Composition of morphisms of affine varieties

[Soli vishkautsan]

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?

[John Cremona]

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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[Soli vishkautsan]

Thanks, 

another workaround is to use 

(f2*f1).post_compose(f3)

which also works.
The same problem when composing the homogenization of these morphisms.

I will add this to trac, unless someone else intervenes :)