Mark van Hoeij, Factoring polynomials and the knapsack problem. − 3 2 + I 2 3 + 3 2 + I 2 + x x + 3 2 + I 2 x − 3 2 − I 2 3 2 + I 2 3 − 3 2 − I 2 + xĭepending on the algebraic extension, this can factor in several different ways.įactor a, sqrt 2 − 2 I sqrt 3 To factor a into linear factors, you must extend the field of coefficients using algebraic extensions.Ī1 ≔ − RootOf _Z 4 − _Z 2 + 1 3 + RootOf _Z 4 − _Z 2 + 1 + x x + RootOf _Z 4 − _Z 2 + 1 x − RootOf _Z 4 − _Z 2 + 1 RootOf _Z 4 − _Z 2 + 1 3 − RootOf _Z 4 − _Z 2 + 1 + x To factor a over the rationals, use the following. The polynomial a is a polynomial over the rationals. The following is a splitting field example. If the second argument K is a single RootOf, a list or set of RootOf s, a single radical, or a list or set of radicals, then the expression is factored over the algebraic number field defined by K. At present this is only implemented for univariate polynomials. If the second argument K is the keyword real or complex, a floating-point factorization is performed over the reals and complexes respectively. If the input, a, is a list, set, equation, range, series, relation, or function, then factor is applied recursively to the components of a. However, it is more expensive to compute. This provides a fully-factored form which can be used to simplify an expression in the same way the normal function is used. If the input, a, is a rational expression, then it is first normalized (see normal ) and the numerator and denominator of the resulting expression are then factored. Note that any integer content (see first example below) is not factored. Thus factor does not necessarily factor into linear factors. For example, if the coefficients are all integers then factor computes all irreducible factors with integer coefficients. If the second argument K is not given, the polynomial is factored over the field implied by the coefficients. To explicitly request Wang's algorithm, which was the default in Maple 2018 and earlier versions, use the option method="Wang". The default is the latter, since it is faster on most examples. Use the ifactor function to factor integers.įor multivariate polynomials with integer coefficients, the factor command offers two algorithms: Wang's algorithm (see ) and the algorithm by Monagan and Tuncer (, ). Nor does it factor integer coefficients in a polynomial. The factor function does NOT factor integers. The factor function computes the factorization of a multivariate polynomial with integer, rational, (complex) numeric, or algebraic number coefficients. Multivariate polynomial with rational coefficients
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