GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#############################################################################
##
## Polymake.gd ConvexForHomalg package Sebastian Gutsche
##
## Copyright 2011-2012 Lehrstuhl B für Mathematik, RWTH Aachen
##
## Gives the Methods for Polymake
##
#############################################################################
####################################
#
# Cone Methods
#
####################################
##
InstallMethod( EXT_CREATE_CONE_BY_RAYS,
"Create Cone in Polymake",
[ IsList ],
POLYMAKE_CREATE_CONE_BY_RAYS
);
##
InstallMethod( EXT_CREATE_CONE_BY_RAYS_UNSAVE,
"Create Cone in Polymake",
[ IsList ],
POLYMAKE_CREATE_CONE_BY_RAYS_UNSAVE
);
##
InstallMethod( EXT_CREATE_CONE_BY_INEQUALITIES,
"create cone in polymake",
[ IsList ],
POLYMAKE_CREATE_CONE_BY_INEQUALITIES
);
##
InstallMethod( EXT_CREATE_CONE_BY_EQUALITIES_AND_INEQUALITIES,
"create cone in polymake",
[ IsList, IsList ],
POLYMAKE_CREATE_CONE_BY_EQUALITIES_AND_INEQUALITIES
);
##
InstallMethod( EXT_CREATE_DUAL_CONE_OF_CONE,
"Create Cone in Polymake",
[ IsExternalPolymakeCone ],
POLYMAKE_CREATE_DUAL_CONE_OF_CONE
);
##
InstallMethod( EXT_GENERATING_RAYS_OF_CONE,
"Create Cone in Polymake",
[ IsExternalPolymakeCone ],
POLYMAKE_GENERATING_RAYS_OF_CONE
);
##
InstallMethod( EXT_RAYS_IN_FACETS,
" for polymake cones.",
[ IsExternalPolymakeCone ],
POLYMAKE_RAYS_IN_FACETS
);
##
InstallMethod( EXT_IS_BOUNDED_POLYTOPE,
" for polymake cones.",
[ IsExternalPolymakePolytope ],
POLYMAKE_IS_BOUNDED_POLYTOPE
);
##
InstallMethod( EXT_LINEAR_SUBSPACE,
"for polymake cones",
[ IsExternalPolymakeCone ],
POLYMAKE_LINEALITY_SPACE_OF_CONE
);
####################################
##
## Fan Methods
##
####################################
##
InstallMethod( EXT_FAN_BY_CONES,
" for lists of cones",
[ IsList ],
POLYMAKE_FAN_BY_CONES
);
##
InstallMethod( EXT_FAN_BY_RAYS_AND_CONES,
" for lists of rays and cones.",
[ IsList, IsList ],
POLYMAKE_FAN_BY_RAYS_AND_CONES
);
##
InstallMethod( EXT_FAN_BY_RAYS_AND_CONES_UNSAVE,
"for lists of rays and cones.",
[ IsList, IsList ],
POLYMAKE_FAN_BY_RAYS_AND_CONES_UNSAVE
);
####################################
##
## PolytopeMethods
##
####################################
##
InstallMethod( EXT_CREATE_POLYTOPE_BY_POINTS,
"create polytope in polymake.",
[ IsList ],
POLYMAKE_CREATE_POLYTOPE_BY_POINTS
);
##
InstallMethod( EXT_CREATE_POLYTOPE_BY_INEQUALITIES,
"create polytope in polymake.",
[ IsList ],
POLYMAKE_CREATE_POLYTOPE_BY_INEQUALITIES
);
##
InstallMethod( EXT_LATTICE_POINTS_OF_POLYTOPE,
" for polymake polytopes.",
[ IsExternalPolymakePolytope ],
POLYMAKE_LATTICE_POINTS_OF_POLYTOPE
);
##
InstallMethod( EXT_VERTICES_OF_POLYTOPE,
" for polymake polytopes.",
[ IsExternalPolymakePolytope ],
POLYMAKE_VERTICES_OF_POLYTOPE
);
####################################
##
## Property functions
##
####################################
##
InstallMethod( EXT_IS_POINTED_CONE,
"Checks if some cone is pointed",
[ IsExternalPolymakeCone ],
POLYMAKE_IS_STRICTLY_CONVEX_CONE
);
##
InstallMethod( EXT_IS_SMOOTH_CONE,
"Checks if some cone is pointed",
[ IsExternalPolymakeCone ],
POLYMAKE_IS_SMOOTH_CONE
);
##
InstallMethod( EXT_IS_VERY_AMPLE_POLYTOPE,
" for homalg polytope.",
[ IsExternalPolymakePolytope ],
POLYMAKE_IS_VERYAMPLE_OBJECT
);
##
InstallMethod( EXT_IS_COMPLETE_FAN,
" for polymake fans.",
[ IsExternalPolymakeFan ],
POLYMAKE_IS_COMPLETE_FAN
);
##
InstallMethod( EXT_IS_POINTED_FAN,
" for polymake fans.",
[ IsExternalPolymakeFan ],
POLYMAKE_IS_POINTED_FAN
);
##
InstallMethod( EXT_IS_SMOOTH_FAN,
" for polymake fans.",
[ IsExternalPolymakeFan ],
POLYMAKE_IS_SMOOTH_FAN
);
##
InstallMethod( EXT_IS_SIMPLICIAL_CONE,
" for polymake cones.",
[ IsExternalPolymakeCone ],
POLYMAKE_IS_SIMPLICIAL_CONE
);
##
InstallMethod( EXT_IS_SIMPLICIAL_POLYTOPE,
" for polymake polytopes.",
[ IsExternalPolymakePolytope ],
POLYMAKE_IS_SIMPLICIAL_OBJECT
);
##
InstallMethod( EXT_IS_SIMPLE_POLYTOPE,
" for polymake polytopes.",
[ IsExternalPolymakePolytope ],
POLYMAKE_IS_SIMPLE_OBJECT
);
##
InstallMethod( EXT_IS_LATTICE_POLYTOPE,
" for polymake polytopes.",
[ IsExternalPolymakePolytope ],
POLYMAKE_IS_LATTICE_OBJECT
);
##
InstallMethod( EXT_IS_NOT_EMPTY_POLYTOPE,
" for polymake polytopes.",
[ IsExternalPolymakePolytope ],
POLYMAKE_IS_NONEMPTY_POLYTOPE
);
##
InstallMethod( EXT_IS_NORMAL_POLYTOPE,
" for polymake polytopes.",
[ IsExternalPolymakePolytope ],
POLYMAKE_IS_NORMAL_OBJECT
);
##
InstallMethod( EXT_IS_REGULAR_FAN,
" for polymake polytopes.",
[ IsExternalPolymakeFan ],
POLYMAKE_IS_REGULAR_OBJECT
);
##
InstallMethod( EXT_IS_FULL_DIMENSIONAL_CONE,
" for polymake cones.",
[ IsExternalPolymakeCone ],
POLYMAKE_IS_FULL_DIMENSIONAL_OBJECT
);
##
InstallMethod( EXT_IS_FULL_DIMENSIONAL_FAN,
" for polymake cones.",
[ IsExternalPolymakeFan ],
POLYMAKE_IS_FULL_DIMENSIONAL_OBJECT
);
##
InstallMethod( EXT_EQUALITIES_OF_CONE,
" for polymake cones.",
[ IsExternalPolymakeCone ],
POLYMAKE_EQUALITIES_OF_CONE
);
##################################
##
## Attribute Methods
##
##################################
##
InstallMethod( EXT_AMBIENT_DIM_OF_CONE,
"computes ambient dim of polymake cone.",
[ IsExternalPolymakeCone ],
POLYMAKE_AMBIENT_DIM_OF_CONE
);
##
InstallMethod( EXT_DIM_OF_CONE,
"computes ambient dim of polymake cone.",
[ IsExternalPolymakeCone ],
POLYMAKE_DIM_OF_CONE
);
##
InstallMethod( EXT_HILBERT_BASIS_OF_CONE,
"computes hilbert basis for polymake cone",
[ IsExternalPolymakeCone ],
POLYMAKE_HILBERT_BASIS_OF_CONE
);
##
InstallMethod( EXT_RAYS_OF_FAN,
" computes fans of polymake fan",
[ IsExternalPolymakeFan ],
POLYMAKE_RAYS_OF_FAN
);
# ##
# InstallMethod( EXT_RAYS_OF_FAN,
# " computes fans of polymake fan",
# [ IsExternalPolymakeCone ],
#
# POLYMAKE_RAYS_OF_FAN
#
# );
##
InstallMethod( EXT_RAYS_IN_MAXCONES_OF_FAN,
" computes fans of polymake fan",
[ IsExternalPolymakeFan ],
POLYMAKE_RAYS_IN_MAXCONES_OF_FAN
);
##
InstallMethod( EXT_NORMALFAN_OF_POLYTOPE,
" computes fans of polymake fan",
[ IsExternalPolymakePolytope ],
POLYMAKE_NORMALFAN_OF_POLYTOPE
);
##
InstallMethod( EXT_DIM_OF_FAN,
" computes fans of polymake fan",
[ IsExternalPolymakeFan ],
POLYMAKE_DIM_OF_FAN
);
##
InstallMethod( EXT_AMBIENT_DIM_OF_FAN,
" computes fans of polymake fan",
[ IsExternalPolymakeFan ],
POLYMAKE_AMBIENT_DIM_OF_FAN
);
##
InstallMethod( EXT_DRAW,
"draws a polymake object",
[ IsExternalPolymakeObject ],
POLYMAKE_DRAW
);
##
InstallMethod( EXT_DEFINING_INEQUALITIES_OF_CONE,
" computes inequalities of polymake cone",
[ IsExternalPolymakeCone ],
POLYMAKE_DEFINING_INEQUALITIES_OF_CONE
);
##
InstallMethod( EXT_FACET_INEQUALITIES_OF_POLYTOPE,
" for polymake polytopes",
[ IsExternalPolymakePolytope ],
POLYMAKE_FACET_INEQUALITIES_OF_POLYTOPE
);
##
InstallMethod( EXT_VERTICES_IN_FACETS,
" for polymake polytopes",
[ IsExternalPolymakePolytope ],
POLYMAKE_RAYS_IN_FACETS
);
##
InstallMethod( EXT_INT_LATTICE_POINTS,
" for polymake polytopes.",
[ IsExternalPolymakePolytope ],
POLYMAKE_INTERIOR_LATTICE_POINTS
);
##
InstallMethod( EXT_CREATE_POLYTOPE_BY_HOMOGENEOUS_POINTS,
"for polymake polytopes.",
[ IsList ],
POLYMAKE_CREATE_POLYTOPE_BY_HOMOGENEOUS_POINTS
);
##
InstallMethod( EXT_HOMOGENEOUS_POINTS_OF_POLYTOPE,
"for polymake polytopes",
[ IsExternalPolymakePolytope ],
POLYMAKE_HOMOGENEOUS_POINTS_OF_POLYTOPE
);
##
InstallMethod( EXT_TAIL_CONE_OF_POLYTOPE,
"for polymake polytopes",
[ IsExternalPolymakePolytope ],
POLYMAKE_TAIL_CONE_OF_POLYTOPE
);
##
InstallMethod( EXT_MINKOWSKI_SUM,
"for polymake polytopes",
[ IsExternalPolymakePolytope, IsExternalPolymakePolytope ],
POLYMAKE_MINKOWSKI_SUM
);
##
InstallMethod( EXT_STELLAR_SUBDIVISION,
"for polymake polytopes",
[ IsExternalPolymakeCone , IsExternalPolymakeFan ],
POLYMAKE_STELLAR_SUBDIVISION
);
##
InstallMethod( EXT_INTERSECTION_OF_CONES,
"for polymake cones",
[ IsExternalPolymakeCone, IsExternalPolymakeCone ],
POLYMAKE_INTERSECTION_OF_CONES
);
##
InstallMethod( EXT_INTERSECTION_OF_POLYTOPES,
"for polymake cones",
[ IsExternalPolymakePolytope, IsExternalPolymakePolytope ],
POLYMAKE_INTERSECTION_OF_POLYTOPES
);
##
InstallMethod( EXT_EQUALITIES_OF_POLYTOPE,
"for polymake polytopes",
[ IsExternalPolymakePolytope ],
POLYMAKE_EQUALITIES_OF_POLYTOPE
);
##
InstallMethod( EXT_LATTICE_POINTS_GENERATORS,
"for polymake polytopes",
[ IsExternalPolymakePolytope ],
POLYMAKE_LATTICE_POINTS_GENERATORS
);
##
InstallMethod( EXT_F_VECTOR,
"for polymake fans",
[ IsExternalPolymakeFan ],
POLYMAKE_F_VECTOR_OF_FAN
);