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 Documentation / Mathematica / Built-in Functions / New in Version 3.0 / Algebraic Computation  /
Factor

  • Factor[ poly ] factors a polynomial over the integers.
  • Factor[ poly , Modulus-> p ] factors a polynomial modulo a prime p.
  • Factor[ poly , Extension-> , , ... ] factors a polynomial allowing coefficients that are rational combinations of the algebraic numbers .
  • Factor applies only to the top level in an expression. You may have to use Map, or apply Factor again, to reach other levels.
  • Factor[ poly , GaussianIntegers->True] factors allowing Gaussian integer coefficients.
  • If any coefficients in poly are complex numbers, factoring is done allowing Gaussian integer coefficients.
  • The exponents of variables need not be positive integers. Factor can deal with exponents that are linear combinations of symbolic expressions.
  • When given a rational expression, Factor effectively first calls Together, then factors numerator and denominator.
  • With the default setting Extension->None, Factor[ poly ] will treat algebraic number coefficients in poly like independent variables.
  • Factor[ poly , Extension->Automatic] will extend the domain of coefficients to include any algebraic numbers that appear in poly.
  • See the Mathematica book: Section 1.4.3, Section 1.4.5Section 3.3.1.
  • See also Implementation NotesA.9.55.3MainBookLinkOldButtonDataA.9.55.3.
  • See also: FactorTerms, FactorSquareFree, Solve, Expand, Simplify, FactorInteger, TrigFactor.

    Further Examples

    We factor a few polynomials over the integers.

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    Some polynomials that don't factor over the integers do factor over the integers modulo a prime.

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    Without specifying the appropriate extension field, you cannot factor either of these polynomials into linear factors.

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    Without specifying the appropriate extension field, you cannot factor either of these polynomials into linear factors.

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    You can factor them into linear terms by specifying the extension.

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    Factor will use multiple-angle formulas for with the setting Trig -> True, and using the option GaussianIntegers may do more factorization.

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    Here we factor a polynomial in three variables with 195 terms.

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