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############################################################################
##
## matmeths.gd IRREDSOL Burkhard Höfling
##
## Copyright © 2003–2016 Burkhard Höfling
##
############################################################################
##
#P IsIrreducibleMatrixGroup(<G>)
#O IsIrreducibleMatrixGroup(<G>, <F>)
#O IsIrreducible(<G>, <F>)
##
## see IRREDSOL documentation
##
## IsIrreducible(<G>) is declared in the GAP library
##
DeclareProperty("IsIrreducibleMatrixGroup", IsMatrixGroup);
KeyDependentOperation("IsIrreducibleMatrixGroup", IsMatrixGroup, IsField, ReturnTrue);
DECLARE_IRREDSOL_SYNONYMS("IsIrreducibleMatrixGroup");
DeclareOperation("IsIrreducible", [IsMatrixGroup, IsField]);
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##
#O IsAbsolutelyIrreducible(<G>)
#P IsAbsolutelyIrreducibleMatrixGroup(<G>)
##
## see IRREDSOL documentation
##
DeclareOperation("IsAbsolutelyIrreducible", [IsMatrixGroup]);
DeclareProperty("IsAbsolutelyIrreducibleMatrixGroup", IsMatrixGroup);
DECLARE_IRREDSOL_SYNONYMS("IsAbsolutelyIrreducibleMatrixGroup");
############################################################################
##
#P IsPrimitiveMatrixGroup(<G>)
#O IsPrimitiveMatrixGroup(<G>, <F>)
#P IsPrimitive(<G>)
#O IsPrimitive(<G>, <F>)
##
## see IRREDSOL documentation
##
DeclareProperty("IsPrimitiveMatrixGroup", IsMatrixGroup);
KeyDependentOperation("IsPrimitiveMatrixGroup", IsMatrixGroup, IsField, ReturnTrue);
DECLARE_IRREDSOL_SYNONYMS("IsPrimitiveMatrixGroup");
DeclareProperty("IsPrimitive", IsMatrixGroup); # already a property elsewhere in the library
DeclareOperation("IsPrimitive", [IsMatrixGroup, IsField]);
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##
#A DegreeOfMatrixGroup(<G>)
##
## see IRREDSOL documentation
##
if not IsBound(DegreeOfMatrixGroup) then
# DegreeOfMatrixGroup is also declared identically in primgrp, so to
# avoid warnings we only define it if necessary
DeclareSynonymAttr("DegreeOfMatrixGroup", DimensionOfMatrixGroup);
fi;
DECLARE_IRREDSOL_SYNONYMS_ATTR("DegreeOfMatrixGroup");
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##
#A MinimalBlockDimensionOfMatrixGroup(<G>)
#A MinimalBlockDimensionOfMatrixGroup(<G>, <F>)
#O MinimalBlockDimension(<G>, <F>)
##
## see IRREDSOL documentation
##
## MinimalBlockDImension(<G>) is an attribute declared in the primgrps library
##
DeclareAttribute("MinimalBlockDimensionOfMatrixGroup", IsMatrixGroup);
KeyDependentOperation("MinimalBlockDimensionOfMatrixGroup", IsMatrixGroup, IsField, ReturnTrue);
DECLARE_IRREDSOL_SYNONYMS_ATTR("MinimalBlockDimensionOfMatrixGroup");
DeclareOperation("MinimalBlockDimension", [IsMatrixGroup, IsField]);
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##
#A CharacteristicOfField(<G>)
##
## see IRREDSOL documentation
##
## Characteristic(<G>) is defined in the GAP library
##
DeclareAttribute("CharacteristicOfField", IsMatrixGroup);
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#A RepresentationIsomorphism
##
## see IRREDSOL documentation
##
DeclareAttribute("RepresentationIsomorphism", IsMatrixGroup);
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##
#P IsMaximalAbsolutelyIrreducibleSolubleMatrixGroup(<G>)
##
## see IRREDSOL documentation
##
DeclareProperty("IsMaximalAbsolutelyIrreducibleSolubleMatrixGroup", IsMatrixGroup);
DECLARE_IRREDSOL_SYNONYMS("IsMaximalAbsolutelyIrreducibleSolubleMatrixGroup");
############################################################################
##
#F SmallBlockDimensionOfRepresentation(G, hom, F, limit)
##
## G is a group, F a field, hom a homomorphism G -> GL(n, F), limit an integer
## The function returns an integer k such that Im hom has a block system
## of block dimension k, where k < limit, or k >= limit and G has no
## block system of block dimension < limit
##
DeclareGlobalFunction("SmallBlockDimensionOfRepresentation");
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##
#F ImprimitivitySystemsForRepresentation(G, rep, F, limit)
##
## G is a group, F a finite field, rep: G -> GL(n, F)
##
## If G has no block system with block dimension <= limit, the function
## computes a list of all imprimitivity systems of Im rep as a
## subgroup of GL(n, F). Otherwise, the function computes systems of imprimitivity,
## one of which will have block dimension <= limit.
##
## Each imprimitivity system is represented by a record with the following entries:
## bases: a list of lists of vectors, each list of vectors being a basis of a block
## in the imprimitivity system
## stab1: the stabilizer in G of the first block (i. e., the block with basis bases[1])
## min: true if the block system is a minimal block system amongst the systems returned
##
DeclareGlobalFunction("ImprimitivitySystemsForRepresentation");
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##
#A ImprimitivitySystems(<G>)
#O ImprimitivitySystems(<G>, <F>)
##
## see IRREDSOL documentation
##
DeclareAttribute("ImprimitivitySystems", IsMatrixGroup);
KeyDependentOperation("ImprimitivitySystems", IsMatrixGroup, IsField, ReturnTrue);
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#A TraceField(<G>)
##
## see IRREDSOL documentation
##
DeclareAttribute("TraceField", IsMatrixGroup);
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##
#A SplittingField(<G>)
##
## see IRREDSOL documentation
##
DeclareAttribute("SplittingField", IsMatrixGroup);
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##
#A ConjugatingMatTraceField(<G>)
##
## returns a matrix x such that the matrix entries of G^x lie in the
## trace field of G.
##
DeclareAttribute("ConjugatingMatTraceField", IsMatrixGroup);
############################################################################
##
#E
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