def collect_square(f, term, square):
'''collect_square(x**5+x**2, x, XX) == x*XX**2+XX'''
g = collect(f, term)
h = Poly(g, term)
s = zero
for (e, ), coeff in h.all_terms():
t = square**(e // 2)
if e % 2:
t *= term
s += coeff * t
return s
def separate_odd_pow_terms(f, term):
'''separate_odd_pow_terms(x**3+x**2+x+1, x) = (x**2+1, x**3+x)'''
g = collect(f, term)
h = Poly(g, term)
odd = even = zero
for (e, ), coeff in h.all_terms():
t = term**e * coeff
if e % 2:
odd += t
else:
even += t
return even, odd
def poly_descent(expr):
if expr[0] == '-' and expr[1:].isdigit() or expr.isdigit():
return expr
p = Poly(parse_expr(str(expr)))
vars = set([])
for c in str(expr):
if c.isalpha():
vars.add(c)
assert len(vars) > 0
if len(vars) > 1:
return expr
var = vars.pop()
s = ''
lst = sorted(p.all_terms(), key=lambda x: x[0], reverse=True)
for d, c in lst:
d = d[0]
if d == 0:
if c > 0:
s += f' + {c}'
elif c < 0:
s += f' - {abs(c)}'
elif d == 1:
if c > 0 and c != 1:
s += f' + {c}*{var}'
elif c == 1:
s += f' + {var}'
elif c < 0 and c != -1:
s += f' - {abs(c)}*{var}'
elif c == -1:
s += f' - {var}'
else:
if c > 0 and c != 1:
s += f' + {c}*{var}**{d}'
elif c == 1:
s += f' + {var}**{d}'
elif c < 0 and c != -1:
s += f' - {abs(c)}*{var}**{d}'
elif c == -1:
s += f' - {var}**{d}'
if s[:3] == ' - ':
s = '-' + s[3:]
if s[:3] == ' + ':
s = s[3:]
return s