The monomials of the monomial basis will be ordered according to the monomial ordering used by the implementation
So if you use DynamicPolynomials, it will be grlex
Would it make sense to write a wrapper struct Lex around a dynamicpolynomial and define a new method of leadingmonomial, leadingterm for that? Or will that screw up a representation somehow?
Redirecting all functions might be painful, we could add the comparison function in the type arguments, along with C and T
I am creating a multivariate polynomial and evaluating it wrt varying coefficients, always on a given set of points x_i, and computing its gradient wrt the coefficients (not the variables). For now I am creating the polynomial from scratch for every new value of the coefficients, would there be a smarter way to do it? Function and gradient evaluations are fairly expensive like this
For instance has it been observed to improve perf to use the coefficient as another multiplicative term on each monomial, and then differentiate wrt coefficient and use evaluation with parameter?
or would there be an efficient way to do batch substitutions, multiple substitutions with fixed coefficients and terms?