plural of difference quotient

(mathematical analysis) The slope of a secant as obtained by dividing the vertical difference between two intersections of the secant and a curve with their horizontal distance. When the horizontal distance approaches zero the slope of the secant approaches the derivative of the curve.

plural of Q quotient

(topology) A surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space.

(algebra, ring theory) For a given ring R and ideal I contained in R, another ring, denoted R / I, whose elements are the cosets of I in R.

(algebra) A field all of whose elements can be represented as ordered pairs each of whose components belong to a given integral domain, such that the second component is non-zero, and so that the additive operator is defined like so: (a,b)+(a',b')=(ab'+a'b,bb'), the multiplicative operator is defined coordinate-wise, the zero is (0,1), the unity is (1,1), the additive inverse of (a,b) is (-a,b), equivalence is defined like so: (a,b)≡(a',b') if and only if ab'=a'b, and multiplicative inverse of a non-zero–equivalent element (a,b) is (b,a).

plural of quotient ring

The degree to which someone or something reflects fact rather than fiction; the degree to which something reflects reality.

plural of truth quotient

(mathematics) A formula used in the min-max theorem to find exact eigenvalues, and in eigenvalue algorithms to obtain an eigenvalue approximation from an eigenvector approximation; it has applications in quantum mechanics.