PolynomialTools
GreatestFactorialFactorization
compute a greatest factorial factorization of a univariate polynomial
Calling Sequence
Parameters
Description
Examples
References
GreatestFactorialFactorization(f,x)
f
-
polynomial in x
x
indeterminate
The GreatestFactorialFactorization command computes a greatest factorial factorization [c,[[g1,e1],[g2,e2],...]] of f w.r.t. x. It satisfies the following properties.
f=cg1xg1x−1...g1x−e1+1g2xg2x−1...g2x−e2+1...
gcdgixgix−1...gix−e1+1,gjx+1gjx+ej=1 for 1<=i<=j
c is constant w.r.t. x, and g1,... are nonconstant primitive polynomials w.r.t. x, and 0<e1<e2<... are integers.
The greatest factorial factorization is unique up to multiplication by units.
GreatestFactorialFactorization can handle the same types of coefficients as the Maple function gcd.
If f is constant w.r.t. x, then the return value is f,.
Partial factorizations of the input are not taken into account.
withPolynomialTools:
GreatestFactorialFactorization−x8+x2,x
−1,x,1,x2+x+1,2,x+1,3
GreatestFactorialFactorizationexpandpochhammerx,3pochhammerx,5,x
1,x+2,3,x+4,5
Paule, Peter. "Greatest factorial factorization and symbolic summation." Journal of Symbolic Computation Vol. 20, (1995): 235-268.
Gerhard, Juergen. "Modular algorithms for polynomial basis conversion and greatest factorial factorization." Proceedings of the Seventh Rhine Workshop on Computer Algebra, RWCA pp. 125-141 ed. T. Mulders, 2000.
See Also
gcd
pochhammer
PolynomialTools[ShiftlessDecomposition]
PolynomialTools[Translate]
sqrfree
Download Help Document