/usr/share/gap/lib/mgmideal.gd is in gap-libs 4r7p9-1.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 | #############################################################################
##
#W mgmideal.gd GAP library Andrew Solomon
##
##
#Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file contains the declaration of operations for magma ideals.
##
#############################################################################
#############################################################################
##
##
## Left Magma Ideals
##
##
#############################################################################
#############################################################################
#############################################################################
##
#P IsLeftMagmaIdeal( <D> )
##
## A *left magma ideal* is a submagma (see~"Magmas") which is closed under
## left multiplication by elements of its parent magma.
##
DeclareSynonym("IsLeftMagmaIdeal", IsMagma and IsLeftActedOnBySuperset);
## As a sub magma, a left magma ideal has a Parent (the enclosing magma)
## and as LeftActedOnBySuperset it has a LeftActingDomain.
## We must ensure that these two are the same object when the
## left magma ideal is created.
##
#############################################################################
##
#F LeftMagmaIdeal(<D>, <gens> )
##
## `LeftMagmaIdeal' returns the magma containing the elements in the
## homogeneous list <gens> and closed under left multiplication by elements
## of the magma <D> in which it embeds.
##
## This has to put in the parent and left acting set. Although it is a
## submagma, we can't call the generic submagma creation since that
## requires *magma* generators.
##
##
DeclareGlobalFunction( "LeftMagmaIdeal" );
#############################################################################
##
#O AsLeftMagmaIdeal( <D>, <C> )
##
## Let <D> be a domain and <C> a collection.
## If <C> is a subset of <D>
## `AsLeftMagmaIdeal' returns the LeftMagmaIdeal with generators <C>,
## and with parent <D>.
## Otherwise `fail' is returned.
## Probably more desirable would be to regard <C> as the set of
## elements of <D>.
##
DeclareOperation( "AsLeftMagmaIdeal", [ IsDomain, IsCollection ] );
#############################################################################
##
#A GeneratorsOfLeftMagmaIdeal( <I> )
##
## These are left ideal generators, not magma generators.
##
DeclareSynonymAttr( "GeneratorsOfLeftMagmaIdeal", GeneratorsOfExtLSet );
#############################################################################
##
#O LeftMagmaIdealByGenerators(<D>, <gens> )
##
## is the underlying operation of `LeftMagmaIdeal'
##
DeclareOperation( "LeftMagmaIdealByGenerators", [IsMagma, IsCollection ] );
#############################################################################
#############################################################################
##
##
## Right Magma Ideals
##
##
#############################################################################
#############################################################################
#############################################################################
##
#P IsRightMagmaIdeal( <D> )
##
## A *right magma ideal* is a submagma (see~"Magmas") which is closed under
## right multiplication by elements of its parent magma.
##
DeclareSynonym("IsRightMagmaIdeal", IsMagma and IsRightActedOnBySuperset);
## As a sub magma, a right magma ideal has a Parent (the enclosing magma)
## and as RightActedOnBySuperset it has a RightActingDomain.
## We must ensure that these two are the same object when the
## right magma ideal is created.
##
#############################################################################
##
#F RightMagmaIdeal(<D>, <gens> ) . . . . . . . . . .
##
## `RightMagmaIdeal' returns the magma containing the elements in the
## homogeneous list <gens> and closed under right multiplication by elements
## of the parent magma <D> in which it embeds.
##
##
DeclareGlobalFunction( "RightMagmaIdeal" );
#############################################################################
##
#O AsRightMagmaIdeal( <D>, <C> )
##
## Let <D> be a domain and <C> a collection.
## If <C> is a subset of <D> that forms a RightMagmaIdeal then
## `AsRightMagmaIdeal' returns this RightMagmaIdeal, with parent <D>.
## Otherwise `fail' is returned.
##
DeclareOperation( "AsRightMagmaIdeal", [ IsDomain, IsCollection ] );
#############################################################################
##
#A GeneratorsOfRightMagmaIdeal( <I> )
##
## These are right ideal generators, not magma generators.
##
DeclareSynonymAttr( "GeneratorsOfRightMagmaIdeal", GeneratorsOfExtRSet );
#############################################################################
##
#O RightMagmaIdealByGenerators(<D>, <gens> )
##
## is the underlying operation of `RightMagmaIdeal'
##
DeclareOperation( "RightMagmaIdealByGenerators", [IsMagma, IsCollection ] );
#############################################################################
#############################################################################
##
##
## Two Sided Magma Ideals
##
##
#############################################################################
#############################################################################
#############################################################################
##
#P IsMagmaIdeal( <D> )
##
## A *magma ideal* is a submagma (see~"Magmas") which is closed under
## left and right multiplication by elements of its parent magma.
##
DeclareSynonym("IsMagmaIdeal", IsLeftMagmaIdeal and IsRightMagmaIdeal);
## As a sub magma, a magma ideal has a Parent (the enclosing magma)
## and as LeftActedOnBySuperset it has a LeftActingDomain,
## and as RightActedOnBySuperset it has a RightActingDomain.
## We must ensure that these three are the same object when the
## magma ideal is created.
##
#############################################################################
##
#F MagmaIdeal(<D>, <gens> )
##
## `MagmaIdeal' returns the magma containing the elements in the homogeneous
## list <gens> and closed under left and right multiplication by elements
## of the parent magma <D> in which it emeds.
##
##
DeclareGlobalFunction( "MagmaIdeal" );
#############################################################################
##
#O AsMagmaIdeal( <D>, <C> )
##
## Let <D> be a domain and <C> a collection.
## If <C> is a subset of <D> that forms a MagmaIdeal then
## `AsMagmaIdeal' returns this MagmaIdeal, with parent <D>.
## Otherwise `fail' is returned.
##
DeclareOperation( "AsMagmaIdeal", [ IsDomain, IsCollection ] );
#############################################################################
##
#A GeneratorsOfMagmaIdeal( <I> )
##
## These are ideal generators, not magma generators.
##
DeclareAttribute( "GeneratorsOfMagmaIdeal", IsMagmaIdeal );
#############################################################################
##
#O MagmaIdealByGenerators( <D>, <gens> )
##
## is the underlying operation of `MagmaIdeal'
##
DeclareOperation( "MagmaIdealByGenerators", [IsMagma, IsCollection ] );
#############################################################################
##
#E
|