Reduction, reduced, or reduce may refer to:

Science and technology

Chemistry

Reduction (chemistry) Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a d ...

, part of a reduction-oxidation (redox) reaction in which atoms have their oxidation state changed. ** Organic redox reaction, a redox reaction that takes place with organic compounds ** Ore reduction: see

smelting Smelting is a process of applying heat to ore, to extract a base metal. It is a form of extractive metallurgy. It is used to extract many metals from their ores, including silver, iron, copper, and other base metals. Smelting uses heat and a ...

Computing and algorithms

Reduction (complexity) In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem ...

, a transformation of one problem into another problem *

Reduction (recursion theory) In computability theory, many reducibility relations (also called reductions, reducibilities, and notions of reducibility) are studied. They are motivated by the question: given sets A and B of natural numbers, is it possible to effectively conver ...

, given sets A and B of natural numbers, is it possible to effectively convert a method for deciding membership in B into a method for deciding membership in A? * Bit Rate Reduction, an audio compression method *

Data reduction Data reduction is the transformation of numerical or alphabetical digital information derived empirically or experimentally into a corrected, ordered, and simplified form. The purpose of data reduction can be two-fold: reduce the number of data rec ...

, simplifying data in order to facilitate analysis *

Graph reduction In computer science, graph reduction implements an efficient version of non-strict evaluation, an evaluation strategy where the arguments to a function are not immediately evaluated. This form of non-strict evaluation is also known as lazy evaluati ...

, an efficient version of non-strict evaluation *

L-reduction In computer science, particularly the study of approximation algorithms, an L-reduction ("''linear reduction''") is a transformation of optimization problems which linearly preserves approximability features; it is one type of approximation-preser ...

, a transformation of optimization problems which keeps the approximability features *

Partial order reduction In computer science, partial order reduction is a technique for reducing the size of the state-space to be searched by a model checking or automated planning and scheduling algorithm. It exploits the commutativity of concurrently executed transit ...

, a technique for reducing the size of the state-space to be searched by a model checking algorithm *

Strength reduction In compiler construction, strength reduction is a compiler optimization where expensive operations are replaced with equivalent but less expensive operations. The classic example of strength reduction converts "strong" multiplications inside a loo ...

, a compiler optimization where a function of some systematically changing variable is calculated more efficiently by using previous values of the function *

Variance reduction In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. Every output random variable fro ...

, a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations *

Reduce (computer algebra system) Reduce is a general-purpose computer algebra system geared towards applications in physics. The development of the Reduce computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many scientists from all over the world ha ...

, a general-purpose computer algebra system geared towards applications in physics *

Reduce (higher-order function) In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the res ...

, in functional programming, a family of higher-order functions that process a data structure in some order and build up a return value *

Reduced instruction set computing In computer engineering, a reduced instruction set computer (RISC) is a computer designed to simplify the individual instructions given to the computer to accomplish tasks. Compared to the instructions given to a complex instruction set compu ...

, a CPU design philosophy favoring an instruction set reduced in size and complexity of addressing, to simplify implementation, instruction level parallelism, and compiling

Pure mathematics and statistics

* Reducible as the opposite of

irreducible (mathematics) In mathematics, the concept of irreducibility is used in several ways. * A polynomial over a field may be an irreducible polynomial if it cannot be factored over that field. * In abstract algebra, irreducible can be an abbreviation for irreducible ...

Reduction (mathematics) In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is ...

, the rewriting of an expression into a simpler form *

Beta reduction Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation tha ...

, the rewriting of an expression from lambda calculus into a simpler form *

Dimension reduction Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally ...

, the process of reducing the number of random variables under consideration *

Lattice reduction In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different algorithms, whose running time is usually at least expone ...

, given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors *

Subject reduction In type theory, a type system has the property of subject reduction (also subject evaluation, type preservation or simply preservation) if evaluation of expressions does not cause their type to change. Formally, if Γ ⊢ ''e''1 : ''τ'' and ''e''1 ...

or preservation, a rewrite of an expression that does not change its type *

Reduction of order Reduction of order is a technique in mathematics for solving second-order linear ordinary differential equations. It is employed when one solution y_1(x) is known and a second linearly independent solution y_2(x) is desired. The method also appl ...

, a technique for solving second-order ordinary differential equations *

Reduction of the structure group In differential geometry, a ''G''-structure on an ''n''-manifold ''M'', for a given structure group ''G'', is a principal ''G''- subbundle of the tangent frame bundle F''M'' (or GL(''M'')) of ''M''. The notion of ''G''-structures includes vario ...

, for a

G

-bundle

B

and a map

H \to G

H

-bundle

B_H

such that the pushout

B_H \times_H G

is isomorphic to

B

Reduction system In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduc ...

, reduction strategy, the application of rewriting systems to eliminate reducible expressions *

Reduced form In statistics, and particularly in econometrics, the reduced form of a system of equations is the result of solving the system for the endogenous variables. This gives the latter as functions of the exogenous variables, if any. In econometrics, the ...

, in statistics, an equation which relates the endogenous variable X to all the available exogenous variables, both those included in the regression of interest (W) and the instruments (Z) *

Reduced homology In mathematics, reduced homology is a minor modification made to homology theory in algebraic topology, motivated by the intuition that all of the homology groups of a single point should be equal to zero. This modification allows more concise stat ...

, a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero *

Reduced product In model theory, a branch of mathematical logic, and in algebra, the reduced product is a construction that generalizes both direct product and ultraproduct. Let be a family of structures of the same signature σ indexed by a set ''I'', and let ...

, a construction that generalizes both direct product and ultraproduct *

Reduced residue system In mathematics, a subset ''R'' of the integers is called a reduced residue system modulo ''n'' if: #gcd(''r'', ''n'') = 1 for each ''r'' in ''R'', #''R'' contains φ(''n'') elements, #no two elements of ''R'' are congruent modulo ''n''. Here φ ...

, a set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n *

Reduced ring In ring theory, a branch of mathematics, a ring is called a reduced ring if it has no non-zero nilpotent elements. Equivalently, a ring is reduced if it has no non-zero elements with square zero, that is, ''x''2 = 0 implies ''x'' = ...

, a ring with no non-zero nilpotent elements *

Reduced row echelon form In linear algebra, a matrix is in echelon form if it has the shape resulting from a Gaussian elimination. A matrix being in row echelon form means that Gaussian elimination has operated on the rows, and column echelon form means that Gaussian e ...

, a certain reduced row echelon form of a matrix which completely and uniquely determines its row space *

Reduced word In group theory, a word is any written product of group elements and their inverses. For example, if ''x'', ''y'' and ''z'' are elements of a group ''G'', then ''xy'', ''z''−1''xzz'' and ''y''−1''zxx''−1''yz''−1 are words in the set . Two ...

, in a free group, a word with no adjacent generator-inverse pairs

Medicine

Medical procedures

Lung volume reduction surgery Cardiothoracic surgery is the field of medicine involved in surgical treatment of organs inside the thoracic cavity — generally treatment of conditions of the heart (heart disease), lungs (lung disease), and other pleural or mediastinal struc ...

, a treatment for chronic obstructive pulmonary disease * Selective reduction (or fetal reduction), the practice of reducing the number of fetuses in a multifetal pregnancy *

Reduction (orthopedic surgery) Reduction is a surgical procedure to repair a fracture or dislocation to the correct alignment. Description When a bone fractures, the fragments lose their alignment in the form of displacement or angulation. For the fractured bone to heal witho ...

, a medical procedure to restore a fracture or dislocation to the correct alignment *

Ventricular reduction Ventriculectomy, or ventricular reduction, is a type of operation in cardiac surgery to reduce enlargement of the heart The heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory syst ...

, a type of operation in cardiac surgery * Cosmetic surgery: **

Breast reduction Reduction mammoplasty (also breast reduction and reduction mammaplasty) is the plastic surgery procedure for reducing the size of large breasts. In a breast reduction surgery for re-establishing a functional bust that is proportionate to the woma ...

Jaw reduction Jaw reduction or mandible angle reduction is a type of surgery to narrow the lower one-third of the face—particularly the contribution from the mandible and its muscular attachments. There are several techniques for treatment—including surgical ...

Other uses in medicine

Weight loss Weight loss, in the context of medicine, health, or physical fitness, refers to a reduction of the total body mass, by a mean loss of fluid, body fat ( adipose tissue), or lean mass (namely bone mineral deposits, muscle, tendon, and other co ...

* In epidemiology: **

Relative risk reduction In epidemiology, the relative risk reduction (RRR) or efficacy is the relative decrease in the risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with ...

, the absolute risk reduction by the control event rate ** Absolute risk reduction, the decrease in risk of a given activity or treatment in relation to a control activity or treatment *

Urea reduction ratio The urea reduction ratio (URR) is a dimensionless number used to quantify dialysis treatment adequacy. Definition URR = \frac \times 100\% Where: * Upre is the pre-dialysis urea level * Upost is the post-dialysis urea level Whereas the URR ...

(URR), a dimensionless number used to quantify hemodialysis treatment adequacy

Physics

Dimensional reduction Dimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics, a theory in ''D'' spacetime dimensions can be redefined in a lower number of dimensions ''d'', by taking all the fields ...

, the limit of a compactified theory where the size of the compact dimension goes to zero *

Reduction criterion In quantum information theory, the reduction criterion is a necessary condition a mixed state must satisfy in order for it to be separable. In other words, the reduction criterion is a ''separability criterion''. It was first proved and independe ...

, in quantum information theory, a necessary condition a mixed state must satisfy in order for it to be separable *

Reduced mass In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the mass ...

, the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics * Reduced properties (pressure, temperature, or volume) of a fluid, defined based on the fluid's critical point

Other uses in science and technology

Lithic reduction In archaeology, in particular of the Stone Age, lithic reduction is the process of fashioning stones or rocks from their natural state into tools or weapons by removing some parts. It has been intensely studied and many archaeological industrie ...

, in Stone Age toolmaking, to detach lithic flakes from a lump of tool stone * Noise reduction, in acoustic or signal processing *

Reduction drive A reduction drive is a mechanical device to shift rotational speed. A planetary reduction drive is a small scale version using ball bearings in an epicyclic arrangement instead of toothed gears. Reduction drives are used in engines of all kinds ...

, a mechanical device to shift rotational speed

Arts and media

* ''Reducing'' (film), a 1931 American film *

Reduction (music) In music, a reduction is an arrangement or transcription of an existing score or composition in which complexity is lessened to make analysis, performance, or practice easier or clearer; the number of parts may be reduced or rhythm may be s ...

, music arranged for smaller resources (piano) for easier analysis or performance

Linguistics

Accent reduction Accent reduction, also known as accent modification or accent neutralization, is a systematic approach for learning or adopting a new speech accent. It is the process of learning the sound system (or phonology) and melodic intonation of a langua ...

, modifying one's foreign accent towards that of a native speaker *

Vowel reduction In phonetics, vowel reduction is any of various changes in the acoustic ''quality'' of vowels as a result of changes in stress, sonority, duration, loudness, articulation, or position in the word (e.g. for the Creek language), and which are per ...

, any change in vowel quality perceived as "weakening" ** Vowel reduction in English *

Relaxed pronunciation Relaxation stands quite generally for a release of tension, a return to equilibrium. In the sciences, the term is used in the following ways: * Relaxation (physics), and more in particular: ** Relaxation (NMR), processes by which nuclear magnetiza ...

, slurring of syllables of common words *

Definite article reduction Definite article reduction (DAR) is the term used in recent linguistic work to refer to the use of vowel-less forms of the definite article ''the'' in Northern dialects of English English, for example in the Yorkshire dialect. DAR is often represe ...

, use of vowel-less forms of the English definite article in Northern England

Philosophy

* Reductionism, a range of philosophical systems *

Reductio ad absurdum In logic, (Latin for "reduction to absurdity"), also known as (Latin for "argument to absurdity") or ''apagogical arguments'', is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absu ...

, a form of argument in which a proposition is disproven by following its implications to an absurd consequence *

Eidetic reduction Eidetic reduction is a technique in the study of essences in Edmund Husserl's Phenomenology (philosophy), phenomenology whose goal is to identify the basic components of phenomena. Eidetic reduction requires that a phenomenologist examine the essen ...

, a technique in the study of essences in phenomenology whose goal is to identify the basic components of phenomena *

Intertheoretic reduction In philosophy of science, intertheoretic reduction occurs when a reducing theory makes predictions that perfectly or almost perfectly match the predictions of a reduced theory, while the reducing theory explains or predicts a wider range of phenom ...

, in philosophy of science, one theory makes predictions that perfectly or almost perfectly match the predictions of a second theory

Settlements

* Reductions, settlements in Spanish America intended to control and Christianize Indians *

Indian reductions in the Andes Indian reductions in the Andes ( es, reducciones de indios, links=no) were settlements in the former Inca Empire created by Spanish authorities and populated by the forcible relocation of indigenous Andean populations, called "Indians" by the Spa ...

, settlements in the Andes to control and Christianize Indians

Other uses

Reduction (cooking) In cooking, reduction is the process of thickening and intensifying the flavor of a liquid mixture such as a soup, sauce, wine, or juice by simmering or boiling. Reduction is performed by simmering or boiling a liquid such as a stock, fruit or ve ...

, the process of thickening or intensifying the flavor of a liquid mixture such as a soup, sauce, wine, or juice by evaporation * Reduction (military), the siege and capture of a fortified place *

Reduction (Sweden) In the Great Reduction of 1680, by which the ancient landed nobility lost its power base, the Swedish Crown recaptured lands earlier granted to the nobility. ''Reductions'' ( sv, reduktion) in Sweden and its dominions were the return to the Cro ...

, a return to the Crown of fiefs that had been granted to the Swedish nobility *

Reduce (waste) Waste minimisation is a set of processes and practices intended to reduce the amount of waste produced. By reducing or eliminating the generation of harmful and persistent wastes, waste minimisation supports efforts to promote a more sustainab ...

, practices of minimizing waste * Reduction, Pennsylvania, unincorporated community, United States *

Reduction in rank Reduction in rank may refer to three separate concepts: *In military law, a ''reduction in rank'' or ''degradation'' is a demotion in military rank as punishment for a crime or wrongdoing, imposed by a court-martial or other authority. It may be im ...

, in military law *

Reduction to practice In United States patent law, the reduction to practice is the step in the formation of an invention beyond the conception thereof. Reduction to practice may be either actual (the invention is actually carried out and is found to work for its intende ...

, in United States patent law, the embodiment of the concept of an invention * Ego reduction, predicated on the use of Sigmund Freud's concept of the ego