#9019: Full doctest coverage for sage.categories.map
--------------------------+-------------------------------------------------
Reporter: SimonKing | Owner: nthiery
Type: defect | Status: new
Priority: major | Milestone: sage-4.4.3
Component: categories | Keywords: doctest map composition
Author: Simon King | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Apart from full doctest coverage for sage.categories.map, the patch
provides the following:
1. Test for injectivity and surjectivity of {{{MatrixMorphism}}}:
{{{
sage: V1 = QQ^2
sage: V2 = QQ^3
sage: phi = V1.hom(Matrix([[1,2],[3,4],[5,6]]),V2)
sage: phi.is_injective()
True
sage: phi.is_surjective()
False
sage: psi = V2.hom(Matrix([[1,2,3],[4,5,6]]),V1)
sage: psi.is_injective()
False
sage: psi.is_surjective()
True
}}}
2. Composition of a {{{RingHomomorphism_im_gens}}} with another ring
homomorphism (this used to return a {{{FormalCompositeMap}}}, which is not
very efficient):
{{{
sage: R.<x,y> = QQ[]
sage: S.<a,b> = QQ[]
sage: f = R.hom([a+b,a-b])
sage: g = S.hom(Frac(S))
sage: g*f
Ring morphism:
From: Multivariate Polynomial Ring in x, y over Rational Field
To: Fraction Field of Multivariate Polynomial Ring in a, b over
Rational Field
Defn: x |--> a + b
y |--> a - b
sage: h = S.hom([x+y,x-y])
sage: h*f
Ring endomorphism of Multivariate Polynomial Ring in x, y over Rational
Field
Defn: x |--> 2*x
y |--> 2*y
}}}
3. Comparison of {{{FormalCompositeMap}}}s:
{{{
sage: R.<x,y> = QQ[]
sage: S.<a,b> = QQ[]
sage: f = R.hom([a+b,a-b])
sage: g = S.hom([x+y,x-y])
sage: from sage.categories.map import FormalCompositeMap
sage: H = Hom(R,R,Rings())
sage: m = FormalCompositeMap(H,f,g)
sage: m == loads(dumps(m)) # this used to be False!
True
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9019>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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