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algexact-algsys-false

algexact:false;

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

alpha=15;

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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(alph...

algexact:false;

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algexact-algsys-false

algexact:false;

alpha=15;

a=0.679490067;

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algexact-solve-true

algexact:true;

Y:16/10*b*b*8=60/1000;

solve(Y,b);

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algexact-algsys-false

algexact:false;

alpha=15;

a=0.679490067;

Calculate

algexact-algsys-false

algexact:false;

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

alpha=15;

Calculate

algexact-algsys-false-true

algexact:true;

algsys([x^3+1.3589801...

algexact:false;

Calculate

algexact-algsys-false

algexact:false;

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

alpha=45;

Calculate

algexact-algsys-false

algexact:false;

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

alpha=15;

Calculate

algexact

Run Example
(%i1)algexact:true;
(%o1)                                true
(%i2) eq1:0=I0-U1/R1-(U1-U2)/R12-(U1-U3)/R13;
                            U3 - U1   U2 - U1   U1
(%o2)                   0 = ------- + ------- - -- + I0
                              R13       R12     R1
(%i3) eq2:0=I0-U2/R2-(U2-U1)/R12-(U2-U3)/R23;
                            U3 - U2   U2   U1 - U2
(%o3)                   0 = ------- - -- + ------- + I0
                              R23     R2     R12
(%i4) eq3:0=I0-U3/R3-(U3-U1)/R13-(U3-U2)/R23;
                             U3   U2 - U3   U1 - U3
(%o4)                  0 = - -- + ------- + ------- + I0
                             R3     R23       R13
(%i5) a:matrix(algsys([eq1,eq2,eq3],[U1, U2, U3]));
(%o5) matrix([[U1 = (((3 I0 R1 R2 + 2 I0 R1 R12) R23
 + (3 I0 R1 R13 + 3 I0 R1 R12) R2 + I0 R1 R12 R13) R3
 + (2 I0 R1 R13 R2 + I0 R1 R12 R13) R23 + I0 R1 R12 R13 R2)
/(((R2 + R12 + R1) R23 + (R13 + R12) R2 + (R12 + R1) R13 + R1 R12) R3
 + ((R13 + R1) R2 + (R12 + R1) R13 + R1 R12) R23
 + ((R12 + R1) R13 + R1 R12) R2), U2 = 
(((I0 R12 + 3 I0 R1) R2 R23 + ((2 I0 R12 + 3 I0 R1) R13 + 3 I0 R1 R12) R2) R3
 + ((I0 R12 + 2 I0 R1) R13 + I0 R1 R12) R2 R23)
/(((R2 + R12 + R1) R23 + (R13 + R12) R2 + (R12 + R1) R13 + R1 R12) R3
 + ((R13 + R1) R2 + (R12 + R1) R13 + R1 R12) R23
 + ((R12 + R1) R13 + R1 R12) R2), U3 = 
((((I0 R13 + 3 I0 R1) R2 + (I0 R12 + I0 R1) R13 + 2 I0 R1 R12) R23
 + ((2 I0 R12 + 3 I0 R1) R13 + 3 I0 R1 R12) R2) R3)
/(((R2 + R12 + R1) R23 + (R13 + R12) R2 + (R12 + R1) R13 + R1 R12) R3
 + ((R13 + R1) R2 + (R12 + R1) R13 + R1 R12) R23
 + ((R12 + R1) R13 + R1 R12) R2)]])
(%i6) b:matrix(algsys([eq1,eq2,eq3],[R12, R23, R13]));
(%o6)                   [ [R12 = 0, R23 = 0, R13 = 0] ]
(%i7) 
Run Example
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) tex(algsys([x^4+5*x^3+50*x^2-140*x+168],[x]));
$$\left[ \left[ x={{\sqrt{-{{\left(18\,\left({{56\,\sqrt{782431}\,i
 }\over{3}}+{{301400}\over{27}}\right)^{{{2}\over{3}}}+975\,\left({{
 56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1
 }\over{3}}}+13232\right)\,\sqrt{{{36\,\left({{56\,\sqrt{782431}\,i
 }\over{3}}+{{301400}\over{27}}\right)^{{{2}\over{3}}}-975\,\left({{
 56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1
 }\over{3}}}+26464}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{
 301400}\over{27}}\right)^{{{1}\over{3}}}}}}-53865\,\left({{56\,
 \sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}
 }}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}
 \right)^{{{1}\over{3}}}\,\sqrt{{{36\,\left({{56\,\sqrt{782431}\,i
 }\over{3}}+{{301400}\over{27}}\right)^{{{2}\over{3}}}-975\,\left({{
 56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1
 }\over{3}}}+26464}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{
 301400}\over{27}}\right)^{{{1}\over{3}}}}}}}}}}\over{3\,2^{{{3
 }\over{2}}}}}+{{\sqrt{{{36\,\left({{56\,\sqrt{782431}\,i}\over{3}}+
 {{301400}\over{27}}\right)^{{{2}\over{3}}}-975\,\left({{56\,\sqrt{
 782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}}+
 26464}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27
 }}\right)^{{{1}\over{3}}}}}}}\over{12}}-{{5}\over{4}} \right]  , 
 \left[ x=-{{\sqrt{-{{\left(18\,\left({{56\,\sqrt{782431}\,i}\over{3
 }}+{{301400}\over{27}}\right)^{{{2}\over{3}}}+975\,\left({{56\,
 \sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}
 }+13232\right)\,\sqrt{{{36\,\left({{56\,\sqrt{782431}\,i}\over{3}}+
 {{301400}\over{27}}\right)^{{{2}\over{3}}}-975\,\left({{56\,\sqrt{
 782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}}+
 26464}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27
 }}\right)^{{{1}\over{3}}}}}}-53865\,\left({{56\,\sqrt{782431}\,i
 }\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}}}\over{\left({{
 56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1
 }\over{3}}}\,\sqrt{{{36\,\left({{56\,\sqrt{782431}\,i}\over{3}}+{{
 301400}\over{27}}\right)^{{{2}\over{3}}}-975\,\left({{56\,\sqrt{
 782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}}+
 26464}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27
 }}\right)^{{{1}\over{3}}}}}}}}}}\over{3\,2^{{{3}\over{2}}}}}+{{
 \sqrt{{{36\,\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27
 }}\right)^{{{2}\over{3}}}-975\,\left({{56\,\sqrt{782431}\,i}\over{3
 }}+{{301400}\over{27}}\right)^{{{1}\over{3}}}+26464}\over{\left({{56
 \,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3
 }}}}}}}\over{12}}-{{5}\over{4}} \right]  , \left[ x={{\sqrt{-{{
 \left(18\,\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}
 \right)^{{{2}\over{3}}}+975\,\left({{56\,\sqrt{782431}\,i}\over{3}}+
 {{301400}\over{27}}\right)^{{{1}\over{3}}}+13232\right)\,\sqrt{{{36
 \,\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)
 ^{{{2}\over{3}}}-975\,\left({{56\,\sqrt{782431}\,i}\over{3}}+{{
 301400}\over{27}}\right)^{{{1}\over{3}}}+26464}\over{\left({{56\,
 \sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}
 }}}}+53865\,\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27
 }}\right)^{{{1}\over{3}}}}\over{\left({{56\,\sqrt{782431}\,i}\over{3
 }}+{{301400}\over{27}}\right)^{{{1}\over{3}}}\,\sqrt{{{36\,\left({{
 56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{2
 }\over{3}}}-975\,\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400
 }\over{27}}\right)^{{{1}\over{3}}}+26464}\over{\left({{56\,\sqrt{
 782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}}}}}}}
 }}\over{3\,2^{{{3}\over{2}}}}}-{{\sqrt{{{36\,\left({{56\,\sqrt{
 782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{2}\over{3}}}-975
 \,\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)
 ^{{{1}\over{3}}}+26464}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+
 {{301400}\over{27}}\right)^{{{1}\over{3}}}}}}}\over{12}}-{{5}\over{4
 }} \right]  , \left[ x=-{{\sqrt{-{{\left(18\,\left({{56\,\sqrt{
 782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{2}\over{3}}}+975
 \,\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)
 ^{{{1}\over{3}}}+13232\right)\,\sqrt{{{36\,\left({{56\,\sqrt{782431}
 \,i}\over{3}}+{{301400}\over{27}}\right)^{{{2}\over{3}}}-975\,\left(
 {{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1
 }\over{3}}}+26464}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{
 301400}\over{27}}\right)^{{{1}\over{3}}}}}}+53865\,\left({{56\,
 \sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}
 }}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}
 \right)^{{{1}\over{3}}}\,\sqrt{{{36\,\left({{56\,\sqrt{782431}\,i
 }\over{3}}+{{301400}\over{27}}\right)^{{{2}\over{3}}}-975\,\left({{
 56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1
 }\over{3}}}+26464}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{
 301400}\over{27}}\right)^{{{1}\over{3}}}}}}}}}}\over{3\,2^{{{3
 }\over{2}}}}}-{{\sqrt{{{36\,\left({{56\,\sqrt{782431}\,i}\over{3}}+
 {{301400}\over{27}}\right)^{{{2}\over{3}}}-975\,\left({{56\,\sqrt{
 782431}\,i}\over{3}}+{{301400}\over{27}}\right)^{{{1}\over{3}}}+
 26464}\over{\left({{56\,\sqrt{782431}\,i}\over{3}}+{{301400}\over{27
 }}\right)^{{{1}\over{3}}}}}}}\over{12}}-{{5}\over{4}} \right] 
  \right] $$
(%o2)                                false
(%i3) 

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