@@ -1,706 +1,706 @@
-REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
-
-
-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;
-
-
-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
-
-
-sign (-15/2);
-
-
--1
-
-
-round 12.5;
-
-
-13
-
-
-ceiling 12.5;
-
-
-13
-
-
-floor 12.5;
-
-
-12
-
-
-% 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;
-
-
-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 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;
-
-
-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
-
-
-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
-
-
-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
-
-
-ws - a;
-
-
-0
-  % should be 0.
-
-precision 20;
-
-
-6
-  % functions will be computed to 20 places.
-
-sin 1.5;
-
-
-0.99749498660405443094
-
-
-asin ws;
-
-
-1.5
-
-
-precision 50;
-
-
-20
-  % fuctions computed to 50 places.
-
-sin 1.5;
-
-
-0.99749498660405443094172337114148732270665142592212
-
-
-asin ws;
-
-
-1.5
-
-
-precision 6;
-
-
-50
-
-
-comment   If argument or value are complex, functions are not computed
-when dmode is ROUNDED;
- $
-
-
-
-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 
-  %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);
-
-
- - 1 + 1.22461e-16*i
- % should be -1 (except for computational error.)
-
-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 - 1.25983e-15*i
-
-
-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 + 7.23718e-17*i
-
-
-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 + 1.83691e-16*i
-
-
-acoth 0.3;
-
-
-0.30952 + 1.5708*i
-
-
-coth ws;
-
-
-0.3 - 5.57196e-17*i
-
-
-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
-
-
-a := 1+i;
-
-
-a := 1 + i
- % any a such that - pi < repart a <= pi should work.
-
-atan2(sin a,cos a);
-
-
-1 + i
-
-
-ws - a;
-
-
-0
- % should be 0;
-
-end;
-(TIME:  elem 300 300)
+REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
+
+
+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;
+
+
+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
+
+
+sign (-15/2);
+
+
+-1
+
+
+round 12.5;
+
+
+13
+
+
+ceiling 12.5;
+
+
+13
+
+
+floor 12.5;
+
+
+12
+
+
+% 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;
+
+
+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 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;
+
+
+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
+
+
+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
+
+
+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
+
+
+ws - a;
+
+
+0
+  % should be 0.
+
+precision 20;
+
+
+6
+  % functions will be computed to 20 places.
+
+sin 1.5;
+
+
+0.99749498660405443094
+
+
+asin ws;
+
+
+1.5
+
+
+precision 50;
+
+
+20
+  % fuctions computed to 50 places.
+
+sin 1.5;
+
+
+0.99749498660405443094172337114148732270665142592212
+
+
+asin ws;
+
+
+1.5
+
+
+precision 6;
+
+
+50
+
+
+comment   If argument or value are complex, functions are not computed
+when dmode is ROUNDED;
+ $
+
+
+
+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 
+  %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);
+
+
+ - 1 + 1.22461e-16*i
+ % should be -1 (except for computational error.)
+
+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 - 1.25983e-15*i
+
+
+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 + 7.23718e-17*i
+
+
+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 + 1.83691e-16*i
+
+
+acoth 0.3;
+
+
+0.30952 + 1.5708*i
+
+
+coth ws;
+
+
+0.3 - 5.57196e-17*i
+
+
+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
+
+
+a := 1+i;
+
+
+a := 1 + i
+ % any a such that - pi < repart a <= pi should work.
+
+atan2(sin a,cos a);
+
+
+1 + i
+
+
+ws - a;
+
+
+0
+ % should be 0;
+
+end;
+(TIME:  elem 300 300)