/usr/share/gap/lib/polyrat.gd is in gap-libs 4r7p5-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 | #############################################################################
##
#W polyrat.gd GAP Library Alexander Hulpke
##
##
#Y Copyright (C) 1996, Lehrstuhl D für 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
##
#############################################################################
##
#F APolyProd(<a>,<b>,<p>) . . . . . . . . . . polynomial product a*b mod p
##
## <ManSection>
## <Func Name="APolyProd" Arg='a,b,p'/>
##
## <Description>
## return a</E>b mod p;
## </Description>
## </ManSection>
##
DeclareGlobalFunction("APolyProd");
#############################################################################
##
#F BPolyProd(<a>,<b>,<m>,<p>) . . . . . . polynomial product a*b mod m mod p
##
## <ManSection>
## <Func Name="BPolyProd" Arg='a,b,m,p'/>
##
## <Description>
## return EuclideanRemainder(PolynomialRing(Rationals),a</E>b mod p,m) mod p;
## </Description>
## </ManSection>
##
DeclareGlobalFunction("BPolyProd");
#############################################################################
##
#F PrimitivePolynomial( <f> )
##
## <#GAPDoc Label="PrimitivePolynomial">
## <ManSection>
## <Func Name="PrimitivePolynomial" Arg='f'/>
##
## <Description>
## takes a polynomial <A>f</A> 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
## [<A>newpol</A>,<A>coeff</A>] with rational <A>coeff</A> such that
## <C><A>coeff</A>*<A>newpol</A>=<A>f</A></C>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation("PrimitivePolynomial",[IsPolynomial]);
#############################################################################
##
#F BombieriNorm(<pol>)
##
## <#GAPDoc Label="BombieriNorm">
## <ManSection>
## <Func Name="BombieriNorm" Arg='pol'/>
##
## <Description>
## computes weighted Norm [<A>pol</A>]<M>_2</M> of <A>pol</A> which is a
## good measure for factor coefficients (see <Cite Key="BTW93"/>).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("BombieriNorm");
#############################################################################
##
#A MinimizedBombieriNorm( <f> ) . . . Tschirnhaus transf'd polynomial
##
## <#GAPDoc Label="MinimizedBombieriNorm">
## <ManSection>
## <Attr Name="MinimizedBombieriNorm" Arg='f'/>
##
## <Description>
## This function applies linear Tschirnhaus transformations
## (<M>x \mapsto x + i</M>) to the
## polynomial <A>f</A>, trying to get the Bombieri norm of <A>f</A> small. It returns a
## list <C>[<A>new_polynomial</A>, <A>i_of_transformation</A>]</C>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute("MinimizedBombieriNorm",
IsPolynomial and IsRationalFunctionsFamilyElement);
#############################################################################
##
#F RootBound(<f>)
##
## <ManSection>
## <Func Name="RootBound" Arg='f'/>
##
## <Description>
## returns the bound for the norm of (complex) roots of the rational
## univariate polynomial <A>f</A>.
## </Description>
## </ManSection>
##
DeclareGlobalFunction("RootBound");
#############################################################################
##
#F OneFactorBound(<pol>)
##
## <#GAPDoc Label="OneFactorBound">
## <ManSection>
## <Func Name="OneFactorBound" Arg='pol'/>
##
## <Description>
## returns the coefficient bound for a single factor of the rational
## polynomial <A>pol</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("OneFactorBound");
#############################################################################
##
#F HenselBound(<pol>,[<minpol>,<den>]) . . . Bounds for Factor coefficients
##
## <#GAPDoc Label="HenselBound">
## <ManSection>
## <Func Name="HenselBound" Arg='pol,[minpol,den]'/>
##
## <Description>
## returns the Hensel bound of the polynomial <A>pol</A>.
## If the computation takes place over an algebraic extension, then
## the minimal polynomial <A>minpol</A> and denominator <A>den</A> must be given.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("HenselBound");
#############################################################################
##
#F TrialQuotientRPF(<f>,<g>,<b>)
##
## <ManSection>
## <Func Name="TrialQuotientRPF" Arg='f,g,b'/>
##
## <Description>
## returns <M><A>f</A>/<A>g</A></M> if coefficient bounds are given by list <A>b</A>.
## </Description>
## </ManSection>
##
DeclareGlobalFunction("TrialQuotientRPF");
#############################################################################
##
#F TryCombinations(<f>,...)
##
## <ManSection>
## <Func Name="TryCombinations" Arg='f,...'/>
##
## <Description>
## trial divisions after Hensel factoring.
## </Description>
## </ManSection>
##
DeclareGlobalFunction("TryCombinations");
DeclareGlobalFunction("HeuGcdIntPolsExtRep"); # to permit recursive call
DeclareGlobalFunction("HeuGcdIntPolsCoeffs"); # univariate version
#############################################################################
##
#F PolynomialModP(<pol>,<p>)
##
## <#GAPDoc Label="PolynomialModP">
## <ManSection>
## <Func Name="PolynomialModP" Arg='pol,p'/>
##
## <Description>
## for a rational polynomial <A>pol</A> this function returns a polynomial over
## the field with <A>p</A> elements, obtained by reducing the coefficients modulo
## <A>p</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("PolynomialModP");
#############################################################################
##
#E
|