Hello, Here is an example of the underlying problem
sage: a = -x/(2*x-4) sage: e = lambda e: taylor(e,x,3,4) sage: e(a) -3/2 + x - 3 - (x - 3)^2 + (x - 3)^3 - (x - 3)^4 sage: type(_) <class 'sage.calculus.calculus.SymbolicArithmetic'> sage: b = e(a)._maxima_(); b x-(x-3)^4+(x-3)^3-(x-3)^2-9/2 What happens is that is able to construct a SymbolicArithmetic object that has things like they should be. When it then reconstructs a maxima object from that, maxima performs the simplification. See ticket #2025 --Mike On Feb 2, 2008 2:00 PM, pgdoyle <[EMAIL PROTECTED]> wrote: > > > > On Feb 1, 8:59 am, "William Stein" <[EMAIL PROTECTED]> wrote: > > > On Jan 31, 2008 7:59 AM, pgdoyle <[EMAIL PROTECTED]> wrote: > > > > > > > > > > > > > On Jan 31, 12:29 am, "William Stein" <[EMAIL PROTECTED]> wrote: > > > > > > On Jan 30, 2008 3:48 PM, pgdoyle <[EMAIL PROTECTED]> wrote: > > > > > > > I would like to take the Taylor series of a matrix. But I find I > > > > > can't even put a Taylor polynomial into a matrix without its being > > > > > simplified. > > > > > > > sage: f=-x/(2*x-4); f > > > > > -x/(2*x - 4) > > > > > sage: g=taylor(f,x,1,1); g > > > > > 1/2 + x - 1 > > > > > sage: matrix(1,[g]) > > > > > [x - 1/2] > > > > > sage: m=matrix(1,[f]); m > > > > > [-x/(2*x - 4)] > > > > > sage: m.apply_map(lambda e: taylor(e,x,1,1)) > > > > > [x - 1/2] > > > > > > > Any suggestions? > > > > > > You're already doing it exactly correctly. Try a higher degree > > > > approximation to avoid confusion: > > > > > > sage: m = matrix(1,[-x/(2*x-4)]) > > > > sage: m.apply_map(lambda e: taylor(e,x,1,4)) > > > > [x + (x - 1)^4 + (x - 1)^3 + (x - 1)^2 - 1/2] > > > > > William: > > > > > Sorry - I didn't make the issue clear enough. When I ask for the > > > Taylor polynomial at x=1, I want a polynomial in x-1. And that's what > > > I get, except that when I put this polynomial into a matrix, 1/2 + x - > > > 1 gets simplified to x-1/2. Your example shows this behavior very > > > clearly. > > > > That's weird. Most of the polynomial is not simplified except the -1/2 is > > moved to the end. Note that the rest of the terms stay put. I wonder > > why Maxima does that. (No clue.) Note that it isn't a complete loss; all > > the other terms remain exactly as you wanted. > > > > It's not just that the constant term gets moved: The 1/2 gets > combined with the -1 in the linear term x-1. > > Also, I don't see how this could be the fault of Maxima: > > sage: %maxima > sage: f:taylor(-x/(2*x-4),x,1,5) > sage: m:[f] > sage: m*2 > 1/2+(x-1)+(x-1)^2+(x-1)^3+(x-1)^4+(x-1)^5 > [1/2+(x-1)+(x-1)^2+(x-1)^3+(x-1)^4+(x-1)^5] > [1+2*(x-1)+2*(x-1)^2+2*(x-1)^3+2*(x-1)^4+2*(x-1)^5] > > Note how Maxima has the terms in the expected order for a power > series, and preserves this order, without doing any simplification, > when putting it the expression into a matrix. > > Cheers, > > Peter > > > sage: m = matrix(1,[-x/(2*x-4)]) > > sage: m.apply_map(lambda e: taylor(e,x,0,4)) > > [x^4/32 + x^3/16 + x^2/8 + x/4] > > sage: m.apply_map(lambda e: taylor(e,x,0,4)) > > [x^4/32 + x^3/16 + x^2/8 + x/4] > > sage: m.apply_map(lambda e: taylor(e,x,1,4)) > > [x + (x - 1)^4 + (x - 1)^3 + (x - 1)^2 - 1/2] > > sage: m.apply_map(lambda e: taylor(e,x,2,4)) > > [-1/(x - 2) - 1/2] > > sage: m.apply_map(lambda e: taylor(e,x,3,4)) > > [x - (x - 3)^4 + (x - 3)^3 - (x - 3)^2 - 9/2] > > sage: m[0,0].taylor(x,3,4) > > -3/2 + x - 3 - (x - 3)^2 + (x - 3)^3 - (x - 3)^4 > > > > I'm sure this can be fixed, so I've made a bug report: > > > > http://trac.sagemath.org/sage_trac/ticket/2025 > > > > -- William > > > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
