Artifact 03e2912f3570ea5c425281cc806f2de41c296e44100d9f467c4721e3663b7604:
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r36/xlog/COMPLEX.LOG
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2011-09-02 18:13:33
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REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ... % 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 abs(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 - 1.25983163303e-15*i 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 + 1.22460635382e-16*i 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; 2.71828182845904524 pi; 3.14159265358979324 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); 0.841470984807896507 sin(1.0 + 1.0*i); 1.29845758141597729 + 0.634963914784736108*i cos(0.0 + 0.0*i); 1 cos(1.0 - 0.0*i); 0.540302305868139717 cos(1.0 + 1.0*i); 0.833730025131149049 - 0.988897705762865096*i tan(0.0 + 0.0*i); 0 tan(1.0 + 0.0*i); 1.55740772465490223 tan(1.0 + 1.0*i); 0.271752585319511717 + 1.08392332733869454*i asin(1.0 + 1.0*i); 0.666239432492515255 + 1.06127506190503565*i acos(1.0 + 1.0*i); 0.904556894302381364 - 1.06127506190503565*i atan(1.0 + 1.0*i); 1.01722196789785137 + 0.402359478108525094*i log(1.0 + 1.0*i); 0.346573590279972655 + 0.78539816339744831*i asin 2; 1.57079632679489662 - 1.31695789692481671*i sin ws; 2.0 acos 2; 1.31695789692481671*i cos ws; 2.0 atan(1+i); 1.01722196789785137 + 0.402359478108525094*i tan ws; 1 + i log(2+i); 0.804718956217050187 + 0.463647609000806116*i exp ws; 2.0 + i e**(i*pi); - 1 e**i; 0.540302305868139717 + 0.841470984807896507*i z := sqrt i; z := 0.707106781186547524 + 0.707106781186547524*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; (TIME: complex 810 850)