The factor command was updated in Maple 2019. An improved Multivariate Polynomial Factoring Algorithm, Mathematics of Computation 32, (1978). Factoring multivariate polynomials with many factors and huge coefficients. Using Sparse Interpolation in Hensel Lifting. Mark van Hoeij, Factoring polynomials and the knapsack problem. X + 3 2 + I 2 − 3 2 + I 2 3 + 3 2 + I 2 + x 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. Maple T A The approach used in this example serves also to address nonlinear. To factor a into linear factors, you must extend the field of coefficients using algebraic extensions.Ī1 ≔ x + RootOf _Z 4 − _Z 2 + 1 − RootOf _Z 4 − _Z 2 + 1 3 + RootOf _Z 4 − _Z 2 + 1 + x x − RootOf _Z 4 − _Z 2 + 1 RootOf _Z 4 − _Z 2 + 1 3 − RootOf _Z 4 − _Z 2 + 1 + x I recommand Maxima integer factor, ifactor() square root, sqrt(3). 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 a is a series but not an exact series, then factor is applied recursively to the components of a (that is, its coefficients). If a is an exact series, that is, a series object with no order term, then it is first converted to a polynomial before applying factor. If the input, a, is a list, set, equation, range, 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. This means this number also falls in the category of "large prime times small factors", whereas the hard case is "product of two primes of comparable magnitude".Multivariate polynomial with rational coefficients The truth is that neither wolframalpha, maple, nor mathematica knows the factorization of $10^$ is a prime with 225 decimals.
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