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# encoding=utf8
import PyNormaliz_cpp
from PyNormaliz_cpp import *
class Cone:
def __init__(self, *args, **kwargs):
input_list = [k for k in args]
for i in kwargs:
current_input = kwargs[i]
if type(current_input) == list and len(current_input) > 0 and type(current_input[0]) != list:
kwargs[i] = [current_input]
elif type(current_input) == bool and current_input == True:
kwargs[i] = current_input = [[]]
elif type(current_input) == bool and current_input == False:
kwargs.pop(i)
self.cone = PyNormaliz_cpp.NmzCone(input_list,**kwargs)
def __process_keyword_args(self, keywords):
input_list = []
for i in keywords:
if keywords[i] == True:
input_list.append(i)
return input_list
def print_properties(self):
props = PyNormaliz_cpp.NmzListConeProperties()
goals = props[0]
for x in goals:
if (PyNormaliz_cpp.NmzIsComputed(self.cone, x)):
print(x + ":")
print(PyNormaliz_cpp.NmzResult(self.cone, x))
print("\n")
def __str__(self):
return "<Normaliz Cone>"
def __repr__(self):
return "<Normaliz Cone>"
def Compute(self, *args):
return PyNormaliz_cpp.NmzCompute(self.cone, args)
def setVerbose(self, verbose=True):
return NmzSetVerbose(self.cone, verbose)
# This one is not like the others!
def IntegerHull(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IntegerHull")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
new_inner_cone = PyNormaliz_cpp.NmzResult(self.cone, "IntegerHull")
return_cone = Cone.__new__(Cone)
return_cone.cone = new_inner_cone
return return_cone
def ProjectCone(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ProjectCone")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
new_inner_cone = PyNormaliz_cpp.NmzResult(self.cone, "ProjectCone")
return_cone = Cone.__new__(Cone)
return_cone.cone = new_inner_cone
return return_cone
def EuclideanVolume(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Volume")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzGetEuclideanVolume(self.cone)
def HilbertSeries(self, **kwargs):
try:
as_hsop = kwargs["HSOP"]
except KeyError:
as_hsop = 28
input_list = self.__process_keyword_args(kwargs)
input_list.append("HilbertSeries")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
if as_hsop == 28:
return PyNormaliz_cpp.NmzHilbertSeries(self.cone)
if type(as_hsop) == bool:
return PyNormaliz_cpp.NmzHilbertSeries(self.cone, as_hsop)
raise TypeError("If HSOP is given, it must be True or False")
def EhrhartSeries(self, **kwargs):
try:
as_hsop = kwargs["HSOP"]
except KeyError:
as_hsop = 28
input_list = self.__process_keyword_args(kwargs)
input_list.append("EhrhartSeries")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
if as_hsop == 28:
return PyNormaliz_cpp.NmzHilbertSeries(self.cone)
if type(as_hsop) == bool:
return PyNormaliz_cpp.NmzHilbertSeries(self.cone, as_hsop)
raise TypeError("If HSOP is given, it must be True or False")
def Polynomial(self, **kwargs):
return PyNormaliz_cpp.NmzGetPolynomial(self.cone)
def NrCoeffQuasiPol(self, bound=-1):
return PyNormaliz_cpp.NmzSetNrCoeffQuasiPol(self.cone, bound)
def SymmetrizedCone(self, **kwargs):
new_inner_cone = PyNormaliz_cpp.NmzSymmetrizedCone(self.cone)
if new_inner_cone == None:
return None
return_cone = Cone.__new__(Cone)
return_cone.cone = new_inner_cone
return return_cone
def HilbertSeriesExpansion(self,degree):
return NmzGetHilbertSeriesExpansion(self.cone,degree)
def WeightedEhrhartSeriesExpansion(self,degree):
return NmzGetWeightedEhrhartSeriesExpansion(self.cone,degree)
def PrettyPolynomialTuple(self, numCoefficients, denCoefficients):
"""
Strings for numerator and denominator of the a hilbert series.
Parameters
----------
numCoefficients : list
The coefficients for the numerator.
denCofficients : list
The coefficients for the denominator where the value represents the
exponent of 't' and the frequency indicates the outer coefficient.
Returns
-------
PrettyPolynomialTuple: tuple of strings
Examples
--------
>>> numCoefficients = [3, 7, 4, -4, -6, 5]
>>> denCoefficients = [1, 1, 2, 2, 2, 4]
>>> PrettyPolynomialTuple(numCoefficients,denCoefficients)
('(3 + 7t + 4t² - 4t³ - 6t⁴ + 5t⁵)', '(1 - t)² (1 - t²)³ (1 - t⁴)')
"""
def to_sup(s):
sups = {u'0': u'\u2070',
u'1': u'\xb9',
u'2': u'\xb2',
u'3': u'\xb3',
u'4': u'\u2074',
u'5': u'\u2075',
u'6': u'\u2076',
u'7': u'\u2077',
u'8': u'\u2078',
u'9': u'\u2079'}
if s is 1:
return ''
# lose the list comprehension
return ''.join(sups.get(str(char), str(char)) for char in str(s))
def getNumerator(coefficients):
numerator = ''
def isPositive(x):
return x > 0
firstNonZero = next(
(i for i, x in enumerate(coefficients) if x != 0), 0)
for exp, coefficient in enumerate(coefficients):
if coefficient is 0:
continue
# Exponent is 0 so keep only the coefficient
if exp is 0:
numerator += '({}{!s}'.format('-' if not isPositive(coefficient)
else '', abs(coefficient))
# Only include sign if `coefficient` is negative
elif i is firstNonZero:
numerator += '{}{!s}t{}'.format('-' if not isPositive(
coefficient) else '', abs(coefficient), to_sup(exp))
else:
numerator += ' {}{!s}t{}'.format('+ ' if isPositive(
coefficient) else '- ', abs(coefficient), to_sup(exp))
numerator += ')'
return numerator
def getDenominator(coefficients):
exponents = [(inner, coefficients.count(inner))
for inner in set(coefficients)]
denominator = ' '.join('(1 - t{}){}'. format(to_sup(x[0]) if x[
0] is not 1 else '', to_sup(x[1]) if x[1] is not 1 else '') for x in exponents)
return denominator
num = getNumerator(numCoefficients)
den = getDenominator(denCoefficients)
prettyPolynomial = (num, den)
return prettyPolynomial
def PrintPrettyHilbertSeries(self, numCoefficients, denCoefficients):
"""
Make a pretty hilbert series string
Parameters
----------
numCoefficients : list of ints
The coefficients for the numerator.
denCofficients : list of ints
The coefficients for the denominator where the value represents
the exponent of 't' and the frequency indicates the outer
coefficient.
Returns
-------
PrintPrettyHilbertSeries : string
Examples
--------
>>> numCoefficients = [3, 7, 4, -4, -6, 5]
>>> deCoefficients = [1, 1, 2, 2, 2, 4]
>>> PrintPrettyHilbertSeries(numCoefficients,deCoefficients)
(3 + 7t + 4t² - 4t³ - 6t⁴ + 5t⁵)
--------------------------------
(1 - t)² (1 - t²)³ (1 - t⁴)
"""
num, den = self.PrettyPolynomialTuple(numCoefficients, denCoefficients)
prettyPolynomial = '{:^}\n{:-^{width}}\n{:^{width}}'.format(
num, '', den, width=max(len(den),len(num)))
return prettyPolynomial
def PrintHilbertSeries(self):
hilbert_series=self.HilbertSeries()
shift=hilbert_series[2]
shift=[ 0 for x in range(1,shift) ]
numerator=shift+hilbert_series[0]
denominator=hilbert_series[1]
print(self.PrintPrettyHilbertSeries(numerator,denominator))
return None
# Auto generated stuff
def Generators(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Generators")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Generators")
def ExtremeRays(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ExtremeRays")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "ExtremeRays")
def VerticesOfPolyhedron(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("VerticesOfPolyhedron")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "VerticesOfPolyhedron")
def SupportHyperplanes(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("SupportHyperplanes")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "SupportHyperplanes")
def HilbertBasis(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("HilbertBasis")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "HilbertBasis")
def ModuleGenerators(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ModuleGenerators")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "ModuleGenerators")
def Deg1Elements(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Deg1Elements")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Deg1Elements")
def ModuleGeneratorsOverOriginalMonoid(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ModuleGeneratorsOverOriginalMonoid")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "ModuleGeneratorsOverOriginalMonoid")
def Sublattice(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Sublattice")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Sublattice")
def ExcludedFaces(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ExcludedFaces")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "ExcludedFaces")
def OriginalMonoidGenerators(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("OriginalMonoidGenerators")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "OriginalMonoidGenerators")
def MaximalSubspace(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("MaximalSubspace")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "MaximalSubspace")
def Equations(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Equations")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Equations")
def Congruences(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Congruences")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Congruences")
def Grading(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Grading")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Grading")
def Dehomogenization(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Dehomogenization")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Dehomogenization")
def WitnessNotIntegrallyClosed(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("WitnessNotIntegrallyClosed")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "WitnessNotIntegrallyClosed")
def TriangulationSize(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("TriangulationSize")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "TriangulationSize")
def TriangulationDetSum(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("TriangulationDetSum")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "TriangulationDetSum")
def ReesPrimaryMultiplicity(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ReesPrimaryMultiplicity")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "ReesPrimaryMultiplicity")
def GradingDenom(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("GradingDenom")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "GradingDenom")
def UnitGroupIndex(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("UnitGroupIndex")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "UnitGroupIndex")
def InternalIndex(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("InternalIndex")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "InternalIndex")
def ExternalIndex(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ExternalIndex")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "ExternalIndex")
def Multiplicity(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Multiplicity")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Multiplicity")
def RecessionRank(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("RecessionRank")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "RecessionRank")
def AffineDim(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("AffineDim")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "AffineDim")
def ModuleRank(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ModuleRank")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "ModuleRank")
def Rank(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Rank")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Rank")
def EmbeddingDim(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("EmbeddingDim")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "EmbeddingDim")
def IsPointed(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IsPointed")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "IsPointed")
def IsDeg1ExtremeRays(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IsDeg1ExtremeRays")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "IsDeg1ExtremeRays")
def IsDeg1HilbertBasis(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IsDeg1HilbertBasis")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "IsDeg1HilbertBasis")
def IsIntegrallyClosed(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IsIntegrallyClosed")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "IsIntegrallyClosed")
def IsReesPrimary(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IsReesPrimary")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "IsReesPrimary")
def IsInhomogeneous(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IsInhomogeneous")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "IsInhomogeneous")
def Triangulation(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Triangulation")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Triangulation")
def InclusionExclusionData(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("InclusionExclusionData")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "InclusionExclusionData")
def StanleyDec(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("StanleyDec")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "StanleyDec")
def ClassGroup(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ClassGroup")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "ClassGroup")
def ConeDecomposition(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("ConeDecomposition")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "ConeDecomposition")
def HilbertQuasiPolynomial(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("HilbertQuasiPolynomial")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "HilbertQuasiPolynomial")
def EhrhartQuasiPolynomial(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("HilbertQuasiPolynomial")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "HilbertQuasiPolynomial")
def IsTriangulationNested(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IsTriangulationNested")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "IsTriangulationNested")
def IsTriangulationPartial(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IsTriangulationPartial")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "IsTriangulationPartial")
def WeightedEhrhartQuasiPolynomial(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("WeightedEhrhartQuasiPolynomial")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "WeightedEhrhartQuasiPolynomial")
def WeightedEhrhartSeries(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("WeightedEhrhartSeries")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "WeightedEhrhartSeries")
def Integral(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Integral")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Integral")
def VirtualMultiplicity(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("VirtualMultiplicity")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "VirtualMultiplicity")
def IsGorenstein(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("IsGorenstein")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "IsGorenstein")
def GeneratorOfInterior(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("GeneratorOfInterior")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "GeneratorOfInterior")
def VerticesFloat(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("VerticesFloat")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "VerticesFloat")
def Volume(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("Volume")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "Volume")
def SuppHypsFloat(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("SuppHypsFloat")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "SuppHypsFloat")
def LatticePoints(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("LatticePoints")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "LatticePoints")
def EuclideanIntegral(self, **kwargs):
input_list = self.__process_keyword_args(kwargs)
input_list.append("EuclideanIntegral")
PyNormaliz_cpp.NmzCompute(self.cone, input_list)
return PyNormaliz_cpp.NmzResult(self.cone, "EuclideanIntegral")
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