def polynomialNonZeroCondition(eqns, var, andNonOne = False):
variables = get_all_variables(eqns)
prod = Polynomial.fromVariableName(var)
for i in variables:
prod = prod * Polynomial.fromVariableName(i)
if andNonOne:
prod = prod * (Polynomial.constantPolynomial(1) -
Polynomial.fromVariableName(i))
return prod - Polynomial.constantPolynomial(1)
def _solveExactlyOverNumberField(univariatePoly, nf, timeout):
variable = univariatePoly.variables()[0]
def convertXtoY(p):
return p.substitute({'x' : Polynomial.fromVariableName('y')})
univariatePoly = univariatePoly.convertCoefficients(convertXtoY)
univariatePoly = univariatePoly.substitute(
{ variable : Polynomial.constantPolynomial(
Polynomial.fromVariableName('x'))})
if not nf:
assert univariatePoly.isConstant()
newSolution = Polynomial.fromVariableName('x')
newNf = univariatePoly.getConstant()
newExpressionForX = Polynomial.constantPolynomial(0)
else:
nf = convertXtoY(nf)
pariStr = "PRIAVTEsEONF = rnfequation(nfinit(%s), %s, 1)" % (
nf, univariatePoly)
print pariStr
print timeout
r = pari.pari_eval(pariStr, timeout = timeout)
# print r
newNf = Polynomial.parseFromMagma(pari.pari_eval(
"PRIAVTEsEONF[1]", timeout = timeout))
newExpressionForX = Polynomial.parseFromMagma(pari.pari_eval(
"PRIAVTEsEONF[2].pol", timeout = timeout))
factor = int(pari.pari_eval(
"PRIAVTEsEONF[3]", timeout = timeout))
newSolution = (
Polynomial.fromVariableName('x')
- Polynomial.constantPolynomial(factor) * newExpressionForX)
return newSolution, newNf, newExpressionForX
def get_additional_eqns_independent(t, N):
# make sure cusps have indices
# dictionary associating the decoration change vectors to Ptolemy coordinates
d = {}
for i, tet in zip(range(len(t.tet_list)), t.tet_list):
for coord in simplex_coords_with_fixed_sum(4, N):
if not N in coord:
v = [0 for x in range((N-1) * t.num_or_cusps)]
for j, k in zip(range(4), coord):
for p in range(k):
v[ tet.cusp_index[j] + p * t.num_or_cusps ] += 1
d[c_parameter_var(coord, i)] = v
variables = find_independent_integer_vectors(d)
return [
Polynomial.fromVariableName(var) - Polynomial.constantPolynomial(1)
for var in variables]
def turn_pair_to_Polynomial(p):
if p[0] == +1:
return Polynomial.fromVariableName(p[1])
else:
return -Polynomial.fromVariableName(p[1])
def c_parameter(coords, tet_index):
"""
Same as c_parameter_var but returns it as Polynomial type.
"""
return Polynomial.fromVariableName(
c_parameter_var(coords, tet_index))
def convertXtoY(p):
return p.substitute({'x' : Polynomial.fromVariableName('y')})
