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The ring R[x] of polynomials in a variable x.

A sequence of polynomials p_i(x), for i=0, 1, 2, ..., where p_i(x) is exactly of degree i for all i.

The difference between the highest and lowest degrees of a polynomial.

The vertex of a polytope is a point where edges of the polytope meet.

A tensor g whose discriminant satisfies g=g_(11)g_(22)-g_(12)^2>0.

The relationship x precedes y is written x≺y. The relation x precedes or is equal to y is written x<=y.

alpha is called a predecessor if there is no ordinal number beta such that beta+1=alpha.

An operator in logic which returns either true or false.

A prime field is a finite field GF(p) for p is prime.

An n-manifold which cannot be "nontrivially" decomposed into other n-manifolds.