def _convertToMonicNf(nf, timeout):
pariStr = "PRIVATEconvertToMonicNf = nfinit(%s, 3)" % nf.printMagma()
print pariStr
print timeout
r = pari.pari_eval(pariStr, timeout = timeout)
nf = Polynomial.parseFromMagma(
pari.pari_eval("PRIVATEconvertToMonicNf[1].pol", timeout = timeout))
newExpressionForX = Polynomial.parseFromMagma(
pari.pari_eval("PRIVATEconvertToMonicNf[2].pol", timeout = timeout))
return nf, newExpressionForX
def parse_primary_decomposition(s_with_backslash):
"""
>>> p = parse_primary_decomposition(_magma_sample)
>>> len(p)
1
>>> p = p[0]
>>> len(p)
3
>>> str(p[0])
'- 1 + c_01_0'
>>> str(p[1])
'1 + c_02_0 + t'
>>> str(p[2])
'1 + t + t^2'
"""
s = re.search(
"PRIMARY=DECOMPOSITION=BEGINS=HERE\s*"
"("
"\[\s*"
"(([^\]]*\[[^\]]*\],?\s*)*)"
"\]\s*"
")+"
"PRIMARY=DECOMPOSITION=ENDS=HERE",
s_with_backslash,re.DOTALL)
if not s:
raise Exception, "Invalid Primary Decomposition"
s_with_backslash = s.group(2)
s = processEndOfLineBackslashes(s_with_backslash)
components = re.findall(
"Ideal of Polynomial ring.*?"
"Dimension (\d+).*?"
"(Size of variety over algebraically closed field: (\d+).*?)?"
"Groebner basis:\s*"
"\[([^\]]*)\]",
s)
def parseNumberOfPoints(s):
if s == '':
return None
else:
return int(s)
components= [
PrimeIdeal(
[ Polynomial.parseFromMagma(p) for p in polys.split(',') ],
dimension = int(dimension),
numberOfPoints = parseNumberOfPoints(numberOfPoints))
for dimension, tmp, numberOfPoints, polys in components]
return components
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 process_file(trig_file):
d,in_filename = tempfile.mkstemp()
tmp_in_file = open(in_filename, 'wb')
tmp_in_file.write("r f %s\n" % trig_file)
tmp_in_file.write("set precision 15\n")
tmp_in_file.write("set digits_printed 120 f\n")
tmp_in_file.write("print solution_type\n")
tmp_in_file.write("print volume\n")
#tmp_in_file.write("print complex_volume\n")
tmp_in_file.write("quit\n")
tmp_in_file.close()
l = subprocess.Popen("ulimit -t 1; snap <" + in_filename, shell=True, stdout = subprocess.PIPE)
s = l.stdout.read()
if not ("solution type: geometric" in s or "solution type: nongeometric" in s):
return None
try:
os.unlink(in_filename)
except:
pass
d,in_filename = tempfile.mkstemp()
tmp_in_file = open(in_filename, 'wb')
tmp_in_file.write("r f %s\n" % trig_file)
tmp_in_file.write("set degree 7\n")
tmp_in_file.write("set precision 15\n")
tmp_in_file.write("set digits_printed 120 f\n")
tmp_in_file.write("compute invariant_trace_field\n")
tmp_in_file.write("quit\n")
tmp_in_file.close()
l = subprocess.Popen("ulimit -t 20; snap <" + in_filename, shell=True, stdout = subprocess.PIPE)
s2 = l.stdout.read()
try:
os.unlink(in_filename)
except:
pass
r = re.search("Complex volume: (.*)",s)
rcvol = '"-"'
icvol = '"-"'
if r:
cvol = number(r.group(1))
rcvol = str(cvol.real())
icvol = str(cvol.imag())
r = re.search("Volume is: (.*)", s)
if r:
rcvol = r.group(1)
f = re.search("Invariant trace field: (.*) \[",s2)
fp = '-'
fdeg = '-'
if f:
fp = f.group(1)
fdeg = str(Polynomial.parseFromMagma(fp).degree())
if re.search(r"\(-?\d+,-?\d+\)", trig_file):
if "(0,0)" in trig_file: # manifold is cusped if there is an unfilled cusped
oc = "cusped"
else:
oc = "closed"
else:
oc = "cusped"
t = read_triangulation_from_file(trig_file)
return ('"%s",%s,%d,%s,%s,"%s",%s'
% (trig_file.split('/')[-1].replace('.trig',''),
oc,
t.num_tets,
rcvol, icvol, fp, fdeg))