How to Simplify a system of equations and find possible substitions (symbolic toolbox?

Hello,

i've got 8 symbolic expressions and i want to simplify this system of equations together. So i've there identical expressions in 2 or more equations the number of mathematical computations can be reduced.

It is a symbolic problem using the symbolic toolbox.

[Dyuman Joshi]

What does "simplify" mean in this context?

What are the expressions? And what is the expected output?

[Torben]

the System is the partial derivation of a voltage equation for the 8 parameters x1...x8. So the output are 8 equations

dU_dx1, dU_dx2 ...

Now i could simplify every equation on its own. But i think if i could simplify all 8 equations together there could be parts that could be calculated only once and then "reused" in other equations.

[Dyuman Joshi]

What would you do with the simplifed system? Solve it for the parameters?

[Torben]

Using the 8 derivations directly for some kind of online RLS-algorithm

Answer 1

[Walter Roberson]

If you use matlabFunction and request that it be written to a file, then the default is to optimize. The optimization step involves searching for common subexpressions and assigning them to variables and reusing the variables.

The end result is a .m file that is intended for numeric calculation.

Caution: not very long ago, optimization was badly broken, so test before trusting.

[Torben]

badly broken?

[Steven Lord]

If you're not using matlabFunction you could use the subexpr function.

[Walter Roberson]

I haven't tested over the last couple of releases, but not very long ago, the optimization phase had a series of problems for a number of years. It was completely unusuable for longer expressions.