On 18 November 2014 13:38, Soli vishkautsan <[email protected]> wrote:
> I am trying to compose 3 affine automorphisms of the Markoff surface.
> The following code produces an error:
>
> A.<x,y,z> = AffineSpace(QQ,3)
> M = A.subscheme([x^2+y^2+z^2-3*x*y*z])
> H = Hom(M,M)
> f1 = H([3*y*z-x,y,z])
> f2 = H([x,3*x*z-y,z])
> f3 = H([x,y,3*x*y-z])
> f3*f2*f1
>
> What am I doing wrong?
This could be a bug. Both f3*f2 and f2*f1 work ok, returning
"Composite maps". Also (f3*f2)*(f2*f1) works (not what you want of
course. It looks to me as if the people who implemented Composite
maps did not define the * operator to work with a combination of
Composite and ordinary maps.
Silly workaround:
sage: id = H([x,y,z])
sage: (f3*f2)*(f1*id)
Composite map:
From: Closed subscheme of Affine Space of dimension 3 over Rational
Field defined by:
-3*x*y*z + x^2 + y^2 + z^2
To: Closed subscheme of Affine Space of dimension 3 over Rational
Field defined by:
-3*x*y*z + x^2 + y^2 + z^2
Defn: Generic endomorphism of Closed subscheme of Affine Space of
dimension 3 over Rational Field defined by:
-3*x*y*z + x^2 + y^2 + z^2
then
Generic endomorphism of Closed subscheme of Affine Space of
dimension 3 over Rational Field defined by:
-3*x*y*z + x^2 + y^2 + z^2
then
Generic endomorphism of Closed subscheme of Affine Space of
dimension 3 over Rational Field defined by:
-3*x*y*z + x^2 + y^2 + z^2
then
Generic endomorphism of Closed subscheme of Affine Space of
dimension 3 over Rational Field defined by:
-3*x*y*z + x^2 + y^2 + z^2
John Cremona
>
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