Hi,
I would like to perform Taylor expansion for functions F: \mathbb{R}^{n}
\rightarrow \mathbb{R}^{n} (i.e.) functions with n-dimensional domain and
range. I believe this functionality is non-existent at the moment and would
like to get some pointers on how I may go about it.
I can walk the expression tree creating corresponding expressions for each
term in F. Following are some issues that I would like to work around:
- it appears that sympy automatically rearranges variables inside each term
of the expression as it sees fit. This is not acceptable as such an
expansion will start dealing with non-commutative entities very
soon: http://docs.sympy.org/latest/tutorial/manipulation.html
In: expr = 3*y**2*x
In: expr
Out[12]: 3*x*y**2
In: expr =y**2*3*x
In: expr
Out[14]: 3*x*y**2
- I would like to introduce some bracket notation for non-commutative
products. Right now, the brackets are plainly discarded:
In: 3*(y**2)*x
Out[15]: 3*x*y**2
- I would like to treat undefined functions as part of the Taylor expansion
and I might be able to
use http://docs.sympy.org/latest/modules/functions/index.html
- If I need to create new sympy types in the process, how do I go about it?
Regards,
Mahesh
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