def as_terms(self):
"""Transform an expression to a list of terms. """
from sympy.core import Add, Mul, S
from sympy.core.exprtools import decompose_power
gens, terms = set([]), []
for term in Add.make_args(self):
coeff, _term = term.as_coeff_Mul()
coeff = complex(coeff)
cpart, ncpart = {}, []
if _term is not S.One:
for factor in Mul.make_args(_term):
if factor.is_number:
try:
coeff *= complex(factor)
except ValueError:
pass
else:
continue
if factor.is_commutative:
base, exp = decompose_power(factor)
cpart[base] = exp
gens.add(base)
else:
ncpart.append(factor)
coeff = coeff.real, coeff.imag
ncpart = tuple(ncpart)
terms.append((term, (coeff, cpart, ncpart)))
gens = sorted(gens, key=Basic.sorted_key)
k, indices = len(gens), {}
for i, g in enumerate(gens):
indices[g] = i
result = []
for term, (coeff, cpart, ncpart) in terms:
monom = [0]*k
for base, exp in cpart.iteritems():
monom[indices[base]] = exp
result.append((term, (coeff, tuple(monom), ncpart)))
return result, gens
def as_terms(self):
"""Transform an expression to a list of terms. """
from sympy.core import Add, Mul, S
from sympy.core.exprtools import decompose_power
gens, terms = set([]), []
for term in Add.make_args(self):
coeff, _term = term.as_coeff_Mul()
coeff = complex(coeff)
cpart, ncpart = {}, []
if _term is not S.One:
for factor in Mul.make_args(_term):
if factor.is_number:
try:
coeff *= complex(factor)
except ValueError:
pass
else:
continue
if factor.is_commutative:
base, exp = decompose_power(factor)
cpart[base] = exp
gens.add(base)
else:
ncpart.append(factor)
coeff = coeff.real, coeff.imag
ncpart = tuple(ncpart)
terms.append((term, (coeff, cpart, ncpart)))
gens = sorted(gens, key=Basic.sorted_key)
k, indices = len(gens), {}
for i, g in enumerate(gens):
indices[g] = i
result = []
for term, (coeff, cpart, ncpart) in terms:
monom = [0] * k
for base, exp in cpart.iteritems():
monom[indices[base]] = exp
result.append((term, (coeff, tuple(monom), ncpart)))
return result, gens
def _parallel_dict_from_expr_if_gens(exprs, opt):
"""Transform expressions into a multinomial form given generators. """
k, indices = len(opt.gens), {}
for i, g in enumerate(opt.gens):
indices[g] = i
polys = []
for expr in exprs:
poly = {}
if expr.is_Equality:
expr = expr.lhs - expr.rhs
for term in Add.make_args(expr):
coeff, monom = [], [0] * k
for factor in Mul.make_args(term):
if not _not_a_coeff(factor) and factor.is_Number:
coeff.append(factor)
else:
try:
if opt.series is False:
base, exp = decompose_power(factor)
if exp < 0:
exp, base = -exp, Pow(base, -S.One)
else:
base, exp = decompose_power_rat(factor)
monom[indices[base]] = exp
except KeyError:
if not factor.free_symbols.intersection(opt.gens):
coeff.append(factor)
else:
raise PolynomialError("%s contains an element of "
"the set of generators." %
factor)
monom = tuple(monom)
if monom in poly:
poly[monom] += Mul(*coeff)
else:
poly[monom] = Mul(*coeff)
polys.append(poly)
return polys, opt.gens
def _parallel_dict_from_expr_if_gens(exprs, opt):
"""Transform expressions into a multinomial form given generators. """
k, indices = len(opt.gens), {}
for i, g in enumerate(opt.gens):
indices[g] = i
polys = []
for expr in exprs:
poly = {}
if expr.is_Equality:
expr = expr.lhs - expr.rhs
for term in Add.make_args(expr):
coeff, monom = [], [0]*k
for factor in Mul.make_args(term):
if not _not_a_coeff(factor) and factor.is_Number:
coeff.append(factor)
else:
try:
if opt.series is False:
base, exp = decompose_power(factor)
if exp < 0:
exp, base = -exp, Pow(base, -S.One)
else:
base, exp = decompose_power_rat(factor)
monom[indices[base]] = exp
except KeyError:
if not factor.free_symbols.intersection(opt.gens):
coeff.append(factor)
else:
raise PolynomialError("%s contains an element of "
"the set of generators." % factor)
monom = tuple(monom)
if monom in poly:
poly[monom] += Mul(*coeff)
else:
poly[monom] = Mul(*coeff)
polys.append(poly)
return polys, opt.gens
def _parallel_dict_from_expr_if_gens(exprs, opt):
"""Transform expressions into a multinomial form given generators. """
k, indices = len(opt.gens), {}
for i, g in enumerate(opt.gens):
indices[g] = i
polys = []
for expr in exprs:
poly = {}
for term in Add.make_args(expr):
coeff, monom = [], [0] * k
for factor in Mul.make_args(term):
if factor.is_Number:
coeff.append(factor)
else:
try:
base, exp = decompose_power(factor)
if exp < 0:
exp, base = -exp, Pow(base, -S.One)
monom[indices[base]] = exp
except KeyError:
if not factor.has(*opt.gens):
coeff.append(factor)
else:
raise PolynomialError(
"%s contains an element of the generators set"
% factor)
monom = tuple(monom)
if monom in poly:
poly[monom] += Mul(*coeff)
else:
poly[monom] = Mul(*coeff)
polys.append(poly)
return polys, opt.gens
def _parallel_dict_from_expr_if_gens(exprs, opt):
"""Transform expressions into a multinomial form given generators. """
k, indices = len(opt.gens), {}
for i, g in enumerate(opt.gens):
indices[g] = i
polys = []
for expr in exprs:
poly = {}
for term in Add.make_args(expr):
coeff, monom = [], [0]*k
for factor in Mul.make_args(term):
if factor.is_Number:
coeff.append(factor)
else:
try:
base, exp = decompose_power(factor)
if exp < 0:
exp, base = -exp, Pow(base, -S.One)
monom[indices[base]] = exp
except KeyError:
if not factor.has(*opt.gens):
coeff.append(factor)
else:
raise PolynomialError("%s contains an element of the generators set" % factor)
monom = tuple(monom)
if monom in poly:
poly[monom] += Mul(*coeff)
else:
poly[monom] = Mul(*coeff)
polys.append(poly)
return polys, opt.gens
def test_decompose_power():
assert decompose_power(x) == (x, 1)
assert decompose_power(x**2) == (x, 2)
assert decompose_power(x**(2 * y)) == (x**y, 2)
assert decompose_power(x**(2 * y / 3)) == (x**(y / 3), 2)
def _parallel_dict_from_expr_no_gens(exprs, opt):
"""Transform expressions into a multinomial form and figure out generators. """
if opt.domain is not None:
def _is_coeff(factor):
return factor in opt.domain
elif opt.extension is True:
def _is_coeff(factor):
return factor.is_algebraic
elif opt.greedy is not False:
def _is_coeff(factor):
return factor is S.ImaginaryUnit
else:
def _is_coeff(factor):
return factor.is_number
gens, reprs = set(), []
for expr in exprs:
terms = []
if expr.is_Equality:
expr = expr.lhs - expr.rhs
for term in Add.make_args(expr):
coeff, elements = [], {}
for factor in Mul.make_args(term):
if not _not_a_coeff(factor) and (factor.is_Number
or _is_coeff(factor)):
coeff.append(factor)
else:
if opt.series is False:
base, exp = decompose_power(factor)
if exp < 0:
exp, base = -exp, Pow(base, -S.One)
else:
base, exp = decompose_power_rat(factor)
elements[base] = elements.setdefault(base, 0) + exp
gens.add(base)
terms.append((coeff, elements))
reprs.append(terms)
gens = _sort_gens(gens, opt=opt)
k, indices = len(gens), {}
for i, g in enumerate(gens):
indices[g] = i
polys = []
for terms in reprs:
poly = {}
for coeff, term in terms:
monom = [0] * k
for base, exp in term.items():
monom[indices[base]] = exp
monom = tuple(monom)
if monom in poly:
poly[monom] += Mul(*coeff)
else:
poly[monom] = Mul(*coeff)
polys.append(poly)
return polys, tuple(gens)
def test_decompose_power():
assert decompose_power(x) == (x, 1)
assert decompose_power(x**2) == (x, 2)
assert decompose_power(x**(2*y)) == (x**y, 2)
assert decompose_power(x**(2*y/3)) == (x**(y/3), 2)
def _parallel_dict_from_expr_no_gens(exprs, opt):
"""Transform expressions into a multinomial form and figure out generators. """
if opt.domain is not None:
def _is_coeff(factor):
return factor in opt.domain
elif opt.extension is True:
def _is_coeff(factor):
return factor.is_algebraic
elif opt.greedy is not False:
def _is_coeff(factor):
return False
else:
def _is_coeff(factor):
return factor.is_number
gens, reprs = set([]), []
for expr in exprs:
terms = []
if expr.is_Equality:
expr = expr.lhs - expr.rhs
for term in Add.make_args(expr):
coeff, elements = [], {}
for factor in Mul.make_args(term):
if not _not_a_coeff(factor) and (factor.is_Number or _is_coeff(factor)):
coeff.append(factor)
else:
if opt.series is False:
base, exp = decompose_power(factor)
if exp < 0:
exp, base = -exp, Pow(base, -S.One)
else:
base, exp = decompose_power_rat(factor)
elements[base] = exp
gens.add(base)
terms.append((coeff, elements))
reprs.append(terms)
if not gens:
if len(exprs) == 1:
arg = exprs[0]
else:
arg = (exprs,)
raise GeneratorsNeeded("specify generators to give %s a meaning" % arg)
gens = _sort_gens(gens, opt=opt)
k, indices = len(gens), {}
for i, g in enumerate(gens):
indices[g] = i
polys = []
for terms in reprs:
poly = {}
for coeff, term in terms:
monom = [0]*k
for base, exp in term.items():
monom[indices[base]] = exp
monom = tuple(monom)
if monom in poly:
poly[monom] += Mul(*coeff)
else:
poly[monom] = Mul(*coeff)
polys.append(poly)
return polys, tuple(gens)
def _parallel_dict_from_expr_no_gens(exprs, opt):
"""Transform expressions into a multinomial form and figure out generators. """
if opt.domain is not None:
def _is_coeff(factor):
return factor in opt.domain
elif opt.extension is True:
def _is_coeff(factor):
return ask(Q.algebraic(factor))
elif opt.greedy is not False:
def _is_coeff(factor):
return False
else:
def _is_coeff(factor):
return factor.is_number
gens, reprs = set([]), []
for expr in exprs:
terms = []
for term in Add.make_args(expr):
coeff, elements = [], {}
for factor in Mul.make_args(term):
if factor.is_Number or _is_coeff(factor):
coeff.append(factor)
else:
base, exp = decompose_power(factor)
if exp < 0:
exp, base = -exp, Pow(base, -S.One)
elements[base] = exp
gens.add(base)
terms.append((coeff, elements))
reprs.append(terms)
if not gens:
if len(exprs) == 1:
arg = exprs[0]
else:
arg = (exprs, )
raise GeneratorsNeeded("specify generators to give %s a meaning" % arg)
gens = _sort_gens(gens, opt=opt)
k, indices = len(gens), {}
for i, g in enumerate(gens):
indices[g] = i
polys = []
for terms in reprs:
poly = {}
for coeff, term in terms:
monom = [0] * k
for base, exp in term.iteritems():
monom[indices[base]] = exp
monom = tuple(monom)
if monom in poly:
poly[monom] += Mul(*coeff)
else:
poly[monom] = Mul(*coeff)
polys.append(poly)
return polys, tuple(gens)