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. > > *) 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.
