Taylor Expansion for F: Rn -> Rn

[mahe...@vt.edu]

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