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

Algebra Calculator

#### Gfactor

Function: gfactor (<expr>) Factors the polynomial <expr> over the Gaussian integers (that is, the integers with the imaginary unit `%i` adjoined). This is like `factor (<expr>, <a>^2+1)` where <a> is `%i`.

Example:

```          (%i1) gfactor (x^4 - 1);
(%o1)           (x - 1) (x + 1) (x - %i) (x + %i)```

There are also some inexact matches for `gfactor`. Try `?? gfactor` to see them.

```(%o1)                                true
(%i2) ```

### Related Examples

##### gfactor-transpose

term:[x^2-8*x+15,x^2-...

gfactor(term);

[transpose(term),tran...

Calculate

? gfactor;

Calculate

##### gfactor

f(x,y,z):=-y^2*z^10+2...

gfactor(f(x,y,z));

Calculate

##### gfactor-plot2d

eq1: x^5 - x^4 + 3*x^...

gfactor(eq1);

plot2d(x^5 - x^4 + 3*...

Calculate

##### gfactor-plot2d

eq1: x^5 - x^4 + 3*x^...

gfactor(eq1);

plot2d(x^5 - x^4 + 3*...

Calculate

##### gfactor-sqrt

M: X^6 + sqrt(2)*X^5...

F: gfactor(M);

Calculate

s:x^3+x^2+3*x+3;

A:gfactor(s);

solve(A);

Calculate

##### gfactor-sqrt

M: X^6 + sqrt(2)*X^5...

F: gfactor(M);

Calculate

##### gfactor-ratsimp-solve-sqrt

ratsimp((x^2+sqrt(3)*...

gfactor(x^4-x^2+1);

sol:solve(x^4-x^2+1);

Calculate

##### gfactor-linsolve

eq1:x*4+y-2=y;

eq2:x+2=y;

linsolve([eq1,eq2],[x...

Calculate