comment
This is a demonstration of the working of elementary functions available
in the Reduce system. It is not intended as an accuracy test. Other
functions become available if certain library packages are loaded.
-------
Integer functions that work in all domain modes, independent of switch
NUMVAL, so long as their arguments evaluate to real numbers.
Functions of one argument:
FIX, SGN, ROUND, CEILING, FLOOR
(The following functions are available only in symbolic mode, so they
are not tested here: ISQRT, ICBRT, ILOG2, IROOTN);
fix a; % will be evaluated only if a evaluates to a real number.
a := 27/4;
fix a;
fix 12.345;
sign (-15/2);
round 12.5;
ceiling 12.5;
floor 12.5;
% isqrt 12.5;
% icbrt 12.5;
% ilog2 130.7;
% irootn(72,4);
% irootn(72,3/2); % this will not evaluate.
comment Functions which require arguments which evaluate to integers:
Function of one argument: FACTORIAL
Fumction of two arguments: PERM, CHOOSE;$
factorial 10;
perm(5,10); % permutations of 5 out of 10.
choose(5,10); % choose 5 out of 10;
comment
These functions are evaluated in dmodes ROUNDED and COMPLEX-ROUNDED
(ON ROUNDED,COMPLEX) so long as their arguments and values evaluate
to real numbers and NUMVAL (normally ON) is ON.
Variable treated as function of no arguments: E, PI.
Functions of one argument:
EXP, LOG, LN, LOG10, NORM, ARG, SQRT,
RAD2DEG, RAD2DMS, DEG2RAD, DEG2DMS, DMS2DEG, DMS2RAD,
SIN, ASIN, COS, ACOS, TAN, ATAN, COT, ACOT, SEC, ASEC, CSC, ACSC,
SINH, ASINH, COSH, ACOSH, TANH, ATANH, COTH, ACOTH, SECH, ASECH,
CSCH, ACSCH.
Functions of two arguments:
EXPT, LOGB, HYPOT, ATAN2.
Function evaluation is carried out to the precision specified in the
latest PRECISION statement.
(The following functions are available only in symbolic mode, so they
are not tested here:
SIND, ASIND, COSD, ACOSD, TAND, ATAND, COTD, ACOTD, SECD, ASECD,
CSCD, ACSCD, ATAN2D, CBRT);
on rounded; precision 6;
a := exp 3;
log a;
ln a;
log10 1000;
norm (-12.345); % for real x, this is equivalent to ABS x.
arg (-12.345); % for real x, this -> if x<0 then pi else 0.0.
sqrt 3;
ws**2;
deg2rad 30;
rad2deg ws;
a := deg2dms 12.345; % a will be a list.
dms2deg ws;
dms2rad a;
rad2deg ws;
asin 0.5;
sin ws;
acos 0.5;
cos ws;
atan 0.5;
tan ws;
acot 0.5;
cot ws;
asec 3;
sec ws;
acsc 3;
csc ws;
asinh 0.5;
sinh ws;
acosh 2;
cosh ws;
atanh 0.5;
tanh ws;
acoth 2;
coth ws;
sech 1;
asech ws;
csch 1;
acsch ws;
expt(2,1.234);
logb(ws,2);
hypot(3,4);
a := -3*pi/4; % any -pi<a<=pi should work.
atan2(sin a,cos a);
ws - a; % should be 0.
precision 20; % functions will be computed to 20 places.
sin 1.5;
asin ws;
precision 50; % fuctions computed to 50 places.
sin 1.5;
asin ws;
precision 6;
comment If argument or value are complex, functions are not computed
when dmode is ROUNDED; $
sin(1+i); % complex argument.
asin 2; % value would be complex.
on complex; %now complex arguments and complex results will be handled.
comment Complex functions of one argument:
EXP, LOG, NORM, ARG, SQRT,
SIN, ASIN, COS, ACOS, TAN, ATAN, COT, ACOT, SEC, ASEC, CSC, ACSC,
SINH, ASINH, COSH. ACOSH, TANH, ATANH, COTH, ACOTH, SECH, ASECH,
CSCH, ACSCH.
(The following functions are available only in symbolic mode, so they
are not tested here:
SIND, ASIND, COSD, ACOSD, TAND, ATAND, COTD, ACOTD, SECD, ASECD,
CSCD, ACSCD.)
Complex function of two variables: EXPT, LOGB, ATAN2;
e**(pi*i); % should be -1 (except for computational error.)
log(1+i);
exp ws;
norm(5*exp(2i));
arg(5*exp(2i));
sqrt(1+i);
ws**2;
asin 2;
sin ws;
acos 2;
cos ws;
atan(1+i);
tan ws;
acot(1+i);
cot ws;
asec 0.1;
sec ws;
acsc 0.1;
csc ws;
sinh(1+i);
asinh ws;
cosh(1+i);
acosh ws;
atanh 2;
tanh ws;
acoth 0.3;
coth ws;
asech(1-i);
sech ws;
acsch(1-i);
csch ws;
expt(1+i,1-i);
logb(ws,1+i);
a := 1+i; % any a such that - pi < repart a <= pi should work.
atan2(sin a,cos a);
ws - a; % should be 0;
end;