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algexact-algsys-false

algexact:false;

algsys([x^3+1,3589801...

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algexact-algsys-cos-false-sin-true

algexact:true;

algsys([x^3+(cos(%pi/...

algexact:false;

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algexact-algsys-cos-false-sin-true

algexact:true;

algsys([x^3+(cos(alph...

algexact:false;

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algexact-algsys-false

algexact:false;

eq1:eps^3+a*eps^2+b=0;

alpha=45;

Calculate

algexact-algsys-cos-false-sin-true

algexact:true;

algsys([x^3+(cos(alph...

algexact:false;

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algexact-algsys-false

algexact:false;

eq1:eps^3+a*eps^2+b=0;

alpha=15;

Calculate

algexact-false-find_root

algexact:false;

find_root(7200*x*(x^6...

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algexact-false-solve

algexact:false;

solve(7200*x*(x^6-1)/...

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algexact-algsys-cos-false-sin-true

algexact:true;

algsys([x^3+(cos(alph...

algexact:false;

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algexact-algsys-false

algexact:false;

eq1:eps^3+a*eps^2+b=0;

alpha=60;

Calculate

algexact

Run Example
(%i1)algexact:true;
(%o1)                                true
(%i2) algsys([x^3+(cos(alpha)/sin(alpha)/5.49)*x^2-(cos(alpha)^2*241.27/%pi/75000/5.49^2)=0],[x]);
                              2
(%o2) [[x = expt((sqrt(37) cos (alpha)
                     3
      55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
 sqrt(-----------------------------------------------------))
                           sin(alpha)
             3/2
/(56159001 61    %pi sin(alpha))
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)  1
 - ------------------------------------------------------------------, -)
                                            3                          3
                    1032509122684461 %pi sin (alpha)
             2                     2                          2
 + (10000 cos (alpha))/(2712609 sin (alpha) expt((sqrt(37) cos (alpha)
                     3
      55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
 sqrt(-----------------------------------------------------))
                           sin(alpha)
             3/2
/(56159001 61    %pi sin(alpha))
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)
 - ------------------------------------------------------------------, 
                                            3
                    1032509122684461 %pi sin (alpha)
1     100 cos(alpha)
-)) - ---------------], 
3     1647 sin(alpha)
      sqrt(3) %i   1                    2
[x = (---------- - -) expt((sqrt(37) cos (alpha)
          2        2
                     3
      55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
 sqrt(-----------------------------------------------------))
                           sin(alpha)
             3/2
/(56159001 61    %pi sin(alpha))
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)  1
 - ------------------------------------------------------------------, -)
                                            3                          3
                    1032509122684461 %pi sin (alpha)
             sqrt(3) %i   1     2
 + (10000 (- ---------- - -) cos (alpha))
                 2        2
                                                                    3
                                       2             55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
                           sqrt(37) cos (alpha) sqrt(-----------------------------------------------------)
             2                                                            sin(alpha)
/(2712609 sin (alpha) expt(--------------------------------------------------------------------------------
                                                               3/2
                                                    56159001 61    %pi sin(alpha)
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)
 - ------------------------------------------------------------------, 
                                            3
                    1032509122684461 %pi sin (alpha)
1     100 cos(alpha)
-)) - ---------------], 
3     1647 sin(alpha)
        sqrt(3) %i   1                    2
[x = (- ---------- - -) expt((sqrt(37) cos (alpha)
            2        2
                     3
      55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
 sqrt(-----------------------------------------------------))
                           sin(alpha)
             3/2
/(56159001 61    %pi sin(alpha))
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)  1
 - ------------------------------------------------------------------, -)
                                            3                          3
                    1032509122684461 %pi sin (alpha)
           sqrt(3) %i   1     2
 + (10000 (---------- - -) cos (alpha))
               2        2
                                                                    3
                                       2             55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
                           sqrt(37) cos (alpha) sqrt(-----------------------------------------------------)
             2                                                            sin(alpha)
/(2712609 sin (alpha) expt(--------------------------------------------------------------------------------
                                                               3/2
                                                    56159001 61    %pi sin(alpha)
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)
 - ------------------------------------------------------------------, 
                                            3
                    1032509122684461 %pi sin (alpha)
1     100 cos(alpha)
-)) - ---------------]]
3     1647 sin(alpha)
(%i3) algexact:false;
(%o3)                                false
(%i4) algsys([x^3+(cos(alpha)/sin(alpha)/5.49)*x^2-(cos(alpha)^2*241.27/%pi/75000/5.49^2)=0],[x]);
                              2
(%o4) [[x = expt((sqrt(37) cos (alpha)
                     3
      55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
 sqrt(-----------------------------------------------------))
                           sin(alpha)
             3/2
/(56159001 61    %pi sin(alpha))
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)  1
 - ------------------------------------------------------------------, -)
                                            3                          3
                    1032509122684461 %pi sin (alpha)
             2                     2                          2
 + (10000 cos (alpha))/(2712609 sin (alpha) expt((sqrt(37) cos (alpha)
                     3
      55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
 sqrt(-----------------------------------------------------))
                           sin(alpha)
             3/2
/(56159001 61    %pi sin(alpha))
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)
 - ------------------------------------------------------------------, 
                                            3
                    1032509122684461 %pi sin (alpha)
1     100 cos(alpha)
-)) - ---------------], 
3     1647 sin(alpha)
      sqrt(3) %i   1                    2
[x = (---------- - -) expt((sqrt(37) cos (alpha)
          2        2
                     3
      55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
 sqrt(-----------------------------------------------------))
                           sin(alpha)
             3/2
/(56159001 61    %pi sin(alpha))
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)  1
 - ------------------------------------------------------------------, -)
                                            3                          3
                    1032509122684461 %pi sin (alpha)
             sqrt(3) %i   1     2
 + (10000 (- ---------- - -) cos (alpha))
                 2        2
                                                                    3
                                       2             55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
                           sqrt(37) cos (alpha) sqrt(-----------------------------------------------------)
             2                                                            sin(alpha)
/(2712609 sin (alpha) expt(--------------------------------------------------------------------------------
                                                               3/2
                                                    56159001 61    %pi sin(alpha)
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)
 - ------------------------------------------------------------------, 
                                            3
                    1032509122684461 %pi sin (alpha)
1     100 cos(alpha)
-)) - ---------------], 
3     1647 sin(alpha)
        sqrt(3) %i   1                    2
[x = (- ---------- - -) expt((sqrt(37) cos (alpha)
            2        2
                     3
      55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
 sqrt(-----------------------------------------------------))
                           sin(alpha)
             3/2
/(56159001 61    %pi sin(alpha))
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)  1
 - ------------------------------------------------------------------, -)
                                            3                          3
                    1032509122684461 %pi sin (alpha)
           sqrt(3) %i   1     2
 + (10000 (---------- - -) cos (alpha))
               2        2
                                                                    3
                                       2             55101226617 sin (alpha) - 462214000000 %pi cos(alpha)
                           sqrt(37) cos (alpha) sqrt(-----------------------------------------------------)
             2                                                            sin(alpha)
/(2712609 sin (alpha) expt(--------------------------------------------------------------------------------
                                                               3/2
                                                    56159001 61    %pi sin(alpha)
                       3                         2           3
   231107000000 %pi cos (alpha) - 55101226617 cos (alpha) sin (alpha)
 - ------------------------------------------------------------------, 
                                            3
                    1032509122684461 %pi sin (alpha)
1     100 cos(alpha)
-)) - ---------------]]
3     1647 sin(alpha)
(%i5) 
Run Example
algexact:true;
(%o1)                                true
(%i2) algsys([carg(0.4*(%i*w+10)/(%i*w*(%i*w+1)*(%i*w+4)))=-%pi],[w]);
(%o2)                                 []
(%i3) 
Run Example
algexact:false;
(%o1)                                false
(%i2) eq1:eps^3+a*eps^2+b=0;
                                3        2
(%o2)                        eps  + a eps  + b = 0
(%i3) alpha=60;
(%o3)                             alpha = 60
(%i4) a=0.105117479;
(%o4)                           a = 0.105117479
(%i5) b=-8.48616E-06;
(%o5)                     b = - 8.4861600000000008E-6
(%i6) algsys([eps^3+0.105117479*eps^2-8.48616E-06=0],[eps]);
(%o6) [[eps = - 0.10433796427559], [eps = - 0.0094166800578499], 
                                                    [eps = 0.0086371627302606]]
(%i7) 

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