pi) / 4) * 4 / (pi) * (-2)) / 6 + x^2 * (sqrt((pi) / 4) * 4 / (pi) * 12) / 120))
See also: remez, fpminimax, taylorform
Go back to the list of commands

Name:

TD short form for tripledouble
See also: tripledouble
Go back to the list of commands

Name:

time procedure for timing Sollya code.

Usage:

time(code) : code -> constant

Parameters:

Description:

Example 1:

   > t = time(p=remez(sin(x),10,[-1;1]));
   > write(t,"s were spent computing p = ",p,"\n");
   3.6502763000000000000000000000000000000845612644004e-2s were spent computing p = 9.0486898749977990986908851357759191711354777014602e-17 * x^10 + 2.68762595115123596299959320959141640012683406736586e-6 * x^9 + -2.4247978492521313349073232289246205727856268698001e-16 * x^8 + -1.98344863020965929701245606503586461226130937598776e-4 * x^7 + 2.2748214757753544349162426281857910162575492126267e-16 * x^6 + 8.3333037186560980567697821420813799547276481409702e-3 * x^5 + -8.574715198972066974170696130354953131211051121887e-17 * x^4 + -0.166666661386013237076216566493953847771564552744173 * x^3 + 1.05699558969863875841493332282097022580493449058156e-17 * x^2 + 0.99999999973628365676559825181776417246038944720795 * x + (-3.1206530956601883024316320853642604562810646600878e-19)

Example 2:

   > write(time({ p=remez(sin(x),10,[-1;1]); write("The error is 2^(", log2(dirtyinfnorm(p-sin(x),[-1;1])), ")\n"); }), " s were spent\n");
   The error is 2^(log2(2.39601979446524486606649528289933482070294808074097e-11))
   6.2586596999999999999999999999999999988810894709438e-2 s were spent

Example 3:

   > t = time(bashexecute("sleep 10"));
   > write(~(t-10),"s of execution overhead.\n");
   1.0817670000000000000000000000000003679234935999155e-3s of execution overhead.

Example 4:

   > ratio := time(p=remez(sin(x),10,[-1;1]))/time(nop(10));
   > write("This ratio = ", ratio, " should somehow be independent of the type of machine.\n");
   This ratio = 2.1002859321376900732735524951679859113110863491513 should somehow be independent of the type of machine.
See also: timing, nop
Go back to the list of commands

Name:

timing global variable controlling timing measures in Sollya.

Library names:

void sollya_lib_set_timing_and_print(sollya_obj_t) void sollya_lib_set_timing(sollya_obj_t) sollya_obj_t sollya_lib_get_timing()

Usage:

timing = activation value : on|off -> void timing = activation value ! : on|off -> void timing : on|off

Parameters:

Description:

Example 1:

   > verbosity=1!;
   > timing=on;
   Timing has been activated.
   > p=remez(sin(x),10,[-1;1]);
   Information: Remez: computing the quality of approximation spent 4 ms
   Information: Remez: computing the quality of approximation spent 4 ms
   Information: Remez: computing the quality of approximation spent 4 ms
   Information: computing a minimax approximation spent 30 ms
   Information: assignment spent 34 ms
   Information: full execution of the last parse chunk spent 39 ms
See also: on, off, time
Go back to the list of commands

Names:

tripledouble, TD represents a number as the sum of three IEEE doubles.

Library names:

sollya_obj_t sollya_lib_triple_double(sollya_obj_t) sollya_obj_t sollya_lib_triple_double_obj() int sollya_lib_is_triple_double_obj(sollya_obj_t) sollya_obj_t sollya_lib_build_function_triple_double(sollya_obj_t) #define SOLLYA_TD(x) sollya_lib_build_function_triple_double(x)

Description:

Example 1:

   > verbosity=1!;
   > a = 1+ 2^(-55)+2^(-115);
   > TD(a);
   1.00000000000000002775557561562891353466491600711096
   > prec=110!;
   > TD(a);
   1.000000000000000027755575615628913534664916007110955975699724
See also: halfprecision, single, double, doubleextended, doubledouble, quad, roundcoefficients, implementpoly, fpminimax, printexpansion
Go back to the list of commands

Name:

true the boolean value representing the truth.

Library names:

sollya_obj_t sollya_lib_true() int sollya_lib_is_true(sollya_obj_t)

Description:

Example 1:

   > true && false;
   false
   > 2>1;
   true
See also: false, &&, ||
Go back to the list of commands

Name:

unsuppressmessage unsuppresses the displaying of messages with a certain number

Library names:

void sollya_lib_unsuppressmessage(sollya_obj_t, ...); void sollya_lib_v_unsuppressmessage(sollya_obj_t, va_list);

Usage:

unsuppressmessage(msg num 1, ..., msg num n) : (integer, ..., integer) -> void unsuppressmessage(msg list) : list -> void

Parameters:

Description:

Example 1:

   > verbosity = 1;
   The verbosity level has been set to 1.
   > 0.1;
   Warning: Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   0.1
   > suppressmessage(174);
   > 0.1;
   0.1
   > suppressmessage(174);
   > 0.1;
   0.1

Example 2:

   > verbosity = 12;
   The verbosity level has been set to 12.
   > showmessagenumbers = on;
   Displaying of message numbers has been activated.
   > diff(exp(x * 0.1));
   Warning (174): Rounding occurred when converting the constant "0.1" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   Information (196): formally differentiating a function.
   Information (197): differentiating the expression 'exp(x * 0.1)'
   Information (207): no Horner simplification will be performed because the given tree is already in Horner form.
   exp(x * 0.1) * 0.1
   > suppressmessage([| 174, 207, 196 |]);
   > diff(exp(x * 0.1));
   Information (197): differentiating the expression 'exp(x * 0.1)'
   exp(x * 0.1) * 0.1
   > unsuppressmessage([| 174, 196 |]);

Example 3:

   > verbosity = 12;
   The verbosity level has been set to 12.
   > showmessagenumbers = on;
   Displaying of message numbers has been activated.
   > suppressmessage(207, 387, 390, 388, 391, 196, 195, 197, 205);
   > getsuppressedmessages();
   [|195, 196, 197, 205, 207, 387, 388, 390, 391|]
   > evaluate(x/sin(x) - 1, [-1;1]);
   [0;0.8508157176809256179117532413986501934703966550941]
   > unsuppressmessage(getsuppressedmessages());
   > getsuppressedmessages();
   [| |]
See also: getsuppressedmessages, suppressmessage, unsuppressmessage, verbosity, roundingwarnings
Go back to the list of commands

Name:

var declaration of a local variable in a scope

Usage:

var identifier1, identifier2,... , identifiern : void

Parameters:

Description:

Example 1:

   > exp(x);
   exp(x)
   > a = 3;
   > {var a, b; a=5; b=3; {var a; var b; b = true; a = 1; a; b;}; a; b; };
   1
   true
   5
   3
   > a;
   3
See also: error, proc
Go back to the list of commands

Name:

verbosity global variable controlling the amount of information displayed by commands.

Library names:

void sollya_lib_set_verbosity_and_print(sollya_obj_t) void sollya_lib_set_verbosity(sollya_obj_t) sollya_obj_t sollya_lib_get_verbosity()

Usage:

verbosity = n : integer -> void verbosity = n ! : integer -> void verbosity : integer

Parameters:

Description:

Example 1:

   > verbosity=0!;
   > 1.2+"toto";
   error
   > verbosity=1!;
   > 1.2+"toto";
   Warning: Rounding occurred when converting the constant "1.2" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
   error
   > verbosity=2!;
   > 1.2+"toto";
   Warning: Rounding occurred when converting the constant "1.2" to floating-point with 165 bits.
   If safe computation is needed, try to increase the precision.
   Warning: at least one of the given expressions or a subexpression is not correctly typed
   or its evaluation has failed because of some error on a side-effect.
   Information: the expression or a partial evaluation of it has been the following:
   (1.2) + ("toto")
   error
See also: roundingwarnings, suppressmessage, unsuppressmessage, showmessagenumbers, getsuppressedmessages
Go back to the list of commands

Name:

void the functional result of a side-effect or empty argument resp. the corresponding type

Library names:

sollya_obj_t sollya_lib_void() int sollya_lib_is_void(sollya_obj_t) SOLLYA_EXTERNALPROC_TYPE_VOID

Usage:

void : void | type type

Description:

Example 1:

   > print(void);
   void
   > void;

Example 2:

   > hey = proc() { print("Hello world."); };
   > hey;
   proc()
   {
   print("Hello world.");
   return void;
   }
   > hey();
   Hello world.
   > hey(void);
   Hello world.
   > print(hey());
   Hello world.
   void

Example 3:

   > bashexecute("gcc -fPIC -Wall -c externalprocvoidexample.c");
   > bashexecute("gcc -fPIC -shared -o externalprocvoidexample externalprocvoidexample.o");
   > externalproc(foo, "./externalprocvoidexample", void -> void);
   > foo;
   foo
   > foo();
   Hello from the external world.
   > foo(void);
   Hello from the external world.
   > print(foo());
   Hello from the external world.
   void

Example 4:

   > procedure blub(L = ...) { print("Argument list:", L); };
   > blub(1);
   Argument list: [|1|]
   > blub();
   Argument list: [| |]
   > blub(void);
   Argument list: [|void|]
See also: error, proc, externalproc
Go back to the list of commands

Name:

worstcase searches for hard-to-round cases of a function

Library names:

void sollya_lib_worstcase(sollya_obj_t, sollya_obj_t, sollya_obj_t,                           sollya_obj_t, sollya_obj_t, ...) void sollya_lib_v_worstcase(sollya_obj_t, sollya_obj_t, sollya_obj_t,                             sollya_obj_t, sollya_obj_t, va_list)

Usage:

worstcase(function, preimage precision, preimage exponent range, image precision, error bound) : (function, integer, range, integer, constant) -> void worstcase(function, preimage precision, preimage exponent range, image precision, error bound, filename) : (function, integer, range, integer, constant, string) -> void

Parameters:

Description:

Example 1:

   > worstcase(exp(x),24,[1,2],24,1b-26);
   prec = 165
   x = 1.99999988079071044921875 f(x) = 7.3890552520751953125 eps = 4.5998601423446695596184695493764120138001954979037e-9 = 2^(-27.695763)
   x = 2 f(x) = 7.38905620574951171875 eps = 1.44563608749673018122228379395533417878125150587072e-8 = 2^(-26.043720)
   
See also: round, searchgal, evaluate
Go back to the list of commands

Name:

write prints an expression without separators

Usage:

write(expr1,...,exprn) : (any type,..., any type) -> void write(expr1,...,exprn) > filename : (any type,..., any type, string) -> void write(expr1,...,exprn) >> filename : (any type,...,any type, string) -> void

Parameters:

Description:

Example 1:

   > write(x + 2 + exp(sin(x)));
   > write("Hello\n");
   x + 2 + exp(sin(x))Hello
   > write("Hello","world\n");
   Helloworld
   > write("Hello","you", 4 + 3, "other persons.\n");
   Helloyou7other persons.

Example 2:

   > write("Hello","\n");
   Hello
   > write([|"Hello"|],"\n");
   [|"Hello"|]
   > s = "Hello";
   > write(s,[|s|],"\n");
   Hello[|"Hello"|]
   > t = "Hello\tyou";
   > write(t,[|t|],"\n");
   Hello you[|"Hello\tyou"|]

Example 3:

   > write(x + 2 + exp(sin(x))) > "foo.sol";
   > readfile("foo.sol");
   x + 2 + exp(sin(x))

Example 4:

   > write(x + 2 + exp(sin(x))) >> "foo.sol";
See also: print, printexpansion, printdouble, printsingle, printxml, readfile, autosimplify, display, midpointmode, fullparentheses, evaluate, roundingwarnings, autosimplify
Go back to the list of commands

Name:

_x_ universal name for the mathematical free variable.

Library names:

sollya_obj_t sollya_lib_free_variable() sollya_obj_t sollya_lib_build_function_free_variable() #define SOLLYA_X_ (sollya_lib_build_function_free_variable())

Description:

Example 1:

   > verbosity=1!;
   > sin(a);
   sin(a)
   > b;
   Warning: the identifier "b" is neither assigned to, nor bound to a library function nor external procedure, nor equal to the current free variable.
   Will interpret "b" as "a".
   a
   > _x_;
   a

Example 2:

   > verbosity=1!;
   > sin(y);
   sin(y)
   > f = proc(a) {
       return sin(a + _x_);
     };
   > rename(y,z);
   Information: the free variable has been renamed from "y" to "z".
   > f(1);
   sin(1 + z)

Example 3:

   > f = sin(y);
   > match f with
       sin(a) : { print("sin of a with a =", a);
                  match a with
                    _x_ : { print("a turns out to be the free variable"); }
            default : { print("a is some expression"); };
                }
       _x_ : { print("Free variable") ; }
       default: { print("Something else"); };
   sin of a with a = y
   a turns out to be the free variable
See also: rename, isbound, proc
Go back to the list of commands