This e-mail is too long. Here's the bottom line: I suggest that the
coefficient method on a multivariate polynomial ring take a dictionary
indicating the variables and degrees that you want to restrict your attention
to.
It seems that the multivariate polynomial coefficient function is a bit
inflexible (and inconsistent). I'm looking for some insight about how to
think about the following things.
sage: P.<x,y>=ZZ[]
sage: f=x*y^2+x*y+y+x+1
sage: f.coefficient(y^2)
x
sage: f.coefficient(y^1)
x + 1
sage: f.coefficient(y^0)
1
I realize that y^0 == 1 so that the last line is returning the constant
coefficient (and the implication that y is special to me the user is totally
unseen by the coefficient method). But, the logic seems a bit inconsistent.
I'd suggest that this next line work:
sage: f.coefficient({y:0})
x + 1
Does anyone have any objection? It actually seems like a dictionary of
variables whose exponents you want to control would make a much better
interface to this. In any case, we can maintain both functionalities by
checking the type of the parameter.
And another:
sage: P.<x,y>=QQ[] # DIFFERENT BASE RING THAN LAST TIME
sage: f=x*y^2+x*y+y+x+1
sage: f.coefficient(y^0) # DIFFERENT OUTPUT
x*y^2 + x*y + x + y + 1
What in the world is going on in that last line? (Hmm, I think that it is
getting a 1 so it is thinking that no variables are restricted -- that's
actually consistent, but seems mighty strange.)
Does anyone else agree? Or, have a better suggestion?
--
Joel
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