6.34.19 Factoring a polynomial with coefficients in a Galois field: factor
The factor command can factor univariate polynomials with
coefficients in a Galois field.
-
factor takes one mandatory argument and one optional
argument:
-
expr, an expression or a list of expressions.
- Optionally, α, to specify an extension field.
- factor(expr) returns expr
factored over the field of its coefficients, with the addition of i
in complex mode (see Section 3.5.5). If sqrt is
enabled in the Cas configuration (see Section 3.5.7),
polynomials of order 2 are factorized in complex mode or in real
mode if the discriminant is positive.
factor(expr,α) returns expr
factored over F[α], where F is the field of coefficients
of expr.
- cfactor factors like factor, except the
field includes i whether in real or complex mode.
Examples.
factor can also factorize a univariate polynomial
with coefficients in a Galois field.
Input (for example to
have G=F4):
G:=GF(2,2,[’w’,’G’])
Output:
GF(2,w^2+w+1,[w,G],undef)
Input (for example):
| a:=G(w) |
| factor(a^2*x^2+1)
|
Output:
(G(w+1))*(x+G(w+1))^2