def finite_check(f, x, L):
def check_fx(exprs, x):
return x not in exprs.free_symbols
def check_sincos(expr, x, L):
if type(expr) == sin or type(expr) == cos:
sincos_args = expr.args[0]
if sincos_args.match(a * (pi / L) * x + b) is not None:
return True
else:
return False
expr = sincos_to_sum(TR2(TR1(f)))
res_expr = S.Zero
add_coeff = expr.as_coeff_add()
res_expr += add_coeff[0]
a = Wild('a', properties=[
lambda k: k.is_Integer,
lambda k: k != S.Zero,
])
b = Wild('b',
properties=[
lambda k: x not in k.free_symbols or k == S.Zero,
])
for s in add_coeff[1]:
mul_coeffs = s.as_coeff_mul()[1]
for t in mul_coeffs:
if not (check_fx(t, x) or check_sincos(t, x, L)):
return False, f
res_expr += TR10(s)
return True, res_expr.collect(
[sin(a * (pi / L) * x), cos(a * (pi / L) * x)])
def finite_check(f, x, L):
def check_fx(exprs, x):
return x not in exprs.free_symbols
def check_sincos(_expr, x, L):
if isinstance(_expr, (sin, cos)):
sincos_args = _expr.args[0]
if sincos_args.match(a * (pi / L) * x + b) is not None:
return True
else:
return False
_expr = sincos_to_sum(TR2(TR1(f)))
add_coeff = _expr.as_coeff_add()
a = Wild('a', properties=[
lambda k: k.is_Integer,
lambda k: k != S.Zero,
])
b = Wild('b', properties=[
lambda k: x not in k.free_symbols,
])
for s in add_coeff[1]:
mul_coeffs = s.as_coeff_mul()[1]
for t in mul_coeffs:
if not (check_fx(t, x) or check_sincos(t, x, L)):
return False, f
return True, _expr
def _futrig(e, **kwargs):
"""Helper for futrig."""
from sympy.simplify.fu import (
TR1, TR2, TR3, TR2i, TR10, L, TR10i,
TR8, TR6, TR15, TR16, TR111, TR5, TRmorrie, TR11, TR14, TR22,
TR12)
from sympy.core.compatibility import _nodes
if not e.has(TrigonometricFunction):
return e
if e.is_Mul:
coeff, e = e.as_independent(TrigonometricFunction)
else:
coeff = S.One
Lops = lambda x: (L(x), x.count_ops(), _nodes(x), len(x.args), x.is_Add)
trigs = lambda x: x.has(TrigonometricFunction)
tree = [identity,
(
TR3, # canonical angles
TR1, # sec-csc -> cos-sin
TR12, # expand tan of sum
lambda x: _eapply(factor, x, trigs),
TR2, # tan-cot -> sin-cos
[identity, lambda x: _eapply(_mexpand, x, trigs)],
TR2i, # sin-cos ratio -> tan
lambda x: _eapply(lambda i: factor(i.normal()), x, trigs),
TR14, # factored identities
TR5, # sin-pow -> cos_pow
TR10, # sin-cos of sums -> sin-cos prod
TR11, TR6, # reduce double angles and rewrite cos pows
lambda x: _eapply(factor, x, trigs),
TR14, # factored powers of identities
[identity, lambda x: _eapply(_mexpand, x, trigs)],
TRmorrie,
TR10i, # sin-cos products > sin-cos of sums
[identity, TR8], # sin-cos products -> sin-cos of sums
[identity, lambda x: TR2i(TR2(x))], # tan -> sin-cos -> tan
[
lambda x: _eapply(expand_mul, TR5(x), trigs),
lambda x: _eapply(
expand_mul, TR15(x), trigs)], # pos/neg powers of sin
[
lambda x: _eapply(expand_mul, TR6(x), trigs),
lambda x: _eapply(
expand_mul, TR16(x), trigs)], # pos/neg powers of cos
TR111, # tan, sin, cos to neg power -> cot, csc, sec
[identity, TR2i], # sin-cos ratio to tan
[identity, lambda x: _eapply(
expand_mul, TR22(x), trigs)], # tan-cot to sec-csc
TR1, TR2, TR2i,
[identity, lambda x: _eapply(
factor_terms, TR12(x), trigs)], # expand tan of sum
)]
e = greedy(tree, objective=Lops)(e)
return coeff*e
def test_TR2():
assert TR2(tan(x)) == sin(x) / cos(x)
assert TR2(cot(x)) == cos(x) / sin(x)
assert TR2(tan(tan(x) - sin(x) / cos(x))) == 0