Hi David, On 2019-03-09, David Roe <roed.m...@gmail.com> wrote: > I think the right thing to do is to change that definition to the normal > definition of equality of ideals, which we can implement by just checking > that each generator is contained in the other ideal.
I see reasons why this is /not/ the right thing to do, at least not for each instance of an ideal comparison resp. containment test. The problem is that ideal containment and equality tests can be very expensive (involving Gröbner basis computations), and thus it would be hardly feasible to use ideals as, say, keys in dictionaries. Also, the hash of ideals would be needed to be modified in an expensive way, as it ought to be compatible with the equality test. > We'll also need to > improve ideals in ZZ['x'] a bit, since non-principal ideals don't implement > containment checking: It certainly is implemented --- just not by doing "p in I". You don't want that you innocently ask "p in I", and then Sage is occupied with the computation of a Gröbner basis for the next few hours. If you really need a mathematically correct containment test and are aware that it may be expensive, you can explicitly request it. But for many cases, a quick and dirty mathematically wrong but computationally sound containment test (or equality test for ideals) suffices. Best regards, Simon -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
