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#############################################################################
##
#W polyrat.gd GAP Library Alexander Hulpke
##
#H @(#)$Id: polyrat.gd,v 4.14 2003/04/29 22:02:07 gap Exp $
##
#Y Copyright (C) 1996, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
#Y (C) 1999 School Math and Comp. Sci., University of St. Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file contains attributes, properties and operations for univariate
## polynomials over the rationals
##
Revision.polyrat_gd:=
"@(#)$Id: polyrat.gd,v 4.14 2003/04/29 22:02:07 gap Exp $";
#############################################################################
##
#F APolyProd(<a>,<b>,<p>) . . . . . . . . . . polynomial product a*b mod p
##
## return a*b mod p;
DeclareGlobalFunction("APolyProd");
#############################################################################
##
#F BPolyProd(<a>,<b>,<m>,<p>) . . . . . . polynomial product a*b mod m mod p
##
## return EuclideanRemainder(PolynomialRing(Rationals),a*b mod p,m) mod p;
DeclareGlobalFunction("BPolyProd");
#############################################################################
##
#F PrimitivePolynomial( <f> )
##
## takes a polynomial <f> with rational coefficients and computes a new
## polynomial with integral coefficients, obtained by multiplying with the
## Lcm of the denominators of the coefficients and casting out the content
## (the Gcd of the coefficients). The operation returns a list
## [<newpol>,<coeff>] with rational <coeff> such that
## `<coeff>\*<newpol>=<f>'.
##
DeclareOperation("PrimitivePolynomial",[IsPolynomial]);
#############################################################################
##
#F BombieriNorm(<pol>)
##
## computes weighted Norm [pol]_2 of <pol> which is a good measure for
## factor coeffietients (see \cite{BTW93}).
##
DeclareGlobalFunction("BombieriNorm");
#############################################################################
##
#A MinimizedBombieriNorm( <f> ) . . . Tschirnhaus transf'd polynomial
##
## This function applies linear Tschirnhaus transformations
## ($x \mapsto x + i$) to the
## polynomial <f>, trying to get the Bombieri norm of <f> small. It returns a
## list `[<new_polynomial>, <i_of_transformation>]'.
##
DeclareAttribute("MinimizedBombieriNorm",
IsPolynomial and IsRationalFunctionsFamilyElement);
#############################################################################
##
#F RootBound(<f>)
##
## returns the bound for the norm of (complex) roots of the rational
## univariate polynomial <f>.
##
DeclareGlobalFunction("RootBound");
#############################################################################
##
#F OneFactorBound(<pol>)
##
## returns the coefficient bound for a single factor of the rational
## polynomial <pol>.
##
DeclareGlobalFunction("OneFactorBound");
#############################################################################
##
#F HenselBound(<pol>,[<minpol>,<den>]) . . . Bounds for Factor coefficients
##
## returns the Hensel bound of the polynomial <pol>.
## If the computation takes place over an algebraic extension, then
## the minimal polynomial <minpol> and denominator <den> must be given.
##
DeclareGlobalFunction("HenselBound");
#############################################################################
##
#F TrialQuotientRPF(<f>,<g>,<b>)
##
## returns $<f>/<g>$ if coefficient bounds are given by list <b>.
##
DeclareGlobalFunction("TrialQuotientRPF");
#############################################################################
##
#F TryCombinations(<f>,...)
##
## trial divisions after Hensel factoring.
DeclareGlobalFunction("TryCombinations");
DeclareGlobalFunction("HeuGcdIntPolsExtRep"); # to permit recursive call
DeclareGlobalFunction("HeuGcdIntPolsCoeffs"); # univariate version
#############################################################################
##
#F PolynomialModP(<pol>,<p>)
##
## for a rational polynomial <pol> this function returns a polynomial over
## the field with <p> elements, obtained by reducing the coefficients modulo
## <p>.
DeclareGlobalFunction("PolynomialModP");
#############################################################################
##
#E polyrat.gd . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
##
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