def split_affine(expr):
"""
Split an affine scalar function into its three components, namely variable,
coefficient, and translation from origin.
Raises
------
ValueError
If ``expr`` is non affine.
"""
if expr.is_Number:
return AffineFunction(None, None, expr)
# Handle super-quickly the calls like `split_affine(x+1)`, which are
# the majority.
if expr.is_Add and len(expr.args) == 2:
if expr.args[0].is_Number and expr.args[1].is_Symbol:
# SymPy deterministically orders arguments -- first numbers, then symbols
return AffineFunction(expr.args[1], 1, expr.args[0])
# Fallback
poly = expr.as_poly()
if not (poly.is_univariate and poly.is_linear) or not LM(poly).is_Symbol:
raise ValueError
return AffineFunction(LM(poly), LC(poly), poly.TC())
def split_affine(expr):
"""
split_affine(expr)
Split an affine scalar function into its three components, namely variable,
coefficient, and translation from origin.
:raises ValueError: If ``expr`` is non affine.
"""
if expr.is_Number:
return AffineFunction(None, None, expr)
poly = expr.as_poly()
if not (poly.is_univariate and poly.is_linear) or not LM(poly).is_Symbol:
raise ValueError
return AffineFunction(LM(poly), LC(poly), poly.TC())
def sectionSeparate(formula, lmax):
x = symbols('x', real=True)
pos = set([
x - LM(f).args[0] for f in Add.make_args(formula)
if len(f.atoms(StepFunc))
])
pos.update([0, lmax])
pos = list(sorted(pos))
st = 0
formularr = []
# print("Line Segment Function")
for en in pos[1:]:
# print(formula.expand(lim=st, func=True))
formularr.append((formula.expand(lim=st, func=True), (x, st, en)))
st = en
return formularr
def calS(f, g, t):
x_gamma = lcm(LM(f, order=t), LM(g, order=t))
S = x_gamma / LT(f, order=t) * f - x_gamma / LT(g, order=t) * g
return S
def s_polynomial(f, g):
return expand(lcm(LM(f), LM(g)) * (1 / LT(f) * f - 1 / LT(g) * g))