Hi there,
I'm trying to work with multivariate polynomials in SAGE and here are
3 features that I would like. Assume f is a multi-poly:
* f.coefficients() for multivariate polynomials. I would like to get
all the coefficients of f in a list, according to the term order
attached to its ring (this would basically the equivalent of the
univariate case). For example:
{{{
sage: # lex ordering
sage: R.<x,y> = MPolynomialRing(QQ,2,order='lex')
sage: f=23*x^6*y^7 + x^3*y+6
sage: f
23*x^6*y^7 + x^3*y+6
sage: f.coefficients()
[23, 1, 6]
}}}
Another example where we use revlex ordering:
{{{
sage: # revlex ordering
sage: R.<x,y> = MPolynomialRing(QQ,2,order='revlex')
sage: f=23*x^6*y^7 + x^3*y+6
sage: f
6 + x^3*y + 23*x^6*y^7
sage: f.coefficients()
[6,1,23]
}}}
Does such function make sense?
* random_element() for multivariate polynomials would be really nice
to have. In addition, I think it would be a good idea to specify
certain additional parameters:
* d : maximum total degree of each term. I'm using total degree here
to mimic the univariate case, but I'd like to hear other suggestions.
* n: how many terms of total degree at most d we must generate.
For example:
{{{
sage: R.<x,y> = MPolynomialRing(QQ,2,order='lex')
sage: # generate a poly of total degree 3, with 2 terms in it
sage: R.random_element(d=3, n=2)
2*x^2*y + x*y
}}
* A function to compute the pth norm of a polynomials. I don't think
this is hard to implement, it's just that no one has had a use for it
yet :)
Feedback and suggestion would be greatly appreciated.
didier
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