Feature #1150
New fn: transform ideal with ring hom
Description
Do we want a new fun for transforming an ideal with a ringhom?TransformIdeal(const ideal& I, const RingHom& phi)
[taken from a photo of the whiteboard]
History
#1 Updated by John Abbott about 4 years ago
- Description updated (diff)
What is this supposed to mean? Does it mean the ideal generated by {phi(f) | f in I}
? What else could it mean?
When might it be useful?
Short example: let $P = QQ[x]$ and let phi
send x |-> x^2
, so phi
is not surjective.
Let $I$ be the ideal generated by $x$. Then ${phi(f) | f in I}@ is not an ideal.
Let G
be any set of generators of I
. Then given the proposed definition in line 1 of this note,
we have that phi(G)
is a set of generators of phi(I)
.
Given this defn, impl should be easy... but is it useful for anyone?