Note: round these parts, we use != for inequality. /= is a divide in-place. That is:
sage: a = 4 sage: a /= 2 sage: print a 2 On Sat, 22 Sep 2007, Jason Grout wrote: > > > Is there any quantifier elimination functionality in SAGE? If not, is > there any interest in trying to incorporate QEPCAD, which uses > cylindrical algebraic decomposition to eliminate quantifiers in > statements. In other words, QEPCAD takes the statement > > there exists an x such that a*x^2 + b*x + c = 0 and a /= 0 > > and eliminates the quantifier and answers that: > > a /= 0 and 4 a c - b^2 <= 0 > > In other words, it gives you the conditions of a solution satisfying > your original statement. > > Mathematica has such functionality and I believe that Maple does as > well. REDUCE has the functionality in the REDLOG package. > > I couldn't find a license for QEPCAD, and the library that QEPCAD > depends on (SACLIB) is not GPL. However, we could ask if they would > release it under GPL for us. > > References: > > QEPCAD: http://www.cs.usna.edu/~qepcad/B/QEPCAD.html > > REDUCE REDLOG package: http://www.algebra.fim.uni-passau.de/~redlog/ > > Mathematica implementation (Resolve, Reduce, FindInstance, > CylindricalDecomposition, etc.): > > http://reference.wolfram.com/mathematica/tutorial/Quantifiers.html > > http://reference.wolfram.com/mathematica/tutorial/TheRepresentationOfSolutionSets.html > > http://reference.wolfram.com/mathematica/tutorial/Inequalities-ManipulatingEquationsAndInequalities.html > > http://reference.wolfram.com/mathematica/tutorial/EquationsAndInequalitiesOverDomains.html > > > > I've used this functionality in Mathematica to solve some problems, and > it seemed like the Mathematica implementation was more powerful than the > QEPCAD implementation (i.e., Mathematica would do problems after QEPCAD > would give up because the problem was too hard). I bring all this up > because it has been useful and cool to use this in the past and I don't > want to forget to mention it to SAGE, in case it hasn't been considered > before. > > -Jason > > > > > > --~--~---------~--~----~------------~-------~--~----~ 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
