Factor
Usage Message: Factor[poly] factors a polynomial over the integers. Factor[poly, Modulus->p] factors a polynomial
modulo a prime p. Factor[poly, Extension->{a1, a2, ... }] factors a polynomial allowing coefficients that are rational combinations of the algebraic numbers
ai. Attributes[Factor] = {Listable, Protected} Options: Extension
-> None
GaussianIntegers
-> False
Modulus
-> 0
Trig
-> False
Notes: The Factor function by default computes factors that can be expressed using integer coefficients. A polynomial that cannot be factored without introducing non-integer coefficients is called an irreducible polynomial. For example, the fact that
In[1]:= Factor[x^2 - 2 y^2]
2 2
Out[1]= x - 2 y
returns an unfactored result indicates that this is an irreducible polynomial. The non-integer coefficients needed to represent the factors of this
polynomial can be specified using the Extension
option.
In[2]:= Factor[x^2 - 2 y^2, Extension -> Sqrt[2]]
Out[2]= -((-x + Sqrt[2] y) (x + Sqrt[2] y))
Known Bugs The Factor function in Version 3.0 of Mathematica can return a result with an incorrect sign for certain rational functions. Here is an example one such incorrect result.
In[1]:= expr = (x^2 y + 2^15 x^2 y^2)/((1+y)(x+2^15 x y^4))
2 2 2
x y + 32768 x y
Out[1]= ------------------------
4
(1 + y) (x + 32768 x y )
In[2]:= Factor[expr]
x y (1 + 32768 y)
Out[2]= -(----------------------)
4
(1 + y) (1 + 32768 y )
This error can affect any function that uses Factor, including FactorList
, FactorSquareFree
, FactorSquareFreeList
, Cancel
, Together
, Simplify
, and FullSimplify
. This error is known to be rare, but an explicit characterization of this error is not available, and there are no known workarounds. A necessary but not sufficient condition for this error to occur is the presence of a monomial factor in the numerator or denominator of a rational function. It is expected that this error will be corrected for the next version of Mathematica. We apologize for any difficulties caused by this error. If you have other questions about this behavior, please contact Technical Support
.
Additional Online Documentation:
Mathematica 3.0
http://documents.wolfram.com/v3/RefGuide/Factor.html
Mathematica 4.0
http://documents.wolfram.com/v4/RefGuide/Factor.html
Questions or comments? Send email to support@wolfram.com.
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