In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, resolvent meaning "that which resolves" may refer to:
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Resolvent formalism in operator theory
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Resolvent set In linear algebra and operator theory, the resolvent set of a linear operator is a set of complex numbers for which the operator is in some sense "well-behaved". The resolvent set plays an important role in the resolvent formalism.
Definitions
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in operator theory, the set of points where an operator is "well-behaved"
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Feller process#Resolvent in probability theory
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Resolvent (Galois theory)
In Galois theory, a discipline within the field of abstract algebra, a resolvent for a permutation group ''G'' is a polynomial whose coefficients depend polynomially on the coefficients of a given polynomial ''p'' and has, roughly speaking, a r ...
of an equation for a permutation group, in particular:
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Resolvent quadratic
In Galois theory, a discipline within the field of abstract algebra, a resolvent for a permutation group ''G'' is a polynomial whose coefficients depend polynomially on the coefficients of a given polynomial ''p'' and has, roughly speaking, a rati ...
of a cubic equation
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Resolvent cubic
In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four:
:P(x)=x^4+a_3x^3+a_2x^2+a_1x+a_0.
In each case:
* The coefficients of the resolvent cubic can be obta ...
of a quartic equation
In logic:
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Resolvent (logic)
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically ...
, the clause produced by a resolution
* In the
consensus theorem
In Boolean algebra, the consensus theorem or rule of consensus is the identity:
:xy \vee \barz \vee yz = xy \vee \barz
The consensus or resolvent of the terms xy and \barz is yz. It is the conjunction of all the unique literals of the terms, ...
, the term produced by a consensus in Boolean logic
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