How can I simplify polynomials to a canonical form?

[t0mdd]

My application needs a way to extract the coefficients from a polynomial string after it has been simplified, math.simplify is producing some peculiar looking results:
1 - z^4 + z^5 - z^6 + z^2 - 7z^2 - z^8 simplifies to 1 + z ^ 5 + -z ^ 8 - 6 * z ^ 2 - (z ^ 4 + z ^ 6)

I am not sure what else it could look like so I am not comfortable using it just yet. I would prefer a more predictable form where the coefficients can be easily extracted, something like 1 + z ^ 5 - z ^ 8 - 6 * z ^ 2 - z ^ 4 - z ^ 6 would be better.

For general polynomials something like each term satisfying the regex
(coefficient)?(\*)?(variable(\^number)?)? and joined by + would be good. Is there some way of doing this or if not would you consider adding something like this? If so I would be willing to help.

Thanks,
Tom

[josdejong]

Mathjs doesn't have a ready made function to normalize a polynomial. It would be an interesting addition.

It could be interesting to see if we can improve simplify to do this better out of the box. Right now you can alter the rules that simplify uses yourself, so you could play around with that and come up with a set of rules that can be used to normalize a polynomial. It is also possible to parse the expression and then transform it yourself, applying rules needed to normalize the expression.

Docs:

• https://mathjs.org/docs/reference/functions/simplify.html
• https://mathjs.org/docs/expressions/expression_trees.html → search for transform