/usr/share/gap/lib/galois.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 | #############################################################################
##
#W galois.gd GAP library Alexander Hulpke
##
##
#Y Copyright (C) 2002 The GAP Group
##
## This file contains the declarations for the computation of Galois Groups.
##
#############################################################################
##
#V InfoGalois
##
## <ManSection>
## <InfoClass Name="InfoGalois"/>
##
## <Description>
## is the info class for the Galois group recognition functions.
## </Description>
## </ManSection>
##
DeclareInfoClass("InfoGalois");
#############################################################################
##
#F GaloisType(<f>[,<cand>])
##
## <#GAPDoc Label="GaloisType">
## <ManSection>
## <Func Name="GaloisType" Arg='f[,cand]'/>
##
## <Description>
## Let <A>f</A> be an irreducible polynomial with rational coefficients. This
## function returns the type of Gal(<A>f</A>)
## (considered as a transitive permutation group of the roots of <A>f</A>). It
## returns a number <A>i</A> if Gal(<A>f</A>) is permutation isomorphic to
## <C>TransitiveGroup(<A>n</A>,<A>i</A>)</C> where <A>n</A> is the degree of <A>f</A>.
## <P/>
## Identification is performed by factoring
## appropriate Galois resolvents as proposed in <Cite Key="MS85"/>. This function
## is provided for rational polynomials of degree up to 15. However, in some
## cases the required calculations become unfeasibly large.
## <P/>
## For a few polynomials of degree 14, a complete discrimination is not yet
## possible, as it would require computations, that are not feasible with
## current factoring methods.
## <P/>
## This function requires the transitive groups library to be installed (see
## <Ref Sect="Transitive Permutation Groups"/>).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute("GaloisType",IsRationalFunction);
#############################################################################
##
#F ProbabilityShapes(<f>)
##
## <#GAPDoc Label="ProbabilityShapes">
## <ManSection>
## <Func Name="ProbabilityShapes" Arg='f'/>
##
## <Description>
## Let <A>f</A> be an irreducible polynomial with rational coefficients. This
## function returns a list of the most likely type(s) of Gal(<A>f</A>)
## (see <Ref Func="GaloisType"/>), based
## on factorization modulo a set of primes.
## It is very fast, but the result is only probabilistic.
## <P/>
## This function requires the transitive groups library to be installed (see
## <Ref Sect="Transitive Permutation Groups"/>).
## <Example><![CDATA[
## gap> f:=x^9-9*x^7+27*x^5-39*x^3+36*x-8;;
## gap> GaloisType(f);
## 25
## gap> TransitiveGroup(9,25);
## [1/2.S(3)^3]3
## gap> ProbabilityShapes(f);
## [ 25 ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("ProbabilityShapes");
DeclareGlobalFunction("SumRootsPol");
DeclareGlobalFunction("ProductRootsPol");
DeclareGlobalFunction("Tschirnhausen");
DeclareGlobalFunction("TwoSeqPol");
DeclareGlobalFunction("GaloisSetResolvent");
DeclareGlobalFunction("GaloisDiffResolvent");
DeclareGlobalFunction("ParityPol");
#############################################################################
##
#E
|