**Algebraically true theorems**

** Definition**
: Given

- hypotheses polynomial (equations) H={h_1,...,h_r} generating a proper ideal

- a thesis T given by one polynomial equation

we say that the statement H ==> T is

if

On the other hand, geometrically speaking, we are working over an algebraically closed field.

NF(1, Ideal(h_1,...,h_r, t*k-1)).

If it is 0, theorem is algebraically true, else it is not true.

Sat(

ie. the set of polynomials f such that for some power

So a theorem is algebraically true iff (1)=Sat(