> In your problem would it make more sense to have an API based around 
eliminating variables rather than solving for them? 

That might work. Eventually, the solution gets passed to some numerical 
code that needs to have values for all the symbols that obey the 
constraints in the system of linear and non-linear equations that I am 
solving. My goal is to find the relationships between the symbols and it 
helps the numerical stability to sample certain symbols in a special way, 
which is why I have a "priority" of symbols that I'd want to be 
independent, if possible.

Solving the same system of equations twice works for me. Even the largest 
system I can imagine using in the near future would use would have <25 
variables and <10 equations. Sometimes the system of equations is 
underdetermined and sometimes over. Either is fine for my use case.
On Friday, April 9, 2021 at 8:21:10 PM UTC-4 Oscar wrote:

> On Sat, 10 Apr 2021 at 01:17, [email protected]
> <[email protected]> wrote:
> >
> > This almost worked for me as is. My desired dependent variables are [w, 
> y]. If I just pass those, then I don't get the solution for z=1. So I did 
> two solves:
> >
> > 1. Solve with my desired dependent variables (e.g. [w, y])
> > 2. Identify the set of variables that are not in the solution (as keys 
> or in the values) and add those to my list of desired dependent varaibles 
> ([x])
> > 3. Solve the same set of equations again with the new minimal set of 
> variables ([w, x, y])
>
> In your problem would it make more sense to have an API based around
> eliminating variables rather than solving for them?
>

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