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Sat May 30 16:09:26 PDT 1992 REDUCE 3.4.1, 15-Jul-92 ... 1: 1: 2: 2: 3: 3: 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; 5: 5: Time: 3128 ms 6: 6: Quitting Sat May 30 16:09:30 PDT 1992