def __init__(self, monomials = ()):
# combine monomials with the same variables and exponents
# and bring them into canonical order
assert isinstance(monomials, tuple)
# create for each monomial a dictionary
# with key being the variables and exponents
# and value being the coefficient
listOfVarsCoeffDicts = [
{ monomial.getVars() : monomial.getCoefficient() }
for monomial in monomials]
# combine the dictionaries using sum
combinedVarsCoeffDict = basicAlgorithms.combineDicts(
listOfVarsCoeffDicts,
_operatorTypePolicy)
# turn dictionary into a list of pairs (vars, coefficient)
# in canonical order
orderedTupleOfVarsCoeffPairs = (
basicAlgorithms.dictToOrderedTupleOfPairs(combinedVarsCoeffDict))
# turn pairs into monomials, skip trivial monomials
combinedMonomials = [
Monomial(coefficient, vars)
for vars, coefficient in orderedTupleOfVarsCoeffPairs
if _coefficientIsNonTrivial(coefficient)]
# convert to tuple
self._monomials = tuple(combinedMonomials)
def __mul__(self, other):
assert isinstance(other, Monomial)
# Compute coefficient
coefficient = _operatorTypePolicy(
self._coefficient, other._coefficient, operator.mul)
# Compute the variables
varDict = basicAlgorithms.combineDicts(
[dict(self._vars),dict(other._vars)],
operator.add)
return Monomial(coefficient, varDict)
