compute a greatest factorial factorization of a univariate polynomial - Maple Help

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PolynomialTools[GreatestFactorialFactorization] - compute a greatest factorial factorization of a univariate polynomial

Calling Sequence

GreatestFactorialFactorization(f,x)

Parameters

f

-

polynomial in x

x

-

indeterminate

Description

• 

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=cg1xg1x1...g1xe1+1g2xg2x1...g2xe2+1... 

  

 gcdgixgix1...gixe1+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&comma;.

• 

Partial factorizations of the input are not taken into account.

Examples

withPolynomialTools&colon;

GreatestFactorialFactorizationx8&plus;x2&comma;x

1&comma;x&comma;1&comma;x2&plus;x&plus;1&comma;2&comma;x&plus;1&comma;3

(1)

GreatestFactorialFactorizationexpandpochhammerx&comma;3pochhammerx&comma;5&comma;x

1&comma;x&plus;2&comma;3&comma;x&plus;4&comma;5

(2)

See Also

gcd, pochhammer, PolynomialTools, PolynomialTools[ShiftlessDecomposition], PolynomialTools[Translate], sqrfree

References

  

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.


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