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EquivariantMap ** EquivariantMap -- computes the product of two equivariant morphisms

Synopsis

Description

This method computes the cartesian product of two equivariant morphisms.

i1 : R = makeCharacterRing 3;
i2 : X = generalizedFlagVariety("A",2,{1,2},R);
i3 : Y = generalizedFlagVariety("A",2,{1},R);
i4 : f = flagMap(X,Y); -- the projection of Fl(1,2;3) onto Gr(2,3)
i5 : h = f ** f

o5 = an "equivariant map" of GKM varieties 

o5 : EquivariantMap
i6 : peek h

o6 = EquivariantMap{cache => CacheTable{}                                                                        }
                    ptsMap => HashTable{({set {0}, set {0, 1}}, {set {0}, set {0, 1}}) => ({set {0}}, {set {0}})}
                                        ({set {0}, set {0, 1}}, {set {0}, set {0, 2}}) => ({set {0}}, {set {0}})
                                        ({set {0}, set {0, 1}}, {set {1}, set {0, 1}}) => ({set {0}}, {set {1}})
                                        ({set {0}, set {0, 1}}, {set {1}, set {1, 2}}) => ({set {0}}, {set {1}})
                                        ({set {0}, set {0, 1}}, {set {2}, set {0, 2}}) => ({set {0}}, {set {2}})
                                        ({set {0}, set {0, 1}}, {set {2}, set {1, 2}}) => ({set {0}}, {set {2}})
                                        ({set {0}, set {0, 2}}, {set {0}, set {0, 1}}) => ({set {0}}, {set {0}})
                                        ({set {0}, set {0, 2}}, {set {0}, set {0, 2}}) => ({set {0}}, {set {0}})
                                        ({set {0}, set {0, 2}}, {set {1}, set {0, 1}}) => ({set {0}}, {set {1}})
                                        ({set {0}, set {0, 2}}, {set {1}, set {1, 2}}) => ({set {0}}, {set {1}})
                                        ({set {0}, set {0, 2}}, {set {2}, set {0, 2}}) => ({set {0}}, {set {2}})
                                        ({set {0}, set {0, 2}}, {set {2}, set {1, 2}}) => ({set {0}}, {set {2}})
                                        ({set {1}, set {0, 1}}, {set {0}, set {0, 1}}) => ({set {1}}, {set {0}})
                                        ({set {1}, set {0, 1}}, {set {0}, set {0, 2}}) => ({set {1}}, {set {0}})
                                        ({set {1}, set {0, 1}}, {set {1}, set {0, 1}}) => ({set {1}}, {set {1}})
                                        ({set {1}, set {0, 1}}, {set {1}, set {1, 2}}) => ({set {1}}, {set {1}})
                                        ({set {1}, set {0, 1}}, {set {2}, set {0, 2}}) => ({set {1}}, {set {2}})
                                        ({set {1}, set {0, 1}}, {set {2}, set {1, 2}}) => ({set {1}}, {set {2}})
                                        ({set {1}, set {1, 2}}, {set {0}, set {0, 1}}) => ({set {1}}, {set {0}})
                                        ({set {1}, set {1, 2}}, {set {0}, set {0, 2}}) => ({set {1}}, {set {0}})
                                        ({set {1}, set {1, 2}}, {set {1}, set {0, 1}}) => ({set {1}}, {set {1}})
                                        ({set {1}, set {1, 2}}, {set {1}, set {1, 2}}) => ({set {1}}, {set {1}})
                                        ({set {1}, set {1, 2}}, {set {2}, set {0, 2}}) => ({set {1}}, {set {2}})
                                        ({set {1}, set {1, 2}}, {set {2}, set {1, 2}}) => ({set {1}}, {set {2}})
                                        ({set {2}, set {0, 2}}, {set {0}, set {0, 1}}) => ({set {2}}, {set {0}})
                                        ({set {2}, set {0, 2}}, {set {0}, set {0, 2}}) => ({set {2}}, {set {0}})
                                        ({set {2}, set {0, 2}}, {set {1}, set {0, 1}}) => ({set {2}}, {set {1}})
                                        ({set {2}, set {0, 2}}, {set {1}, set {1, 2}}) => ({set {2}}, {set {1}})
                                        ({set {2}, set {0, 2}}, {set {2}, set {0, 2}}) => ({set {2}}, {set {2}})
                                        ({set {2}, set {0, 2}}, {set {2}, set {1, 2}}) => ({set {2}}, {set {2}})
                                        ({set {2}, set {1, 2}}, {set {0}, set {0, 1}}) => ({set {2}}, {set {0}})
                                        ({set {2}, set {1, 2}}, {set {0}, set {0, 2}}) => ({set {2}}, {set {0}})
                                        ({set {2}, set {1, 2}}, {set {1}, set {0, 1}}) => ({set {2}}, {set {1}})
                                        ({set {2}, set {1, 2}}, {set {1}, set {1, 2}}) => ({set {2}}, {set {1}})
                                        ({set {2}, set {1, 2}}, {set {2}, set {0, 2}}) => ({set {2}}, {set {2}})
                                        ({set {2}, set {1, 2}}, {set {2}, set {1, 2}}) => ({set {2}}, {set {2}})
                    source => a "GKM variety" with an action of a 3-dimensional torus
                    target => a "GKM variety" with an action of a 3-dimensional torus

See also

Ways to use this method: