&x(C1::FANCONE, ...)::FANCONE C1::FANCONE &x C2::FANCONE
If all arguments are of type FANCONE, then so is the result. The domain of the result is the Cartesian product of the arguments' domains. See CONE[&x] and FAN[&x].
arecompatible(C1::FANCONE, C2::FANCONE, C::name)::boolean
If C1 and C2 have the same domain F, then the (optional) third argument C receives a FANCONE whose domain is F. (In other words, C receives the minimum of C1 and C2.) See CONE[arecompatible] and minimum.
convert(C::FANCONE, POLYHEDRON)::CELL
If applied to a FANCONE, this function returns a CELL whose domain is the conversion the domain of C to a PCOMPLEX. See FAN[convert/PCOMPLEX].
convert(C::FANCONE, affine, v::vec)::CELL
If applied to a FANCONE, this function returns a CELL whose domain is the conversion the domain of C to a PCOMPLEX representing the same fan in affine space (and, if v is given, with origin translated to v). See FAN[convert/affine].
domain(C::FANCONE)::FAN
The domain of C. This is the fan to which it belongs.
maximum(C1::FANCONE, ...)::{FANCONE, 'FAIL'}
The maximum of the given arguments, i.e., the smallest fancone containing them all. If no such cone exists, the functions returns FAIL. All arguments must have the same domain; at least one argument must be given.
minimum(C1::FANCONE, ...)::FANCONE
The minimum of the given arguments, i.e., the largest fancone contained in all of them. All arguments must have the same domain; at least one argument must be given. Note that the minimum is just the intersection of the arguments (but with the additional domain information).
preimage(C::FANCONE, A::{mat, rational, real_infinity})::FANCONE
The result is a FANCONE whose domain is the preimage of the domain of C. See CONE[preimage] and FAN[preimage].
tranversalfan(C::FANCONE, A::name)::FAN
The fan "transversal" to C in domain(C). The optional argument A receives the mat associated with the projection onto the quotient lattice.
The name "transversal fan" was suggested by Gottfried Barthel. In W. Fulton, Introduction to Toric Varieties, Princeton 1993, it is called the "star", and in fact the elements of the transversal fan of C correspond bijectively to the elements of the star of C.