On Jan 18, 2008, at 11:32 AM, William Stein wrote:
>> Let A be a matrix not over ZZ or QQ: >> >> A.adjoint() >> A.inverse() >> >> are not implemented. > > I don't think they should be. There are already (at least) 3 ways > to do this: Wait a sec.... I agree with David K on the adjoint issue. The adjoint doesn't require the fraction field to even be constructed, and it makes perfect sense over non-domains. > sage: A = random_matrix(ZZ,2) > sage: ~A > > [ 1/34 1/17] > [-6/17 5/17] > sage: A.__invert__() > > [ 1/34 1/17] > [-6/17 5/17] > sage: A^(-1) > > [ 1/34 1/17] > [-6/17 5/17] I vaguely recall being stung several times by the lack of an inverse () method. For someone who doesn't know python that well, neither ~ nor __invert__ are obvious alternatives. I don't think it would hurt at all to have an inverse() method. >> For x a commutative ring element: >> >> x.inverse() >> >> is not implemented even if x^-1 exists. > > Same remark as above. > >> sage: x = 7 >> sage: type(x) >> <type 'sage.rings.integer.Integer'> >> sage: x^-1 >> 1/7 >> sage: type(x^-1) >> <type 'sage.rings.rational.Rational'> >> sage: x = -1 >> sage: type(x^-1) >> >> Should the field of fractions be created? Oooh these are hard. We still haven't settled on consistent semantics for the power operator. Given the types of A and B, I'm never sure what to expect the type of A^B to be. For example: sage: type(Integer(2)^Rational(2)) <type 'sage.rings.integer.Integer'> sage: type(Integer(2)^Rational(1/2)) <class 'sage.calculus.calculus.SymbolicArithmetic'> That really bothers me. >> Certaily x.inverse() should return an error for non-units. > > No it shouldn't. It should compute the inverse as an element of a > natural > larger structure. Huh? How do you do this? What's the inverse of 2 mod 6? What is the larger structure? If anything it's the localisation, but that's not "larger". david --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
