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breakup-false-programmode-solve-true

programmode: false;

breakup: true;

solve (x^3 + x^2 - 1);

Calculate

breakup-false-programmode-solve

eq1:V = F * ((C*(1 - ...

programmode: false;

breakup: false;

Calculate

breakup-solve

eq1:V = F * ((C*(1 - ...

breakup:falseres:solv...

Calculate

breakup-false-multiplicities-programmode-solve

eq1:V = F * ((C*(1 - ...

programmode: false;

breakup: false;

Calculate

breakup-false-multiplicities-programmode-solve

eq1:V = F * ((C*(1 - ...

programmode: false;

breakup: false;

Calculate

breakup-solve

eq1:V = F * ((C*(1 - ...

breakup:falseres:solv...

Calculate

breakup-solve

eq1:V = F * ((C*(1 - ...

breakup:falseres:solv...

Calculate

breakup-false-programmode-solve-true

eq1:V = F * ((C*(1 - ...

programmode: false;

breakup: true;

Calculate

breakup-solve

eq1:V = F * ((C*(1 - ...

breakup:falseres:solv...

Calculate

breakup

Run Example
(%i1)eq1:V = F * ((C*(1 - (1/(1 + Y))^(M*H)) / H*Y) + (1 / (1 + Y))^(M*H));
                                                    1
                                       C Y (1 - ----------)
                                                       H M
                              1                 (Y + 1)
(%o1)              V = F (---------- + --------------------)
                                 H M            H
                          (Y + 1)
(%i2) breakup:falseres:solve(eq1, Y);
                                          H M
                               H V (Y + 1)    - F H
(%o2)                     [Y = --------------------]
                                          H M
                               C F (Y + 1)    - C F
(%i3) 
Run Example
? breakup;

 -- Option variable: breakup
     Default value: `true'

     When `breakup' is `true', `solve' expresses solutions of cubic and
     quartic equations in terms of common subexpressions, which are
     assigned to intermediate expression labels (`%t1', `%t2', etc.).
     Otherwise, common subexpressions are not identified.

     `breakup: true' has an effect only when `programmode' is `false'.

     Examples:

          (%i1) programmode: false$
          (%i2) breakup: true$
          (%i3) solve (x^3 + x^2 - 1);

                                  sqrt(23)    25 1/3
          (%t3)                  (--------- + --)
                                  6 sqrt(3)   54
          Solution:

                                                sqrt(3) %i   1
                                                ---------- - -
                          sqrt(3) %i   1            2        2   1
          (%t4)    x = (- ---------- - -) %t3 + -------------- - -
                              2        2            9 %t3        3

                                                sqrt(3) %i   1
                                              - ---------- - -
                        sqrt(3) %i   1              2        2   1
          (%t5)    x = (---------- - -) %t3 + ---------------- - -
                            2        2             9 %t3         3

                                             1     1
          (%t6)                  x = %t3 + ----- - -
                                           9 %t3   3
          (%o6)                    [%t4, %t5, %t6]
          (%i6) breakup: false$
          (%i7) solve (x^3 + x^2 - 1);
          Solution:

                       sqrt(3) %i   1
                       ---------- - -
                           2        2        sqrt(23)    25 1/3
          (%t7) x = --------------------- + (--------- + --)
                       sqrt(23)    25 1/3    6 sqrt(3)   54
                    9 (--------- + --)
                       6 sqrt(3)   54

                                                        sqrt(3) %i   1    1
                                                     (- ---------- - -) - -
                                                            2        2    3

                     sqrt(23)    25 1/3  sqrt(3) %i   1
          (%t8) x = (--------- + --)    (---------- - -)
                     6 sqrt(3)   54          2        2

                                                      sqrt(3) %i   1
                                                    - ---------- - -
                                                          2        2      1
                                                + --------------------- - -
                                                     sqrt(23)    25 1/3   3
                                                  9 (--------- + --)
                                                     6 sqrt(3)   54

                      sqrt(23)    25 1/3             1             1
          (%t9)  x = (--------- + --)    + --------------------- - -
                      6 sqrt(3)   54          sqrt(23)    25 1/3   3
                                           9 (--------- + --)
                                              6 sqrt(3)   54
          (%o9)                    [%t7, %t8, %t9]


(%o1)                                true
(%i2) 
Run Example
breakup: false;
(%o1)                                false
(%i2) eq1:1/(2*%pi*sigma^2) * exp(-(x-mu_x)^2+(y-mu_y)^2)/(2*sigma^2);
                                      2             2
                            (y - mu_y)  - (x - mu_x)
                          %e
(%o2)                     ---------------------------
                                            4
                                 4 %pi sigma
(%i3) eq2:1/(2*%pi*sigma1^2) * exp(-(x-mu_x1)^2+(y-mu_y1)^2)/(2*sigma1^2);
                                      2              2
                           (y - mu_y1)  - (x - mu_x1)
                         %e
(%o3)                    -----------------------------
                                             4
                                 4 %pi sigma1
(%i4) algsys([eq1,eq2],[x,y]);
(%o4)                                 []
(%i5) 

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