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A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means ...

A negative integer is one of the integers ..., -4, -3, -2, -1 obtained by negating the positive integers. The negative integers are commonly denoted Z^-.

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.

A nonempty set is a set containing one or more elements. Any set other than the empty set emptyset is therefore a nonempty set. Nonempty sets are sometimes also called ...

A normal extension is the splitting field for a collection of polynomials. In the case of a finite algebraic extension, only one polynomial is necessary.

In every residue class modulo p, there is exactly one integer polynomial with coefficients >=0 and <=p-1. This polynomial is called the normal polynomial modulo p in the ...

A continuous map f:X->Y between topological spaces is said to be null-homotopic if it is homotopic to a constant map. If a space X has the property that id_X, the identity ...

An algebraic surface of degree eight. The maximum number of ordinary double points known to exist on an octic surface is 168 (the Endraß octics), although the rigorous upper ...

An octomino is an 8-polyomino. There are 369 free (illustrated above), 704 one-sided, and 2725 fixed octominoes.

Any continuous cumulative frequency curve, such as the one illustrated above in the right figure.