def add_assumption(self, lincomb, bound):
"""Assumption of the form [(perm, coef), ..., (perm, coef)] \geq bound."""
# switch on 'assumptions mode'
if self.assumptions is False:
self.assumptions = True
assumption_densities = [-Rational(bound) for x in range(len(self.admissible_perms))]
for densperm, coeff in lincomb:
densperm = PermFlag(densperm)
if self.N < densperm.N: # if too big to fit, then skip
continue
combs = Combinations(range(self.N), densperm.N)
numcombs = combs.cardinality()
# for each admissible permutation, compute the density of densperm in it
for i in range(len(self.admissible_perms)):
admissibleperm = self.admissible_perms[i]
counter = 0 # number of copies of densperm in admissible perm
for c in combs:
admissible_subperm = normalize([admissibleperm.perm[x] for x in c], densperm.N)
admissible_subflag = PermFlag(admissible_subperm)
if admissible_subflag == densperm:
counter += 1
assumption_densities[i] += coeff*Integer(counter)/numcombs
#sys.stdout.write("assumption_densities[i] = %s\n" % str(assumption_densities[i]))
self.assumption_densities.append(assumption_densities)
def _compute_densities(self):
densities = [0 for x in range(len(self.admissible_perms))]
for densperm, coeff in self.density_pattern:
if self.N < densperm.N: # too big to fit, then skip
continue
combs = Combinations(range(self.N), densperm.N)
numcombs = combs.cardinality()
# for each admissible permutation, compute the density of densperm in it
for i in range(len(self.admissible_perms)):
admissibleperm = self.admissible_perms[i]
counter = 0 # number of copies of densperm in admissibleperm
for c in combs:
admissible_subperm = normalize([admissibleperm.perm[x] for x in c], densperm.N)
admissible_subflag = PermFlag(admissible_subperm)
if admissible_subflag == densperm:
counter += 1
densities[i] += coeff*Integer(counter)/numcombs
return densities
def subperm_density(self, perm):
"""
Return density of perm in self.
INPUT:
- perm: permutation of type PermFlag
EXAMPLE:
sage: P = PermFlag("1234765")
sage: P.subperm_density(PermFlag("123"))
22/35
"""
combs = Combinations(self.N, perm.N)
counter = 0
for c in combs:
if self._induced_subpattern(c) == perm.perm:
counter += 1
return Integer(counter) / combs.cardinality()