&<(f1::CFACE, f2::CFACE)::boolean &>(f2::CFACE, f1::CFACE)::boolean f1 &< f2 f2 &> f1
Test whether f1 is a proper face of f2. Both faces must have identical domains.
&<<(f1::CFACE, f2::CFACE)::boolean &>>(f2::CFACE, f1::CFACE)::boolean f1 &<< f2 f2 &>> f1
Test whether f1 is a facet of f2. Both faces must have identical domains.
&<=(f1::CFACE, f2::CFACE)::boolean &>=(f2::CFACE, f1::CFACE)::boolean f1 &<= f2 f2 &>= f1
Test whether f1 is a face of f2. Both faces must have identical domains.
&<>(f1::CFACE, f2::CFACE)::boolean f1 &<> f2
Test whether f1 and f2 represent different faces. This is true if their domains are not identical.
&=(f1::CFACE, f2::CFACE)::boolean f1 &= f2
Test whether f1 and f2 represent the same face. This is false if their domains are not identical.
&x(f1::CFACE, f2::CFACE, ...)::CFACE f1 &x f2
The Cartesian product of the given faces, considered as a face of the Cartesian product of their domains. See CONE[&x].
ambientdim(f::CFACE)::nonnegint
The dimension of the ambient space of f.
codim(f::CFACE)::nonnegint
The codimension of f in its ambient space. See also CONE[codim], dim and corank.
convert(f::CFACE, CONE)::CONE
This functions converts f to the CONE representing the same point set.
convert(f::CFACE, PFACE)::PFACE
The domain of f is converted to a POLYHEDRON, using CONE[convert/POLYHEDRON], and the face of the resulting polyhedron P which is determined by f is returned. Note that this map from the faces of domain(f) to the faces of P may not be injective.
convert(f::CFACE, affine)::PFACE convert(f::CFACE, affine, v::vec)::PFACE
The PFACE representing the same point set, but now as a face of the converted domain convert(domain(f), affine) or convert(domain(f), affine, v). See CONE[convert/affine].
| C := posorthant(3); f := support(C, [0, 2, 1/3]); rays(f); |
| f2 := convert(f, affine, [1, 2, 3]); vertices(f2), rays(f2); |
| domain(f2) &= convert(C, affine, [1, 2, 3]); |
corank(f::CFACE)::nonnegint
The corank of f in the face lattice of its domain. This is the distance between f and the maximal element of the face lattice. See also rank.
dim(f::CFACE)::nonnegint
The dimension of f.
domain(f::CFACE)::CONE
The domain of a CFACE. This is the cone of which it is a face. See also CONE[isface].
dual(f::CFACE)::CFACE
The face dual to f, which is a face of the dual of the domain of f. Note that this is not the same as the cone dual to f, considered as a cone.
hspacenos(f::CFACE)::set(posint)
The set of indices of the facets incident to f. The ordering is that of hspaces(domain(f)), see CONE[hspaces]. This is a low-level routine.
hspaces(f::CFACE)::list(vec)
A list of the normal vectors of the halfspaces of domain(f) containing f. See CONE[hspaces]. Do not make any assumption about the order.
ispointed(f::CFACE)::boolean
Test whether f is pointed. See CONE[ispointed].
isregular(f::CFACE)::boolean isregular(f::CFACE, B::name)::boolean
Test whether f is regular. See CONE[isregular].
maximum(f1::CFACE, f2::CFACE, ...)::CFACE
The maximum of f1, f2 ... in the face lattice. All faces must have the same domain, which will also be the domain of the result. At least one face must be given.
minimum(f1::CFACE, f2::CFACE, ...)::CFACE
The minimum of f1, f2 ... in the face lattice. All faces must have the same domain, which will also be the domain of the result. At least one face must be given.
pred(f::CFACE)::list(CFACE)
A list containing the predecessors of f in the face lattice of domain(f). These are the faces whose rank is one smaller than that of f, or, in other words, the facets of f. See also succ.
preimage(f::CFACE, A::{mat, rational, real_infinity})::CFACE
The preimage of f, considered as a face of the preimage of the domain of f. See CONE[preimage].
rank(f::CFACE)::nonnegint
The rank of f in the face lattice of its domain. This is the distance between f and the minimal element of the lattice (which corresponds to the lineality space of the domain.)
raynos(f::CFACE)::set(posint)
The set of indices of the rays incident to f. The ordering is that of rays(domain(f)), see CONE[rays]. This is a low-level routine.
rays(f::CFACE)::list(vec)
A list of the rays of f. See CONE[rays]. Do not make any assumption about the order.
relint(f::)::vec
A point in the relative interior of f.
succ(f::CFACE)::list(CFACE)
A list containing the successors of f in the face lattice of domain(f). These are the faces whose rank is one bigger than that of f, or, in other words, the faces of which f is a facet. See also pred.