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Sat May 30 16:09:17 PDT 1992 REDUCE 3.4.1, 15-Jul-92 ... 1: 1: 2: 2: 3: 3: Time: 0 ms 4: 4: % Test of Complex Number mode in REDUCE. on complex; (31+i)/74; 31 + I -------- 74 ws/(b+1); 31 + I ------------ 74*(B + 1) % this now comes out right! w:=(x+3*i)**2; 2 W := X + 6*I*X - 9 on gcd; (x**3-7*x**2+x-7)/(x**2+(3+i)*x+3*i); 2 X - (7 + I)*X + 7*I ---------------------- X + 3 off gcd; sqrt(x**4+14*i*x**3-51*x**2-14*i*x+1); 2 X + 7*I*X - 1 % All rounded tests are done twice: first, they are done at the default % precision, in which all rounded operations use standard floating point % logic. Then precision is increased, causing all rounded operations to % use extended precision bigfloat arithmetic. This is necessary to % exercise and test the bigfloat-based arithmetic functions. prec0 := precision 0; PREC0 := 12 % to determine the nominal default precision. % Tests using default precision: on rounded; *** Domain mode COMPLEX changed to COMPLEX-ROUNDED (3.25 + 8.5i) + (6.75 - 8.5i); 10.0 (3.25 + 8.5i) - (6.0 - 9.5i); -2.75 + 18.0*I (1.0 + 10.0*i)*(-6.5 + 2.5*i); -31.5 - 62.5*I (1.2 - 3.4*i)*(-5.6 + 7.8*i); 19.8 + 28.4*I (19.8 + 28.4*i)/(-5.6 + 7.8*i); 1.2 - 3.4*I e; 2.71828182846 pi; 3.14159265359 17*i**2; -17 (-7.0 + 24.0*i)**(1/2); 3.0 + 4.0*I sqrt(-7.0 + 24.0*i); 3.0 + 4.0*I sqrt(-10.12 - 8.16*i); -1.2 + 3.4*I sin(0.0 + 0.0*i); 0 sin(1.0 + 0.0*i); 0.841470984808 sin(1.0 + 1.0*i); 1.29845758142 + 0.634963914785*I cos(0.0 + 0.0*i); 1 cos(1.0 - 0.0*i); 0.540302305868 cos(1.0 + 1.0*i); 0.833730025131 - 0.988897705763*I tan(0.0 + 0.0*i); 0 tan(1.0 + 0.0*i); 1.55740772465 tan(1.0 + 1.0*i); 0.27175258532 + 1.08392332734*I asin(1.0 + 1.0*i); 0.666239432493 + 1.06127506191*I acos(1.0 + 1.0*i); 0.904556894302 - 1.06127506191*I atan(1.0 + 1.0*i); 1.0172219679 + 0.402359478109*I log(1.0 + 1.0*i); 0.34657359028 + 0.785398163397*I asin 2; 1.57079632679 - 1.31695789692*I sin ws; 2.0 acos 2; 1.31695789692*I cos ws; 2.0 atan(1+i); 1.0172219679 + 0.402359478109*I tan ws; 1 + I log(2+i); 0.804718956217 + 0.463647609001*I exp ws; 2.0 + I e**(i*pi); - 1 e**i; 0.540302305868 + 0.841470984808*I z := sqrt i; Z := 0.707106781187 + 0.707106781187*I z**2; I off rounded; *** Domain mode COMPLEX-ROUNDED changed to COMPLEX %-----------------end of normal floating point tests-------------------- precision(prec0+6); 12 % arbitrary precision increase -> bigfloat functions %----------------------start of bigfloat tests-------------------------- on rounded; *** Domain mode COMPLEX changed to COMPLEX-ROUNDED (3.25 + 8.5i) + (6.75 - 8.5i); 10.0 (3.25 + 8.5i) - (6.0 - 9.5i); -2.75 + 18.0*I (1.0 + 10.0*i)*(-6.5 + 2.5*i); -31.5 - 62.5*I (1.2 - 3.4*i)*(-5.6 + 7.8*i); 19.8 + 28.4*I (19.8 + 28.4*i)/(-5.6 + 7.8*i); 1.2 - 3.4*I e; 2.718 28182 84590 4524 pi; 3.141 59265 35897 9324 17*i**2; -17 (-7.0 + 24.0*i)**(1/2); 3.0 + 4.0*I sqrt(-7.0 + 24.0*i); 3.0 + 4.0*I sqrt(-10.12 - 8.16*i); -1.2 + 3.4*I sin(0.0 + 0.0*i); 0 sin(1.0 + 0.0*i); 0.841 47098 48078 96507 sin(1.0 + 1.0*i); 1.298 45758 14159 7729 + 0.634 96391 47847 36108 *I cos(0.0 + 0.0*i); 1 cos(1.0 - 0.0*i); 0.540 30230 58681 39717 cos(1.0 + 1.0*i); 0.833 73002 51311 49049 - 0.988 89770 57628 65096 *I tan(0.0 + 0.0*i); 0 tan(1.0 + 0.0*i); 1.557 40772 46549 0223 tan(1.0 + 1.0*i); 0.271 75258 53195 11717 + 1.083 92332 73386 9454*I asin(1.0 + 1.0*i); 0.666 23943 24925 15255 + 1.061 27506 19050 3565*I acos(1.0 + 1.0*i); 0.904 55689 43023 81364 - 1.061 27506 19050 3565*I atan(1.0 + 1.0*i); 1.017 22196 78978 5137 + 0.402 35947 81085 25094 *I log(1.0 + 1.0*i); 0.346 57359 02799 72655 + 0.785 39816 33974 4831*I asin 2; 1.570 79632 67948 9662 - 1.316 95789 69248 1671*I sin ws; 2.0 acos 2; 1.316 95789 69248 1671*I cos ws; 2.0 atan(1+i); 1.017 22196 78978 5137 + 0.402 35947 81085 25094 *I tan ws; 1 + I log(2+i); 0.804 71895 62170 50187 + 0.463 64760 90008 06116 *I exp ws; 2.0 + I e**(i*pi); - 1 e**i; 0.540 30230 58681 39717 + 0.841 47098 48078 96507 *I z := sqrt i; Z := 0.707 10678 11865 47524 + 0.707 10678 11865 47524 *I z**2; I off rounded; *** Domain mode COMPLEX-ROUNDED changed to COMPLEX % --------------------------------------------------------------------- % The following examples are independent of precision. precision prec0; 18 % restores default precision. % on rationalize; % no longer needed, since it doesn't affect complex. s:= 1.1+2.3i; 11 + 23*I S := ----------- 10 s/4; 11 + 23*I ----------- 40 % this would have had a common factor of 4. x:= a+1.1+2.3i; 10*A + (11 + 23*I) X := -------------------- 10 y:= b+1.2+1.3i; 10*B + (12 + 13*I) Y := -------------------- 10 z:= x/y; 100*A*B + (120 - 130*I)*A + (110 + 230*I)*B + (431 + 133*I) Z := ------------------------------------------------------------- 2 100*B + 240*B + 313 z/4; 100*A*B + (120 - 130*I)*A + (110 + 230*I)*B + (431 + 133*I) ------------------------------------------------------------- 2 4*(100*B + 240*B + 313) % this would have had a common polynomial factor b^2 + ... z*7/4; 7*(100*A*B + (120 - 130*I)*A + (110 + 230*I)*B + (431 + 133*I)) ----------------------------------------------------------------- 2 4*(100*B + 240*B + 313) s/(c^2+c+1); 11 + 23*I ----------------- 2 10*(C + C + 1) % this would have had a common factor of c^2+c+1 clear x; zz:= x^2+(1.1+2.3i)*x+1.2+1.3i; 2 10*X + (11 + 23*I)*X + (12 + 13*I) ZZ := ------------------------------------- 10 ss:=1.23456789x^2+1.3579i*x+5.6789; 2 123456789*X + 135790000*I*X + 567890000 SS := ------------------------------------------ 100000000 % off rationalize; % not needed now. z:= x+1.1+2.3i; 10*X + (11 + 23*I) Z := -------------------- 10 on rationalize; z; 10*X + (11 + 23*I) -------------------- 10 % same as previous answer. off rationalize; 1.23456789x^2+2.3456i*x+7.89; 2 123456789*X + 234560000*I*X + 789000000 ------------------------------------------ 100000000 on factor; x**2+1; (X + I)*(X - I) x**4-1; (X + I)*(X - I)*(X + 1)*(X - 1) x**4+(i+2)*x**3+(2*i+5)*x**2+(2*i+6)*x+6; 2 (X + I*X + 3)*(X + (1 + I))*(X + 1 - I) (2*i+3)*x**4+(3*i-2)*x**3-2*(i+1)*x**2+i*x-1; 2 2 I*((2 - 3*I)*X - I)*(X + I*X - 1) % Multivariate examples: x**2+y**2; (10*B + 10*I*X + (12 + 13*I))*(10*B - 10*I*X + (12 + 13*I)) ------------------------------------------------------------- 100 off factor; factorize(x**2+1); {X - I,X + I} end; 5: 5: Time: 5253 ms plus GC time: 136 ms 6: 6: Quitting Sat May 30 16:09:24 PDT 1992