> > > * Many numerical functions do not work with arbitrary precision. In > Mathematica and Maple, arbitrary precision works seamlessly pretty much > everywhere. In Sage, a lot of functions are hardcoded for double precision. > A first step would be to provide really solid support for basic numerical > calculus (like computing integrals, #8321) by leveraging what's available > in Pari and mpmath. When it comes to things like multivariate optimization, > solving ODEs and PDEs, etc. with arbitrary precision, I don't think there's > any open source software that competes with Mathematica. >
About solving ODE's numerically with high precision, we have recently added an optional TIDES package (which is a state of the art library for this kind of thing), together with an interface to it. Take a look at: http://www.sagemath.org/doc/reference/calculus/sage/calculus/desolvers.html#sage.calculus.desolvers.desolve_tides_mpfr > > * Performance. You often run into a wall as soon as you do anything > slightly complicated in Sage that isn't directly wrapping the right > C/C++/Cython implementation. Bill Hart had an example of computing a > resultant of two large (but not astronomically large) multivariate > polynomials over a finite field, where Magma does it in a minute, Bill's > Julia code does it in 5 seconds, and he had to kill Sage after waiting for > hours... > > Fredrik > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
