factor a multivariate polynomial
field extension over which to factor
The factors command computes the factorization of a multivariate polynomial over the rationals, an algebraic number field, and with real or complex numeric coefficients.
Unlike the factor function where the input is any expression and the output is a product of sums in the general case, the input to the factors function must be a polynomial or a rational function, and the output is a data structure more suitable for programming purposes.
The factorization is returned in the form u,f1,m1,...,fn,mn where a=u⁢f1m1...fnmn where each fk (the factor) is a unit normal irreducible polynomial and each mk (its multiplicity) is a positive integer.
The call factors(a) factors over the field implied by the coefficients present: thus, if all the coefficients are rational, then the polynomial is factored over the rationals.
If the second argument K is the keyword real or complex, a floating-point factorization is performed over R and C respectively. Note, at present this is only implemented for univariate polynomials.
The call factors(a, K) factors the polynomial a over the algebraic number field defined by K. K must be a single RootOf, a list or set of RootOfs, a single radical, or a list or set of radicals.
The following is an example that has a rational function as input.
q ≔ expand⁡z−1⁢z−3expand⁡z−2⁢z−4
q ≔ z2−4⁢z+3z2−6⁢z+8
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