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# Invariant

An invariant is something that does not change under a set of transformations. The property of being an invariant is called invariance.

Examples include:

An important connection exists between conservation laws and the invariance of physical laws with respect to certain transformations. For instance, time invariance implies that energy is conserved, translational invariance implies that momentum is conserved, and rotational invariance implies that angular momentum is conserved.

In mathematics, a fixed point is a value that is an invariant under a mathematical operation such as the application of a mathematical function.

In computer science, optimising compilers and the methodology of Design by contract pay close attention to invariant quantities in computer programs, where the set of transformations involved is the execution of the steps of the computer program.

In music using the twelve tone technique invariance describes the portions of rowss which have been so designed that they remain invariant under the allowable transformations (inversion, retrograde, retrograde-inversion, multiplication). George Perle describes their use as "pivots" or non-tonal ways of emphasizing certain pitches. Invariant rows are also combinatorial.