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The Maxima on-line user's manual

Algebra Calculator

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Breakup Calculator

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.

programmode: false;
 breakup: true;
 solve (x^3 + x^2 - 1);
 breakup: false;
 solve (x^3 + x^2 - 1);

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) 

Breakup Example

Related Examples

breakup-false-programmode-solve-true

programmode: false;

breakup: true;

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

Calculate

breakup-false-multiplicities-programmode-solve

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

programmode: false;

breakup: false;

Calculate

breakup-false-programmode-solve

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

programmode: false;

breakup: false;

Calculate

breakup-false-solve

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

breakup:false;

res:solve(eq1, Y);

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-solve

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

breakup:false;

res:solve(eq1, Y);

Calculate

breakup-false-multiplicities-programmode-solve

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

programmode: false;

breakup: false;

Calculate

breakup-false-programmode-solve-true

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

programmode: false;

breakup: true;

Calculate

breakup-false-programmode-solve-true

programmode: false;

breakup: true;

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

Calculate