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


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