On 5/30/07, William Stein <[EMAIL PROTECTED]> wrote: > > > On 5/30/07, Bobby Moretti <[EMAIL PROTECTED]> wrote: > > Regardless of the discussion here, the behavior in SAGE is tied to > Maxima > > for now. > > > > As an aside, you no longer have to explicitly invoke Maxima. The > following > > is valid as of SAGE 2.5: > > > > sage: eqn = abs(x^2 - x) == 3 > > sage: solve(eq, x) > > .... > > > > Note that we are planning on improving SAGE's equation solving at some > > point. We will have to come up with a plan for dealing with cases like > this, > > where the question is not well-defined. Perhaps some way to assume(x in > > RR)... > > I think the question is well defined -- the answers should all be assumed > to be complex numbers by default. When you solve a cubic, quadratic, > etc., Maxima always gives complex solutions: > > sage: solve(x^2+1==0, x) > [x == -1*I, x == I] > > This is a fairly standard convention. Note that Mathematica and MATLAB > both found complex solutions in the previous posts. The problem in this > particular example is that there are infinitely many complex solutions > to the equation > abs(x^2 - x) == 3 > and that there structure is actually quite complicated (they are the set > of points on an elliptic curve). Just describing them > requires a lot of work. The output of Mathematica/MATLAB in this case > is atrocious -- giving exactly four solution, some complex, when there > are really infinitely many and their structure is complicated -- is > ridiculous. > It's the sort of output that makes a mathematician cringe. A technically > correct solution here would be to write down that "restriction of scalars" > equation that John posted a few emails up, then return the pointset of the > algebraic variety that it defines :-). > > You're right though that it would be great to be able to restrict to the > case that the variable is a real number. > > In any case, solving is a big deal, and I hope we'll rewrite the solving > function to be independent of Maxima at some point. Their algorithm > is described in the documentation for Maxima, and we could like > reimplement > it and do better in the long run given the powerful commutative > algebra functionality available in SAGE.
I'm adding this to the (somewhat enormous) list of SAGE days 4 projects. -- William > > > > -- Bobby Moretti [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-forum URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
