Flat -- intersection of hyperplanes

Functions and methods returning a flat in an hyperplane arrangement:

• closure(Arrangement,Ideal) -- see closure(Arrangement,List) -- closure operation in the intersection lattice
• closure(Arrangement,List) -- closure operation in the intersection lattice
• flat(Arrangement,List) -- make a flat from a list of indices
• Flat ^ Flat -- see meet(Flat,Flat) -- compute the meet operation in the intersection lattice
• meet(Flat,Flat) -- compute the meet operation in the intersection lattice
• Flat | Flat -- see vee(Flat,Flat) -- compute the vee operation in the intersection lattice
• vee(Flat,Flat) -- compute the vee operation in the intersection lattice

Methods that use a flat in an hyperplane arrangement:

• arrangement(Flat) -- get the hyperplane arrangement to which a flat belongs
• euler(Flat) -- see euler(CentralArrangement) -- compute the Euler characteristic of the projective complement
• Flat == Flat -- whether two flats are equal
• rank(Flat) -- compute the rank of a flat
• Arrangement ^ Flat -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• restriction(Arrangement,Flat) -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• restriction(Flat) -- see restriction(Arrangement,Ideal) -- construct the restriction a hyperplane arrangement to a subspace
• Arrangement _ Flat -- see subArrangement(Arrangement,Flat) -- create the hyperplane arrangement containing a flat
• subArrangement(Arrangement,Flat) -- create the hyperplane arrangement containing a flat
• subArrangement(Flat) -- see subArrangement(Arrangement,Flat) -- create the hyperplane arrangement containing a flat
• toList(Flat) -- the indices of a flat

For the programmer

The object Flat is a type, with ancestor classes HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/HyperplaneArrangements.m2:2322:0.