polytools
splits
complete Factorization of a Polynomial
Calling Sequence
Parameters
Description
Examples
splits(a, x)
splits(a, x, b)
a
-
polynomial
x
variable
b
Important: The polytools package has been deprecated. Use the superseding command PolynomialTools[Splits] instead.
The splits function computes the complete factorization of a univariate polynomial.
The univariate polynomial a in x, with rational or algebraic number coefficients or polynomial coefficients, is factored into linear factors.
The factorization is returned in the form u,f1,m1,..,fn,mn where a=uf1m1...fnmn where each fk (the factor) is a unit normal irreducible polynomial and each mk (its multiplicity) is a positive integer.
In the case of three arguments, the third argument b is assigned the extensions of Q on output, where Q is the set of rational numbers.
The command with(polytools,splits) allows the use of the abbreviated form of this command.
withpolytools:
splitsx2+x+1,x
1,x+1+RootOf_Z2+_Z+1,1,x−RootOf_Z2+_Z+1,1
splitsx2+yx+1+y2,x,b
1,x−RootOf_Z2+y_Z+y2+1,1,x+y+RootOf_Z2+y_Z+y2+1,1
RootOf_Z2+y_Z+y2+1
See Also
AFactor
PolynomialTools[Splits]
polytools(deprecated)[split]
RootOf
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