def form_size(expr: Expr) -> typing.Tuple[Size, typing.Optional[Symbol]]:
"""Form a size object from a SymPy expression."""
symbs = expr.atoms(Symbol)
n_symbs = len(symbs)
if n_symbs == 0:
symb = None
coeff_exprs = [expr]
elif n_symbs == 1:
symb = symbs.pop()
coeff_exprs = Poly(expr, symb).all_coeffs()
coeff_exprs.reverse()
else:
raise ValueError(
'Invalid expression', expr,
'expecting single variate polynomial (or number)'
)
if all(i.is_integer for i in coeff_exprs):
dtype = int
else:
dtype = float
if len(coeff_exprs) > 1:
coeffs = np.array(coeff_exprs, dtype=dtype)
cost = SVPoly(coeffs)
elif len(coeff_exprs) == 1:
cost = dtype(coeff_exprs[0])
else:
assert False
return cost, symb
def get_reduced_fraction(numerator_coefs, denominator_coefs, result_deg):
"""
Reduce polynomial division by common factors. So (1+k)/(1+2k+k**2) will be reduced to 1/(1+k)
Items in the coefs list start from the lowest degree ([a, b, c] = a + b*x +c*x**2)
"""
k = var('k')
numerator = sum([coef * k**i for i, coef in enumerate(numerator_coefs)])
denominator = sum(
[coef * k**i for i, coef in enumerate(denominator_coefs)])
reduced_num, reduced_denom = (numerator /
denominator).simplify().as_numer_denom()
reduced_num_coefs, reduced_denom_coefs = Poly(
reduced_num, k).all_coeffs(), Poly(reduced_denom, k).all_coeffs()
reduced_num_coefs.reverse()
reduced_denom_coefs.reverse()
# If the higher degrees are missing from the expression, then the list will have a smaller size then needed.
# Adding zeros as padding to the end.
reduced_num_coefs += [0] * (result_deg + 1 - len(reduced_num_coefs))
reduced_denom_coefs += [0] * (result_deg + 1 - len(reduced_denom_coefs))
return reduced_num_coefs, reduced_denom_coefs
