There's a very inconvenient mismatch of choice in polynomials at the moment:
sage: R.<x,y,z>=QQ[]
sage: f=x+2*y+z
sage: list(f)
[(1, x), (2, y), (1, z)]
As you can see, polynomials are iterable and produce (coefficient,
monomial) pairs. The nasty thing is: that looks like the appropriate input
for a dictionary constructor, and indeed, it sort-of seems to work:
sage: dict(f)
{1: z, 2: y}
except of course that the dict should be keyed by monomials, not by the
coefficients.
We do have:
sage: f.dict()
{(0, 0, 1): 1, (0, 1, 0): 2, (1, 0, 0): 1}
which raises expectations that dict(f) would work reasonably too. It could,
if we would swap to (monomial, coefficient) tuples. When I encountered this
behaviour, I was sure this was some silly typo. It's not: f.__iter__() is
behaving as documented. Is it going to be too painful to try and change
this now?
Incidentally, the correct dictionary (keyed by monomials rather than
exponent vectors) can be obtained via the relatively hard to discover
sage: {R({a:1}):b for a,b in f.dict().iteritems()}
{z: 1, y: 2, x: 1}
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