Thank you very much David,
For now "list" function works for me very well using the approaches I
discussed in last post, except that t makes some problem for "reduce"
function which I asked in my next post. If the problem with "reduce"
won't be solved, the "dict" function would be enough for implementing
the basis changing in multivariate polynomials for sure.
Cheers,
Ahmad
On Dec 1, 10:47 am, David Harvey <[EMAIL PROTECTED]> wrote:
> Hi Ahmad,
>
> Unfortunately I know nothing about multivariate polynomials in sage,
> but in case you didn't already know, there is an easy way to find out
> what methods an object supports. For example I did this:
>
> sage: k = GF(7)
> sage: R = MPolynomialRing(k,2,x)
> sage: x = R.gens()
> sage: g = x[0]^3 + 2*x[1] + 5
>
> Since g.list() doesn't work, I type "g." and then press Tab. I get a
> long list of methods attached to g. Then I see for example that I can
> do:
>
> sage: g.dict()
> {(0, 0): 5, (0, 1): 2, (3, 0): 1}
>
> This is a dictionary representation of the coefficients of g, and
> there are probably other representations available too.
>
> If I type:
>
> sage: g.dict?
>
> I get some documentation on what g.dict() does.
>
> david
>
> On Dec 1, 2007, at 10:37 AM, Ahmad wrote:
>
>
>
> > Hi David,
>
> > I think "list" function is enough for me if I extend the ring in two
> > steps: first with free variables and then I extend it algebraically.
> > Your solution is working for me in this way:
>
> > sage: k = GF(2);
> > sage: WRBasePolyRing = MPolynomialRing(k, 8, x); x =
> > WRBasePolyRing.gens()
> > sage: S = WRBasePolyRing['w']; w = S.gen()
> > sage: WRPolyRing = S.quotient(w^4 + w^3 + w^2 + w + 1, 't'); t =
> > WRPolyRing.gen()
> > sage: X = x[0]*t + x[1]*t^2 + x[2]*t^4 + x[3]* t^8;
> > sage: Y = x[4]*t + x[5]*t^2 + x[6]*t^4 + x[7]* t^8;
> > sage: MyCurve = Y^2+X*Y+X^3+1
> > sage: print MyCurve.list()
>
> > [x0^2*x1 + x0*x1^2 + x0*x2^2 + x1*x2^2 + x0^2*x3 + x2*x3^2 + x3^3 +
> > x2*x4 + x3*x4 + x1*x5 + x3*x5 + x5^2 + x0*x6 + x0*x7 + x1*x7 + 1,
> > x0^2*x1 + x1^3 + x0^2*x2 + x0*x2^2 + x2^2*x3 + x3^3 + x3*x4 + x1*x5 +
> > x2*x5 + x5^2 + x1*x6 + x0*x7 + x3*x7 + x7^2, x0^2*x1 + x0*x2^2 + x2^3
> > + x1^2*x3 + x0*x3^2 + x3^3 + x0*x4 + x3*x4 + x4^2 + x1*x5 + x5^2 +
> > x3*x6 + x0*x7 + x2*x7, x0^3 + x0^2*x1 + x1^2*x2 + x0*x2^2 + x1*x3^2 +
> > x3^3 + x1*x4 + x3*x4 + x0*x5 + x1*x5 + x5^2 + x2*x6 + x6^2 + x0*x7]
>
> > And after that as you mentioned, I can multiply the list by the basis
> > change matrix.
>
> > Thank you again (More question is on the way ... :">)
>
> > Bests,
> > Ahmad
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