Sat May 30 16:09:26 PDT 1992
REDUCE 3.4.1, 15-Jul-92 ...
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Time: 0 ms
4: 4: comment
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, ISQRT, ICBRT, ILOG2.
Function of two arguments: IROOTN
The second argument of IROOTN must evaluate to an integer;
$
fix a;
FIX(A)
% will be evaluated only if a evaluates to a real number.
a := 27/4;
27
A := ----
4
fix a;
6
fix 12.345;
12
sgn (-15/2);
-1
round 12.5;
13
ceiling 12.5;
13
floor 12.5;
12
isqrt 12.5;
3
icbrt 12.5;
2
ilog2 130.7;
7
irootn(72,4);
2
irootn(72,3/2);
3
IROOTN(72,---)
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;
3628800
perm(5,10);
30240
% permutations of 5 out of 10.
choose(5,10);
252
% choose 5 out of 10;
comment
These functions are evaluated in dmodes REALS and COMPLEX-VARIABLE
(ON REALS,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, CBRT,
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,
SIND, ASIND, COSD, ACOSD, TAND, ATAND, COTD, ACOTD, SECD, ASECD,
CSCD, ACSCD.
Functions of two arguments:
EXPT, LOGB, HYPOT, ATAN2, ATAN2D.
Function evaluation is carried out to the precision specified in the
latest PRECISION statement.;
$
on rounded;
precision 6;
12
a := exp 3;
A := 20.0855
log a;
3.0
ln a;
3.0
log10 1000;
3.0
norm (-12.345);
12.345
% for real x, this is equivalent to ABS x.
arg (-12.345);
3.14159
% for real x, this -> if x<0 then pi else 0.0.
sqrt 3;
1.73205
ws**2;
3.0
cbrt 3;
1.44225
ws**3;
3.0
deg2rad 30;
0.523599
rad2deg ws;
30.0
a := deg2dms 12.345;
A := {12,20,42.0}
% a will be a list.
dms2deg ws;
12.345
dms2rad a;
0.215461
rad2deg ws;
12.345
asin 0.5;
0.523599
sin ws;
0.5
acos 0.5;
1.0472
cos ws;
0.5
atan 0.5;
0.463648
tan ws;
0.5
acot 0.5;
1.10715
cot ws;
0.5
asec 3;
1.23096
sec ws;
3.0
acsc 3;
0.339837
csc ws;
3.0
asinh 0.5;
0.481212
sinh ws;
0.5
acosh 2;
1.31696
cosh ws;
2.0
atanh 0.5;
0.549306
tanh ws;
0.5
acoth 2;
0.549306
coth ws;
2.0
sech 1;
0.648054
asech ws;
1
csch 1;
0.850918
acsch ws;
1
sind 30;
0.5
asind ws;
30.0
cosd 30;
0.866025
acosd ws;
30.0
tand 30;
0.57735
atand ws;
30.0
cotd 30;
1.73205
acotd ws;
30.0
secd 30;
1.1547
asecd ws;
30.0
cscd 30;
2.0
acscd ws;
30.0
expt(2,1.234);
2.35218
logb(ws,2);
1.234
hypot(3,4);
5.0
a := -3*pi/4;
A := - 2.35619
% any -pi<a<=pi should work.
atan2(sin a,cos a);
- 2.35619
% this should = a.
a := -135;
A := -135
atan2d(sind a,cosd a);
- 135.0
precision 20;
6
% functions will be computed to 20 places.
sind 60;
0.866 02540 37844 38646 76
asind ws;
60.0
precision 50;
20
% fuctions computed to 50 places.
sind 60;
0.866 02540 37844 38646 76372 31707 52936 18347 14026 26905 19
asind ws;
60.0
precision 6;
50
comment If argument or value are complex, functions are not computed
when dmode is REALS;
$
sin(1+i);
SIN(I + 1)
% complex argument.
asin 2;
ASIN(2)
% value would be complex.
on complex;
*** Domain mode ROUNDED changed to COMPLEX-ROUNDED
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.
Complex function of two variables: EXPT;
$
e**(pi*i);
- 1
log(1+i);
0.346574 + 0.785398*I
exp ws;
1 + I
norm(5*exp(2i));
5.0
arg(5*exp(2i));
2.0
sqrt(1+i);
1.09868 + 0.45509*I
ws**2;
1 + I
asin 2;
1.5708 - 1.31696*I
sin ws;
2.0
acos 2;
1.31696*I
cos ws;
2.0
atan(1+i);
1.01722 + 0.402359*I
tan ws;
1 + I
acot(1+i);
0.553574 - 0.402359*I
cot ws;
1 + I
asec 0.1;
2.99322*I
sec ws;
0.1
acsc 0.1;
1.5708 - 2.99322*I
csc ws;
0.1
sinh(1+i);
0.634964 + 1.29846*I
asinh ws;
1 + I
cosh(1+i);
0.83373 + 0.988898*I
acosh ws;
1 + I
atanh 2;
0.549306 + 1.5708*I
tanh ws;
2.0
acoth 0.3;
0.30952 + 1.5708*I
coth ws;
0.3
asech(1-i);
0.530638 + 1.11852*I
sech ws;
1 - I
acsch(1-i);
0.530638 + 0.452278*I
csch ws;
1 - I
expt(1+i,1-i);
2.80788 + 1.31787*I
logb(ws,1+i);
1 - I
end;
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Time: 3128 ms
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Quitting
Sat May 30 16:09:30 PDT 1992