Substitution (algebra)
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High Quality Content by WIKIPEDIA articles! In algebra, the operation of substitution can be applied in various contexts involving formal objects containing symbols (often called variables or indeterminates); the operation consists of systematically replacing occurrences of some symbol by a given value. A common case of substitution involves polynomials, where substitution of a numerical value for the indeterminate of a (univariate) polynomial amounts to evaluating the polynomial at that value. Substitution can however also applied to other kinds of formal objects built from symbols, for insta...
High Quality Content by WIKIPEDIA articles! In algebra, the operation of substitution can be applied in various contexts involving formal objects containing symbols (often called variables or indeterminates); the operation consists of systematically replacing occurrences of some symbol by a given value. A common case of substitution involves polynomials, where substitution of a numerical value for the indeterminate of a (univariate) polynomial amounts to evaluating the polynomial at that value. Substitution can however also applied to other kinds of formal objects built from symbols, for instance elements of free groups. In order for substitution to be defined, one needs an algebraic structure with an appropriate universal property, that asserts the existence of unique homomorphisms that send indeterminates to specific values; the substitution then amounts to finding the image under such a homomorphism.
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