> >> In sympy there's a method call as_coeffficients_dict() that returns
> all
> >> the terms and their coefficients from an expression. I am if I can do
> >> something like this in Sage.
> > you can do a similar thing, except that the monomials are encoded by
> > their exponents
> >
> > sage: R.<x,a> = ZZ[]
> > sage: p=x^2*a-a^2+a-4
>
> Note that this is not a symbolic expression, but a "proper" polynomial.
> But the original question was about symbolic expressions. Perhaps the
> original poster has a reason for using symbolic expressions?
>
Right, my question is on expressions. That's how I store my data. In
short, I just want something that is like Sympy's as_coefficients_dict for
expressions (I've put its documentation at the end of this msg). However,
based on Dima's feedbacks above, I've written something like this for the
input expression p
vs = p.variables()
pr_p = PolynomialRing(ZZ,vs, None if len(vs) > 1 else 1)(p)
cs = pr_p.coefficients()
ts = map(SR, pr_p.monomials())
return cs,ts
>
> Perhaps the following does what is requested?
> sage: var('x','a')
> (x, a)
> sage: b = (3*x + a*x + 4)
> sage: b.operands()
> [a*x, 3*x, 4]
>
> It would probably not be too dificult to extract the constant
> coefficient of each operand.
>
How do I do get the coefficients of these operands ?
>
> It all depends on what answer you would expect. Say, if you present an
> equal polynomial symbolic expression by
> sage: c = (3+a)*x + 4
> Then you get
> sage: c.operands()
> [(a + 3)*x, 4]
>
Is this what you want? Or do you want that an automatic expansion into a
> sum takes place? In this case it might really be better to use
> polynomials.
>
I don't need automatic expansion, if the input is (3+a)*x + 4, then I want
the output to be something like what sympy's as_coefficients_dict() would
give
In [44]: ((3+x)*y+4).as_coefficients_dict()
Out[44]: defaultdict(<type 'int'>, {1: 4, y*(x + 3): 1})
Doc of sympy's as_coefficients_dict()
Return a dictionary mapping terms to their Rational coefficient.
Since the dictionary is a defaultdict, inquiries about terms which
were not present will return a coefficient of 0. If an expression is
not an Add it is considered to have a single term.
Examples
========
>>> from sympy.abc import a, x
>>> (3*x + a*x + 4).as_coefficients_dict()
{1: 4, x: 3, a*x: 1}
>>> _[a]
0
>>> (3*a*x).as_coefficients_dict()
{a*x: 3}
> Cheers,
> Simon
>
>
>
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