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 _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 main():
parser = create_parser()
# Parse command line options
options, args = parser.parse_args()
if not len(args) == 1:
parser.print_help()
sys.exit(1)
filename = args[0]
if filename[-4:] == ".csv":
outFilenameBase = filename[:-4]
else:
outFilenameBase = filename
outFilename = outFilenameBase + "_complexPlaces.csv"
print "output to", outFilename
censusTable = readCensusTable(filename, convertData=False)
fieldnames = censusTable.header
if not "NumberOfComplexPlaces" in fieldnames:
fieldnames = fieldnames + ["NumberOfComplexPlaces"]
csv_writer = csv.DictWriter(open(outFilename, "w"), fieldnames=fieldnames)
csv_writer.writerow(dict(zip(fieldnames, fieldnames)))
for row in censusTable.listOfDicts:
if row.has_key("InvariantTraceField"):
if row["InvariantTraceField"] and not row["InvariantTraceField"] == "-":
pariStr = "nfinit(%s).r2" % row["InvariantTraceField"]
row["NumberOfComplexPlaces"] = pari.pari_eval(pariStr)
csv_writer.writerow(row)
OutWriter.writerow( dict(zip(RepresentationHeader,
RepresentationHeader)))
for d in RepresentationReader:
d['Linear Combinations'] = '-'
if d['Volume'] and not d['Volume'] == '-':
v = number(d['Volume'])
vfloat = float(d['Volume'])
if vfloat > 1e-10:
pari_cmd = ("lindep([%s],%d)"
% (','.join([str(x)
for x in
volDict.values() + [v]]),
precision))
s = pari_eval(pari_cmd)
if d['Manifold'] == '4_1' and False:
print s
print v
print len(volDict.values() + [v])
assert s[0] == '['
assert s[-2:] == ']~'
s = [int(x) for x in s[1:-2].split(',')]
k = max([max(s),-min(s)])
if k < 1000:
q = '('
q+= '+'.join(['(%d) * %s' % x for x in zip(s[:-1], volDict.keys()) if x[0]])
q+= ') / (%d)' % s[-1]
d['Linear Combinations'] = q
