### The Maxima on-line user's manual

Algebra 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.

`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) ```

### Related Examples

##### breakup-false-multiplicities-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-solve

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

breakup:false;

res:solve(eq1, Y);

Calculate

##### breakup-solve

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

breakup:falseres:solv...

Calculate

##### breakup-false-programmode-solve-true

programmode: false;

breakup: true;

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

Calculate

##### 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-false-programmode-solve-true

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

programmode: false;

breakup: true;

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