On Wed, Jun 3, 2009 at 5:54 PM, James Parson wrote:
>
> Thanks to David Joyner for his response to my original question. His
> method worked nicely. Incidentally, here is the original Maple code
> from the lecture of Doron Zeilberger that I was trying to translate
> into Sage:
>
> with(combinat): P:=(d,x,y)->add(add(a[i,j]*x**i*y**j,i=0..d-
> j),j=0..d);
> V:=d->fseq(seq(a[i,j],i=0..d-j),j=0..d)g;
> E:=d->fseq(P(d,fibonacci(n),fibonacci(n+1)),n=1..nops(V(d))+5) g:
> Q:=(d,x,y)->subs(solve(E(d),V(d)),P(d,x,y));
>
> These lines feature the sort of indexed variables a[i,j] discussed
> above.
>
> (The full lecture from which I took these lines can be found at
> http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/em.html.)
>
There is some pdf cut-and-paste corruption of the example above. The
correct Maple code is:
with(combinat):
P:=(d,x,y)->add(add(a[i,j]*x**i*y**j,i=0..d-j),j=0..d);
V:=d->{seq(seq(a[i,j],i=0..d-j),j=0..d)};
E:=d->{seq(P(d,fibonacci(n),fibonacci(n+1)),n=1..nops(V(d))+5) };
Q:=(d,x,y)->subs(solve(E(d),V(d)),P(d,x,y));
A more direct translation to Sage might be something like this:
sage: P=lambda d,x,y: sum([ sum([ var("a"+str(i)+str(j))*x^i*y^j for i
in [0..d-j]]) for j in [0..d]])
sage: V=lambda d:sum([[var("a"+str(i)+str(j)) for i in [0..d-j]] for j
in [0..d]],[])
sage: E=lambda d: [ P(d,fibonacci(n),fibonacci(n+1)) for n in [1..len(V(d))+5] ]
sage: Q=lambda d,x,y:P(d,x,y).subs_expr(solve(E(d),V(d),solution_dict=True)[0])
sage: Q(1,x,y)
0
sage: Q(2,x,y)
0
sage: Q(3,x,y)
0
sage: Q(4,x,y).factor()
r21*(-y^2 + x*y + x^2 - 1)*(-y^2 + x*y + x^2 + 1)
Regards,
Bill Page.
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