Bill Allombert on Tue, 27 Feb 2007 14:10:12 +0100 |
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Re: Variable ordering |
On Mon, Feb 26, 2007 at 06:32:20AM -0800, William Hart wrote: > > So here's the problem. In the function > toEllipticCurve, the first print statement prints > something like the following: > > u^3 + 6*u^2 + (-17*v + Mod(-17*w + 12, 2*w^3 - 34*w + > 99))*u + (2*v^3 + Mod(6*w, 2*w^3 - 34*w + 99)*v^2 + > Mod(6*w^2 - 34, 2*w^3 - 34*w + 99)*v) > > As you can see, it is a polynomial in u and v with > coefficients in Z[w]/(3*w^3+2*w^2+w-1). > > Now all I want to do is replace u with U/W and v with > V/W in this polynomial. I've tried using the Pari > subst function (with appropriate modifications to the > code). And I've tried exactly what I've written in the > program trace above. But it doesn't work. Here is the > result: > > Mod(6*W^2*V*w^2 + (-17*W^2*U + 6*W*V^2)*w + (U^3 + > 6*W*U^2 + (-17*W*V + 12*W^2)*U + (2*V^3 - 34*W^2*V)), > 2*w^3 - 34*w + 99) You need to create U,V,W before w. Add at the start of your script u;v;U;V;W;w; to ensure that. Beside you can use substvec(...,[u,v],[U/W,V/W]) which is a bit more robust than subst(subst(...,u,U/W),v,V/W). > Now I realise this is a Pari variable order issue, and > indeed, if I change the order of the Pari variables > using the reorder command, it works just fine. If I Do not use reorder() it has been removed in the 2.4 series because it had major issues. > Does someone know how to do these kinds of > substitutions without having to use the Pari reorder > command, or how to use the reorder command in this > instance to make it return a correct answer? You should create your variables in the correct order from the start: do u;v;U;V;W;w and not u;v;w,U;V;W. We are working on a way to allow users to declare variables with fixed priority. Cheers, Bill.