While it would be useful to restrict cases to the reals, it also might be nice to specify any polynomial ring with the solver (though probably quite complex to implement). I admit I haven't used other CAS extensively, but from what I've seen such an easy to use and reconciled feature would likely be something to be desired. Also, why stop at polynomial rings - you could use the same solve interface to solve equations with terms being members of an arbitrary group. Feel free to tell me I'm crazy, just wondering if this is something others would like and if it is feasible.
On May 30, 2:15 pm, "Bobby Moretti" <[EMAIL PROTECTED]> wrote: > 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/ -~----------~----~----~----~------~----~------~--~---
