from sage.all import *
-def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None):
- r"""
- Generate a random rational convex polyhedral cone.
-
- Lower and upper bounds may be provided for both the dimension of the
- ambient space and the number of generating rays of the cone. If a
- lower bound is left unspecified, it defaults to zero. Unspecified
- upper bounds will be chosen randomly.
-
- INPUT:
-
- - ``min_dim`` (default: zero) -- A nonnegative integer representing the
- minimum dimension of the ambient lattice.
-
- - ``max_dim`` (default: random) -- A nonnegative integer representing
- the maximum dimension of the ambient
- lattice.
-
- - ``min_rays`` (default: zero) -- A nonnegative integer representing the
- minimum number of generating rays of the
- cone.
-
- - ``max_rays`` (default: random) -- A nonnegative integer representing the
- maximum number of generating rays of the
- cone.
-
- OUTPUT:
-
- A new, randomly generated cone.
-
- EXAMPLES:
-
- If we set the lower/upper bounds to zero, then our result is
- predictable::
-
- sage: random_cone(0,0,0,0)
- 0-d cone in 0-d lattice N
-
- In fact, as long as we ask for zero rays, we should be able to predict
- the output when ``min_dim == max_dim``::
-
- sage: random_cone(min_dim=4, max_dim=4, min_rays=0, max_rays=0)
- 0-d cone in 4-d lattice N
-
- TESTS:
-
- It's hard to test the output of a random process, but we can at
- least make sure that we get a cone back::
-
- sage: from sage.geometry.cone import is_Cone # long time
- sage: K = random_cone() # long time
- sage: is_Cone(K) # long time
- True
-
- Ensure that an exception is raised when either lower bound is greater
- than its respective upper bound::
-
- sage: random_cone(min_dim=5, max_dim=2)
- Traceback (most recent call last):
- ...
- ValueError: max_dim must be greater than or equal to min_dim.
-
- sage: random_cone(min_rays=5, max_rays=2)
- Traceback (most recent call last):
- ...
- ValueError: max_rays must be greater than or equal to min_rays.
-
- """
-
- # Catch obvious mistakes so that we can generate clear error
- # messages.
-
- if min_dim < 0:
- raise ValueError('min_dim must be nonnegative.')
-
- if min_rays < 0:
- raise ValueError('min_rays must be nonnegative.')
-
- if max_dim is not None:
- if max_dim < 0:
- raise ValueError('max_dim must be nonnegative.')
- if (min_dim > max_dim):
- raise ValueError('max_dim must be greater than or equal to min_dim.')
-
- if max_rays is not None:
- if max_rays < 0:
- raise ValueError('max_rays must be nonnegative.')
- if (min_rays > max_rays):
- raise ValueError('max_rays must be greater than or equal to min_rays.')
-
-
- def random_min_max(l,u):
- r"""
- We need to handle two cases for the upper bounds, and we need to do
- the same thing for max_dim/max_rays. So we consolidate the logic here.
- """
- if u is None:
- # The upper bound is unspecified; return a random integer
- # in [l,infinity).
- return l + ZZ.random_element().abs()
- else:
- # We have an upper bound, and it's greater than or equal
- # to our lower bound. So we generate a random integer in
- # [0,u-l], and then add it to l to get something in
- # [l,u]. To understand the "+1", check the
- # ZZ.random_element() docs.
- return l + ZZ.random_element(u - l + 1)
-
-
- d = random_min_max(min_dim, max_dim)
- r = random_min_max(min_rays, max_rays)
-
- L = ToricLattice(d)
- rays = [L.random_element() for i in range(0,r)]
-
- # The lattice parameter is required when no rays are given, so we
- # pass it just in case.
- return Cone(rays, lattice=L)
-
-
def discrete_complementarity_set(K):
r"""
Compute the discrete complementarity set of this cone.
projects / sage.d.git / blobdiff