Elimination

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

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

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

eliminate_var(f, g, var_elim, generic_point_generator)

Eliminate a 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

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.MPolyRingElem} - array of GCDs eliminated from M.