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A relational system is a structure R=(S,{P_i:i in I},{f_j:j in J}) consisting of a set S, a collection of relations P_i(i in I) on S, and a collection of functions f_j(j in ...

The topology induced by a topological space X on a subset S. The open sets of S are the intersections S intersection U, where U is an open set of X. For example, in the ...

In general, a remainder is a quantity "left over" after performing a particular algorithm. The term is most commonly used to refer to the number left over when two integers ...

Rényi's polynomial is the polynomial (Rényi 1947, Coppersmith and Davenport 1991) that has 29 terms and whose square has 28, making it a sparse polynomial square.

An expression describing a form in which a quantity can be written. For example, all primes p>3 can be "represented as" 6n+/-1.

In a complete metric space, a countable union of nowhere dense sets is said to be meager; the complement of such a set is a residual set.

In a local ring R, there is only one maximal ideal m. Hence, R has only one quotient ring R/m which is a field. This field is called the residue field.

For a given monic quartic equation f(x)=x^4+a_3x^3+a_2x^2+a_1x+a_0, (1) the resolvent cubic is the monic cubic polynomial g(x)=x^3+b_2x^2+b_1x+b_0, (2) where the coefficients ...

A tree of links obtained by repeatedly choosing a crossing, applying the skein relationship to obtain two simpler links, and repeating the process. The tree depth of a ...

A method for predicting the onset of widespread chaos.