On Apr 30, 12:23 am, Robert Bradshaw <rober...@math.washington.edu> wrote:
> > > (RJF) Maxima was designed around exact arithmetic, and generally offers to > > convert floats to their corresponding exact rationals before doing > > anything > > that requires arithmetic. It makes no claims about floats per se, > > partly > > because saying anything sensible is a challenge, compounded by > > particular issues that are not mathematical but practical .. overflow, > > different machine floating point formats, etc > > For the most part, that's how it is with Sage as well, so I'm sure > you'll cut us the same slack :) Actually, it doesn't seem that way to me, and that's why I hesitate to cut you slack:) You refer to RR, which is supposed to be a representation of the REAL NUMBERS. Maxima has machine floats and 'arbitrary precision' floats. And rationals, and of course some other stuff that is symbolic, like e and pi, and sqrt(3). And I suppose it has the concept of real (vs. complex). >We would like to do multi-precision > numerics better, but for machine-precision stuff we leverage NumPy/ > SciPy (and many of the folks there are experts in the field, for any > reasonable definition of expert). I guess I hadn't noticed their contributions here. You can call lapack, but that doesn't mean you are using it correctly. > Of course things like linear algebra > and approximate solutions to differential equations are more well > known than floating point polynomial multiplication. > > >> We do, however, try to avoid > >> algorithms that are known to be numerically unstable. > > > The lack of serious understanding of numerical computation in Sage > > is unfortunate. > > That would be unfortunate if it were true, but thankfully we're a > pretty diverse crowd. I guess I disagree on how much input you really have on such matters. By the way, I think the formulation that you are looking for regarding multiplication of polynomials, may be something like this: Given polynomials P,Q, R with exact rational number coefficients, and where R=P*Q exactly. Now assume that you can represent P, Q exactly using n bits of floating-point precision. How can you compute R', which is the polynomial R but where each coefficient is represented to m bits correctly rounded (perhaps n=m?) using some kind of arithmetic, with some kind of algorithm, as fast as possible. My guess, anyway. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
