I'm trying to wean myself from Mathematica. Here are some issues I've
been
wrestling over with SAGE. I apologize in advance for not showing the
sage output, which I'm sure there is some easy way to generate
automatically
from this file.
1) Taylor series of a rational function.
This works:
sage: cos(x).taylor(x,0,2)
This doesn't:
sage: x/(1+x).taylor(x,0,2)
This is very confusing:
sage: var('x')
sage: x/(1+x).taylor(x,0,2)
BUT, at least this works:
sage: taylor(x/(1+x),x,0,2)
2) Map for matrices. This works:
sage: x=polygen(QQ)
sage: m=(1-x*matrix([[1,1],[1,0]]))^-1; m
sage: matrix([[m[i,j].subs(x=1) for j in range(2)] for i in range(2)])
But, surely there is a direct way substitute x=1 for all entries?
Another thing I found confusing was that this slight variation gave
division by 0.
sage: var('x')
sage: m=(1-x*matrix([[1,1],[1,0]]))^-1; m
sage: matrix([[m[i,j].subs(x=1) for j in range(2)] for i in range(2)])
The problem is that sage hasn't simplified the entries of m. It
thinks
sage: m[1,1]
sage: 1/(1 - x^2/(1 - x))
And I don't see how to get SAGE to reduce this to
(x-1)/(x^2+x-1)
which brings me to
3) How do I get access to maxima's ratsimp?
It's been years since I used Macsyma, but I very fondly remember
ratsimp.
sage: maxima('ratsimp(1/(1 - x^2/(1 - x)))')
I'd like to have ratsimp easily available from SAGE. (And as above,
easily apply it to all entries of a matrix.)
Cheers,
Peter Doyle
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