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A basis of a modular system M is any set of polynomials B_1, B_2, ... of M such that every polynomial of M is expressible in the form R_1B_1+R_2B_2+..., where R_1, R_2, ... ...

A game for which each player has a different set of moves in any position. Every position in an impartial game has a nim-value.

A set of sample problems in unconstrained optimization is given by loading Optimization`UnconstrainedProblems` and evaluating $FindMinimumProblems.

Let S be a collection of subsets of a set X, mu:S->[0,infty] a set function, and mu^* the outer measure induced by mu. The measure mu^_ that is the restriction of mu^* to the ...

A sigma-algebra which is related to the topology of a set. The Borel sigma-algebra is defined to be the sigma-algebra generated by the open sets (or equivalently, by the ...

Integer programming in a special case of linear programming in which all variables are required to take on integer values only. Set covering deployment is an example ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...

If T is a set of axioms in a first-order language, and a statement p holds for any structure M satisfying T, then p can be formally deduced from T in some appropriately ...

Let A be a set. An operation on A is a function from a power of A into A. More precisely, given an ordinal number alpha, a function from A^alpha into A is an alpha-ary ...

Let S be a nonempty set, then an ultrafilter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F. 2. If A,B in F, then A ...