Elimination

StructuralIdentifiability.Bezout_matrixMethod
Bezout_matrix(f, g, var_elim)

Compute the Bezout matrix of two polynomials f, g with respect to var_elim

Inputs:

  • f - first polynomial
  • g - second polynomial
  • var_elim - variable, of which f and g are considered as polynomials

Output:

  • M::MatrixElem - The Bezout matrix
StructuralIdentifiability.Sylvester_matrixMethod
Sylvester_matrix(f, g, var_elim)

Compute the Sylvester matrix of two polynomials f, g with respect to var_elim Inputs:

  • f - first polynomial
  • g - second polynomial
  • var_elim - variable, of which f and g are considered as polynomials

Output:

  • M::MatrixElem - The Sylvester matrix
StructuralIdentifiability.chooseMethod
choose(polys, generic_point_generator)

Input:

  • polys - an array of distinct irreducible polynomials in the same ring
  • generic_point_generator - a generic point generator as described above for one of polys

Output:

  • the polynomial that vanishes at the generic_point_generator
StructuralIdentifiability.eliminate_varMethod
eliminate_var(f, g, var_elim, generic_point_generator)

Eliminate variable from a pair of polynomials

Input:

  • f and g - polynomials
  • var_elim - variable to be eliminated
  • generic_point_generator - a generic point generator object for the factor of the resultant of f and g of interest

Output:

  • polynomial - the desired factor of the resultant of f and g
StructuralIdentifiability.simplify_matrixMethod
simplify_matrix(M)

Eliminate GCD of entries of every row and column

Input:

  • M::MatrixElem - matrix to be simplified

Output:

  • M::MatrixElem - Simplified matrix
  • extra_factors::Vector{AbstractAlgebra.MPolyElem} - array of GCDs eliminated from M.