On Thu, Apr 23, 2009 at 6:44 AM, philabuster <pollock.p...@gmail.com> wrote:
>
> Hi,
>
> I was wondering why Sage expands products of sums in an unexpected
> order:
>
> var('a0,a1,b0,b1,b2,c0,c1,c2,c3,d0,d1,d2,d3,d4')The ordering of these terms is determined by maxima -- Sage doesn't control that at all, just leaving them in the default order maxima chooses. > > expand((a0+a1)*(b0+b1)) > > a1*b1 + a0*b1 + a1*b0 + a0*b0 > And in Maxima: wst...@geom:~/db/wuthrich-twist/data$ sage -maxima Maxima 5.16.3 http://maxima.sourceforge.net Using Lisp CLISP 2.47 (2008-10-23) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) expand((a0+a1)*(b0+b1)); (%o1) a1 b1 + a0 b1 + a1 b0 + a0 b0 -------------------------------- We are currently making a push to rewrite the symbolic calculus part of Sage using the Ginac C++ library instead of Maxima. When that happens, the above will be: sage: var('a0 a1 b0 b1',ns=1) # ns=1 sets a preview mode that enables new symbolics (a0, a1, b0, b1) sage: expand((a0+a1)*(b0+b1)) a0*b0 + a0*b1 + a1*b0 + a1*b1 New symbolics also tend to be easier to work with term-by-term: sage: v = expand((a0+a1)*(b0+b1)) sage: v[0] a0*b0 sage: v[1] a0*b1 sage: v[2] a1*b0 sage: v[3] a1*b1 > expand((a0+a1)*(b0+b1+b2)*(c0+c1+c2+c3)*(d0+d1+d2+d3+d4)) > > a1*b2*c3*d4 + a0*b2*c3*d4 + a1*b1*c3*d4 + a0*b1*c3*d4 + a1*b0*c3*d4 + > a0*b0*c3*d4 + a1*b2*c2*d4 + a0*b2*c2*d4 + a1*b1*c2*d4 + a0*b1*c2*d4 + > a1*b0*c2*d4 + a0*b0*c2*d4 + a1*b2*c1*d4 + a0*b2*c1*d4 + a1*b1*c1*d4 + > a0*b1*c1*d4 + a1*b0*c1*d4 + a0*b0*c1*d4 + a1*b2*c0*d4 + a0*b2*c0*d4 + > a1*b1*c0*d4 + a0*b1*c0*d4 + a1*b0*c0*d4 + a0*b0*c0*d4 + a1*b2*c3*d3 + > a0*b2*c3*d3 + a1*b1*c3*d3 + a0*b1*c3*d3 + a1*b0*c3*d3 + a0*b0*c3*d3 + > a1*b2*c2*d3 + a0*b2*c2*d3 + a1*b1*c2*d3 + a0*b1*c2*d3 + a1*b0*c2*d3 + > a0*b0*c2*d3 + a1*b2*c1*d3 + a0*b2*c1*d3 + a1*b1*c1*d3 + a0*b1*c1*d3 + > a1*b0*c1*d3 + a0*b0*c1*d3 + a1*b2*c0*d3 + a0*b2*c0*d3 + a1*b1*c0*d3 + > a0*b1*c0*d3 + a1*b0*c0*d3 + a0*b0*c0*d3 + a1*b2*c3*d2 + a0*b2*c3*d2 + > a1*b1*c3*d2 + a0*b1*c3*d2 + a1*b0*c3*d2 + a0*b0*c3*d2 + a1*b2*c2*d2 + > a0*b2*c2*d2 + a1*b1*c2*d2 + a0*b1*c2*d2 + a1*b0*c2*d2 + a0*b0*c2*d2 + > a1*b2*c1*d2 + a0*b2*c1*d2 + a1*b1*c1*d2 + a0*b1*c1*d2 + a1*b0*c1*d2 + > a0*b0*c1*d2 + a1*b2*c0*d2 + a0*b2*c0*d2 + a1*b1*c0*d2 + a0*b1*c0*d2 + > a1*b0*c0*d2 + a0*b0*c0*d2 + a1*b2*c3*d1 + a0*b2*c3*d1 + a1*b1*c3*d1 + > a0*b1*c3*d1 + a1*b0*c3*d1 + a0*b0*c3*d1 + a1*b2*c2*d1 + a0*b2*c2*d1 + > a1*b1*c2*d1 + a0*b1*c2*d1 + a1*b0*c2*d1 + a0*b0*c2*d1 + a1*b2*c1*d1 + > a0*b2*c1*d1 + a1*b1*c1*d1 + a0*b1*c1*d1 + a1*b0*c1*d1 + a0*b0*c1*d1 + > a1*b2*c0*d1 + a0*b2*c0*d1 + a1*b1*c0*d1 + a0*b1*c0*d1 + a1*b0*c0*d1 + > a0*b0*c0*d1 + a1*b2*c3*d0 + a0*b2*c3*d0 + a1*b1*c3*d0 + a0*b1*c3*d0 + > a1*b0*c3*d0 + a0*b0*c3*d0 + a1*b2*c2*d0 + a0*b2*c2*d0 + a1*b1*c2*d0 + > a0*b1*c2*d0 + a1*b0*c2*d0 + a0*b0*c2*d0 + a1*b2*c1*d0 + a0*b2*c1*d0 + > a1*b1*c1*d0 + a0*b1*c1*d0 + a1*b0*c1*d0 + a0*b0*c1*d0 + a1*b2*c0*d0 + > a0*b2*c0*d0 + a1*b1*c0*d0 + a0*b1*c0*d0 + a1*b0*c0*d0 + a0*b0*c0*d0 > > This ordering makes it extremely difficult to do index association > from the j-th term of the expansion back into constituent indices of > each sum (i0,i1,i2,i3); for example, (0,1,2,3) corresponds to > a0*b1*c2*d3 and is associated with j=33. A more intuitive left to > right product expansion would have been simpler and more useful when > working with these expansions. Also, other math packages expand these > products in a different order than what's seen in Sage. In the > simpler case (a0+a1)*(b0+b1) I would expect the accepted FOIL ordering > of terms. What was the rationale? > > Given j, how would you calculate (i0,i1,i2,i3,...,ik) considering > Sage's expansion order? > > Your help is appreciated, > > philabuster > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
