#13682: No coercion map with quotients of ring quotients
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Reporter: tscrim | Owner: tscrim
Type: defect | Status: new
Priority: major | Milestone: sage-5.5
Component: coercion | Keywords: ideal, quotient, coercion
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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If you take the quotient ring of a quotient ring, I would expect there to
be a coercion map corresponding to the natural surjection. However this
does not occur:
{{{
sage: R.<x,y> = PolynomialRing(QQ)
sage: S = R.quotient_ring(x^2+y^2)
sage: S
Quotient of Multivariate Polynomial Ring in x, y over Rational Field by
the ideal (x^2 + y^2)
sage: S.has_coerce_map_from(R)
True
sage: T = S.quotient_ring(x^3 - y)
sage: T
Quotient of Multivariate Polynomial Ring in x, y over Rational Field by
the ideal (-x*y^2 - y, x^2 + y^2)
sage: T.has_coerce_map_from(R)
True
sage: T.has_coerce_map_from(S) # this should be true
False
}}}
I suspect the following does not occur either (and is where the problem
lies). If an ideal `I` is contained in an ideal `J`, there is not a
coercion from `R/I -> R/J`.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13682>
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