Updates:
Summary: leading_monom is incorrect
Comment #1 on issue 1647 by smichr: leading_monom is incorrect
http://code.google.com/p/sympy/issues/detail?id=1647
It appears that the problem comes when the new polynomial is made by adding:
p: Poly(y**4 + 11*y**2 - 6*y, y, x, order='grevlex')
p leading monom: (4, 0)
q: Poly(-6*y**3, y, x, order='grevlex')
q leading monom: (3, 0)
p+q: Poly(-6*y**3 + y**4 + 11*y**2 - 6*y, y, x, order='grevlex')
p+q leading monom: (3, 0)
That's right (if the ordering is right) but the ordering is wrong so the
answer is
wrong. If we construct the polynomial without addition then we get the
right answer:
>>> Poly(-6*y**3 + y**4 + 11*y**2 - 6*y, y, x, order='grevlex')
Poly(y**4 - 6*y**3 + 11*y**2 - 6*y, y, x, order='grevlex')
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