rational preimages for projective morphisms returns incorrect points

[bhutz]

The function rational_preimages for projective morphism polynomials, returns points that are not pre-images of the input points. The issue is that the solutions found may only be solutions to some of the equations in the ideal.

I will add a check to insure only correct points are returned.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e43132a

trac 15815: fixed doc test

[chapoton]

I do not see any relation between the ticket description and the actual content of the branch. And I do not understand how the modified test could even pass before the change in the branch.

[bhutz]

Here is a longer description. The goal is to find all rational solutions to a zero dimensional ideal in projective space. The method is just basic elimination theory: compute an elimination ideal and solve one variable at a time. As each variable is solved the values are stored in points. The initial test was to check if there was an actual rational solution, i.e. we had a rational value for each of the N+1 variables. So to answer one question, the test would pass when there was a rational value for all N+1 variables.

The issue is that for higher dimensions there may be multiple equations involving one of the variables, one of which does and one of which does not have a rational solution. These slipped through to give wrong values. The test was modified to check that the "solution" really was a zero for *all* defining equations of the ideal.

As for the content of the branch matching the description. This seems clear to me. This is a modification to the {{rational_preimages}}} function to correct the particular problem I just described in more detail by adding the test I described. However, I did neglect to update it to say that I also added a simple codomain check to ensure that the base point was in the codomain of the function. Is that the point of confusion between description and branch?

If this is still not clear to you with this more verbose description, then I need a more specific question.

[chapoton]

Oops, sorry, I was only looking at the second commit. Thanks for the clarification.

[jdefaria]

All tests passed on longtest

[vbraun]

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