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 __init__(self, coefficient, vars):
"""
>>> M = Monomial(2, (('a', 2), ('b', 3)))
>>> M
Monomial(2, (('a', 2), ('b', 3)))
>>> str(M)
'2 * a^2 * b^3'
"""
self._coefficient = coefficient
if isinstance(vars, dict):
self._vars = basicAlgorithms.dictToOrderedTupleOfPairs(vars)
else:
assert isinstance(vars, tuple)
for var, expo in vars:
assert isinstance(var, str)
assert isinstance(expo, int)
assert expo > 0
self._vars = vars
