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 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 test_TR1():
assert TR1(2 * csc(x) + sec(x)) == 1 / cos(x) + 2 / sin(x)
