Certificate of completion for Groebner Basis

[David Brandfonbrener]

When the Groebner basis is 1, is there a way to find the coefficients for a linear combination of my original generators of the ideal that is equal to 1? 

I want to be able to provably see which polynomials in my set of generators combine to 1. 

[Dima Pasechnik]

On Friday, December 8, 2017 at 10:20:31 PM UTC, David Brandfonbrener wrote:

When the Groebner basis is 1, is there a way to find the coefficients for a linear combination of my original generators of the ideal that is equal to 1? 

I want to be able to provably see which polynomials in my set of generators combine to 1. 

This is called computing a Nullstellensatz certificate. 

In Sage this is done using lift(), see http://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial_element.html#sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict.lift

[David Brandfonbrener]

Thanks! My bad for missing that in the documentation.