Wronskian Tools

get_max_below(t, vect)

Input:

• t - a trie with exponent vectors
• vect - yet another exponent vector

Output:

• a pair (d, v) where v is a vector in the trie which is componentwise ≤ vect and the difference d is as small as possible

massive_eval(polys, eval_dict)

Input:

• polys - a list of polynomials
• eval_dict - dictionary from variables to the values. Missing values are treated as zeroes

Output:

• a list of values of the polynomials

Evaluates a list of polynomials at a point. Assumes that multiplications are relatively expensive (like in truncated power series) so all the monomials are precomputed first and the values of monomials of lower degree are cached and used to compute the values of the monomials of higher degree

monomial_compress(io_equation, ode)

Compresses an input-output equation for the rank computation Input:

• io_equation - input-output equation
• ode - the corresponding ODE model

Output:

• pair (coeffs, terms) such that:
  • sum of coeffs[i] * terms[i] = io_equation
  • coeffs involve only parameters, terms involve only inputs and outputs
  • length of the representation is the smallest possible

wronskian(io_equations, ode)

Input:

• io_equations - a set of io-equations in the form of the Dict as returned by find_ioequations
• ode - the ODE object

Output:

• a list of Wronskians evaluated at a point modulo prime

Computes the Wronskians of io_equations