reduce-historical/r34/xlog/complex.log

Sat Jun 29 13:38:03 PDT 1991
REDUCE 3.4, 15-Jul-91 ...

1: 1: 
2: 2: 
3: 3: % 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


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 


% 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;

4: 4: 
Quitting
Sat Jun 29 13:38:21 PDT 1991