The following functions are only available to polynomials with rations coefficients:
PrimitivePolynomial( f ) F
takes a polynomial f with rational coefficients and computes a new
polynomial with integral coefficients, obtained by multiplying with the
Lcm of the denominators of the coefficients and casting out the content
(the Gcd of the coefficients). The operation returns a list
[newpol,coeff] with rational coeff such that
coeff*newpol=f.
The following operations are used by GAP inside the factorization algorithm but might be of interest also in other contexts.
BombieriNorm( pol ) F
computes weighted Norm [pol]_2 of pol which is a good measure for factor coeffietients (see BTW93).
MinimizedBombieriNorm( f ) A
This function applies linear Tschirnhaus transformations (x->x+i) to the polynomial f, trying to get the bombieri norm of f small. It returns a list [new polynomial, transformation i].
HenselBound( pol, [minpol, den] ) F
minpol and denominator must be given
OneFactorBound( pol ) F
Coefficient bound for single factor of rational polynomial pol
[Top] [Previous] [Up] [Next] [Index]
GAP 4 manual