On 30 October 2012 13:38, Charles Bouillaguet <charles.bouillag...@gmail.com> wrote: > 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.
I think all that Marco meant was that for a general ring, there may be no algorithm to decide invertibility. In this ring, of course there is. John > > 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. > 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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