Brief Introduction

[Conrad Schiff]

Hello All,

  My name is Conrad Schiff.  I am an adjunct professor of physics (with some mathematics and engineering thrown in) at Capitol Technology University, a small technical university outside Washington DC.  II have two interrelated reasons for introducing myself to this group.  

  First, I am developing a class on scientific computing with python based on the Anaconda ecosystem and would like to include some sympy in the mix.  I am an experienced programmer in python but haven't really learned much about sympy so I would need some help.  In exchange, I would be willing to code, document, or test.

  Second, in some way related to the first, I would like to develop certain symbolic functions that I believe complement or extend sympy's scope.  These function deal with symbols in a more abstract way than is usual for a CAS (although maybe I am unaware of similar functionality in sympy).  For example, I would like to be able to have a function 'know' how to (not necessarily when to) transform an integral using the divergence or generalized Stoke's theorems where the integrand satisfies the appropriate assumptions but is otherwise unspecified .  I am looking to be able to guide students in being able to distinguish an integral as a problem (e.g. integrate x^2 from 0 to 1 to get 1/3) from an integral as a concept (e.g. flux integrals and Reynolds transport).  Along these lines I want 'coordinate free' representations of mathematical objects.  For this topic I would need to better understand the scope and philosophy of sympy than I do already.

  Thoughts and comments, appreciated.

Conrad

[Ben]

Caveat: I'm not a SymPy maintainer; just a user.

I'm curious to hear more about what you mean by a function transforming an integral based on assumptions. How would those assumptions be provided to SymPy? Can you illustrate with psuedo-code and latex?

The examples you give seem to draw from Calculus ("integrate x^2 from 0 to 1 to get 1/3") and Physics ("flux integrals and Reynolds transport"). SymPy (or any CAS) is good at Calculus, but the translation of Physics to a mathematical problem addressable by a CAS is (so far) a challenge addressed by humans.

What do you mean by "'coordinate free' representations of mathematical objects"?

Kindly,

Ben

[Oscar Benjamin]

Hi Conrad,

That sounds great. I'm not sure what help you would need in learning
about sympy but there is an introductory tutorial here:
https://docs.sympy.org/latest/tutorial/index.html
This mailing list is a good place to ask specific questions.

There has been some work on vector integrals as part of a GSOC project
this year. I'm not sure to what extent that work matches with what you
want.

Do you mean something fully abstract like using sympy to manipulate
line integrals in terms of say a closed curve simply known as C for a
function that is just given as f or do you mean something slightly
more concrete?

Oscar

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[Faisal Riyaz]

Hello,

My GSoC project is to add support for vector integration over Regions.

We can now define curves, surfaces, and volume regions using their

parametric representation. Some implicitly defined regions are also supported.

But the documentation is not ready yet.

Faisal

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