plural of circle inversion

(geometry, inversive geometry, for a given circle with centre O and radius r) A transformation that maps any point P ≠ O to the point P’ on the ray from O through P for which OP × OP’ = r², and which maps O to the point at infinity.

plural of inverse semigroup

(algebra, group theory) A semigroup in which every element x has an inverse y, such that x = xyx and y = yxy.

(geometry) The branch of geometry concerned with inversion transformations, specifically circle inversions in the Euclidean plane, but also as generalised in non-Euclidean and higher-dimensional spaces.

(software architecture) Abstract principle describing an aspect of some software architecture designs in which the flow of control of a system is inverted in comparison to the traditional architecture, getting the flow of control from a generic code part.

plural of inverse image

The set of points that map to a given point (or set of points) under a specified function.

plural of inverse function

(law) The taking of private property by the government without providing compensation, thus forcing the previous owner to file a lawsuit against the government to recover the value of the property taken.