On Oct 29, 2012, at 4:39 PM, Marco Streng wrote:
> 2012/10/28 Charles Bouillaguet <charles.bouillag...@gmail.com>: >> Hi all, >> >> While playing with the quotient of a polynomial ring with an ideal, I >> encountered several glitches. >> >> *) Trying to compute the inverse of something which is not invertible. >> >> I know it is kind of weird to try this. However, it raises a >> NotImplementedError exception, instead of something more informative such as >> NonInvertible or whatever. I am willing to patch this, but could someone >> tell me what is the correct exception to raise? > > Based on http://docs.python.org/2/library/exceptions.html, it should > be ValueError (unless Sage has a more precise error for this > situation, but I don't think so). > > But in order to be able to raise a ValueError, you need to first > decide whether your element is invertible or not. If such a decision > mechanism is not implemented, then NotImplementedError is the only > possibility. And I guess that is the current situation here. Actually, I beg to differ. What is currently implemented is the following. Let R be a polynomial ring, I be an ideal of R, and f be a non-zero element of R/I. To check whether f is invertible in R/I, we check whether 1 belongs to the ideal (I + <f>). If it is the case, then an inverse exist. Indeed, in this case, there exist g in R such that 1 = [something in I] + g*f. It follows that the class of g in R/I is the inverse of f. But this test in fact **decides** whether an inverse exist. If there exist a g such that f*g = 1 mod I, then by definition there exist two polynomials of R, say f' and g', such that f is the class of f' and g is the class of g' modulo I. Then in R we have f*g = 1 + [something in I]. This automatically implies that 1 belongs to the ideal (I + <f>). Thus, the current implementation should not return "ErrorNotImplemented", it should return "NonInvertible", because we KNOW that it is the case... This is now #13670. However, presently this test uses p.lift(…), and as you pointed out the answer becomes bogus as soon as one tries to invert something non-invertible…. This one is now #13671 . Cheers, --- Charles Bouillaguet http://www.lifl.fr/~bouillaguet/ >> *) Non-deterministic output of some (presumably deterministic) functions >> >> Here is an example : >> >> sage: R.<x1,x2> = QQ[] >> sage: I = R.ideal(x2**2 + x1 - 2, x1**2 - 1) >> sage: test = I.gen(0) + x2*I.gen(1) >> sage: (test).lift( I ) >> [1, x2] # this is correct >> >> sage: R.<x1,x2> = QQ[] >> sage: I = R.ideal(x2**2 + x1 - 2, x1**2 - 1) >> sage: test = I.gen(0) + x2*I.gen(1) >> sage: (test + 1).lift( I ) >> [0, 0] # this is correct > > No it isn't, the correct output would be ValueError, as (test+1) is > not in I. So this is a bug in the "lift" method. > >> >> sage: R.<x1,x2> = QQ[] >> sage: I = R.ideal(x2**2 + x1 - 2, x1**2 - 1) >> sage: test = I.gen(0) + x2*I.gen(1) >> sage: (test).lift( I ) >> [0, 0] # this is WRONG !!! should be [1, x2] >> >> It looks like this could be a caching issue, so I am not sure whether I need >> to open a new ticket for this, or if it is already "catch" by an >> already-opened ticket. > > It is some kind of corruption triggered by the abovementioned bug, so > it may vanish when that bug is fixed. > > Here is a shortened version of your input: > > sage: R.<x1,x2> = QQ[] > sage: I = R.ideal(x2**2 + x1 - 2, x1**2 - 1) > sage: test = I.gen(0) + x2*I.gen(1) > sage: test.lift(I) # correct > [1, x2] > sage: (test+1).lift(I) # invalid input, should give error > [0, 0] > sage: test.lift(I) # incorrect > [0, 0] > > > >> >> *) Segfault >> >> The same kind of problem allows a small piece of code to cause segfaults in >> SAGE (apparently in singular-related stuff) : >> >> sage: R.<x1,x2> = QQ[] >> sage: S = R.quotient_ring( R.ideal(x2**2 + x1 - 2, x1**2 - 1) ) >> sage: 1 / S(x1 + x2) # should raise NotImplementedError >> sage: >> sage: R.<x1,x2> = QQ[] >> sage: S = R.quotient_ring( R.ideal(x2**2 + x1 - 2, x1**2 - 1) ) >> sage: S.is_integral_domain() >> >> ---> BOOM >> >> *) bizarre output of p.lift(….) >> >> When R is a Polynomial Ring, I is an ideal of R, and p is a polynomial of I, >> then p.lift( I ) returns a polynomial combination of a (groebner) basis of I >> which is equal to p. However, when p is not in I, then p.lift( I ) returns >> [0,0,…,0]. I find this a bit strange. Should p.lift(…) raise an exception >> instead? This would be a change of specification, so I guess it should be >> discussed first… >> >> >> >> >> --- >> Charles Bouillaguet >> http://www.lifl.fr/~bouillaguet/ >> >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-devel" group. >> To post to this group, send email to sage-devel@googlegroups.com. >> To unsubscribe from this group, send email to >> sage-devel+unsubscr...@googlegroups.com. >> Visit this group at http://groups.google.com/group/sage-devel?hl=en. >> >> > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To post to this group, send email to sage-devel@googlegroups.com. > To unsubscribe from this group, send email to > sage-devel+unsubscr...@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel?hl=en. > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. 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