#11239: Incorrect coercion of polynomials over finite fields
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Reporter: johanbosman | Owner: robertwb
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.1
Component: coercion | Resolution:
Keywords: finite fields, | Merged in:
polynomials, coercion, sd53 | Reviewers: Jean-Pierre Flori
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | 236effb6198c6192dce0cedc0e53423c68743e3e
u/jpflori/ticket/11239 | Stopgaps:
Dependencies: #8335 |
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Comment (by pbruin):
Here is the way in which I think this bug should be solved conceptually.
It is motivated by the fact that if ''A'' is a commutative ring, the
object ''A''[''x''] in the category of ''A''-algebras represents the
forgetful functor to the category of sets.
- Implement a class `PolynomialRingMorphism` modelling ring homomorphisms
''f'': ''A''[''x''] -> ''C'', where ''A'' and ''C'' are commutative rings.
Note that ''C'' is not required to be a polynomial ring. Such ring
homomorphisms correspond bijectively to pairs (''g'', ''c''), where ''g'':
''A'' -> ''C'' is a ring homomorphism and ''c'' is an element of ''C'',
where the bijection is given by ''g'' = ''f''|,,A,, and ''c'' =
''f''(''x''); cf. the above motivation.
- Have optimised code for the following special case: ''C'' = ''B''[''y'']
where ''B'' is an ''A''-algebra (or: has a coercion map from ''A''), ''g''
is the composition of the obvious maps ''A'' -> ''B'' -> ''C'', and ''c''
= ''y''. In this case, ''f'' is the map ''A''[''x''] -> ''C''[''y''] that
we will declare as the coercion map. Given an element ''p'' of
''A''[''x''], the `PolynomialRingMorphism` in this special case should
just take the list of coefficients of ''p'', map them to ''B'' and hence
construct the desired element ''f''(''p'') of ''B''[''y''].
- If ''C'' = ''B''[''y''], where ''B'' has a coercion map from ''A'', let
`C._coerce_map_from_(A['x'])` return the `PolynomialRingMorphism` for the
above special case.
- A general `PolynomialRingMorphism` could be implemented either in terms
of this special case or independently from it. The first approach would
work as follows: given a general ''f'': ''A''[''x''] -> ''C'' as in the
first point, represented by a pair (''g'', ''c''), applying ''f'' to a
polynomial ''p'' in ''A''[''x''] can be implemented by first mapping ''p''
to ''C''[''y''] (applying ''g'' to the coefficients as in the special
case) and then substituting ''c'' for ''y''.
This is probably not very difficult to implement. This ticket could
function as a temporary solution for the bug it fixes, until we have the
real solution.
--
Ticket URL: <http://trac.sagemath.org/ticket/11239#comment:30>
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