I was wondering if anyone could recommend software to construct a real Nullstellensatz certificate that a system of polynomial equations has no real solution. The system of about 20 polynomials equations is cubic at most. I was interested in something that applied, or is similar to, (Nullstellensatz Linear Algebra (NulLA) Algorithm) as described here https://www.usna.edu/Users/math/margulies/papers/nulla_issac.pdf
My understanding is that if the certificate is of degree 1 then I'll have about 400 linear equations, but that if its of degree 2 then this explodes to 8000 or so. Hence the need for some purpose built software.
Any suggestions or approaches much appreciated (I have a science not math background).
thanks