Investigate representations of ODE systems in modcc

[halfflat]

Point estimate: 10
Feature: #60

Investigate representations as below; document conclusions on wiki or demonstrate proof of concept of choice in code.

The internal representation of an ODE system as specified by a DERIVATIVE block or KINETIC block needs to be such that the following operations are practical:

• Reduce a over-specified (KINETIC) system following a supplied CONSERVE statement.
• Determine system linearity.
• Determine system if system is diagonal.
• Possibly also: determine algebraic kernel of polynomial ODE system.

The reduction operation is necessary to support the semantics of the mechanism as described in the feature. The linearity and diagonal tests are necessary to determine the choice of solver in the mechanism instantiation.

Consider the use of third party packages such as symengine.

[halfflat]

Quick options summary in: https://github.com/eth-cscs/nestmc-proto/wiki/Symbolic-algebra

[halfflat]

It looks like symengine will do the job just fine, despite misgivings regarding documentation!
I'll clean up the symengine demo code and place it somewhere for reference.

[halfflat]

Ready for review: all info is on the Symbolic algebra wiki page.

[bcumming]

Looks like there was quite low overhead to get the functionality that we need from SymEngine.

Can you give the output of your demo code in the wiki?

[halfflat]

Sure thing!