# Reduction

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**Reduction**, **reduced**, or **reduce** may refer to:

## Science and technology

[edit]### Chemistry

[edit]- Reduction (chemistry), 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

### Computing and algorithms

[edit]- Reduction (complexity), a transformation of one problem into another problem
- Reduction (recursion theory), 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, simplifying data in order to facilitate analysis
- Graph reduction, an efficient version of non-strict evaluation
- L-reduction, a transformation of optimization problems which keeps the approximability features
- Partial order reduction, a technique for reducing the size of the state-space to be searched by a model checking algorithm
- Strength reduction, a compiler optimization where a function of some systematically changing variable is calculated more efficiently by using previous values of the function
- Reduce (computer algebra system), a general-purpose computer algebra system geared towards applications in physics
- Reduce (higher-order function), 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, 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

[edit]- Reducible as the opposite of irreducible (mathematics)
- Reduction (mathematics), the rewriting of an expression into a simpler form
- Beta reduction, the rewriting of an expression from lambda calculus into a simpler form
- Dimension reduction, the process of reducing the number of random variables under consideration
- Lattice reduction, given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors
- Subject reduction or preservation, a rewrite of an expression that does not change its type
- Reduction of order, a technique for solving second-order ordinary differential equations
- Reduction of the structure group, for a -bundle and a map an -bundle such that the pushout is isomorphic to
- Reduction system, reduction strategy, the application of rewriting systems to eliminate reducible expressions
- Reduced form, 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, a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero
- Reduced product, a construction that generalizes both direct product and ultraproduct
- Reduced residue system, a set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n
- Reduced ring, a ring with no non-zero nilpotent elements
- Reduced row echelon form, a certain reduced row echelon form of a matrix which completely and uniquely determines its row space
- Reduced word, in a free group, a word with no adjacent generator-inverse pairs
- Variance reduction, a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations

### Medicine

[edit]#### Medical procedures

[edit]- Lung volume reduction surgery, 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), a medical procedure to restore a fracture or dislocation to the correct alignment
- Ventricular reduction, a type of operation in cardiac surgery
- Cosmetic surgery:

#### Other uses in medicine

[edit]- Weight loss
- In epidemiology:
- Relative risk reduction, 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 (URR), a dimensionless number used to quantify hemodialysis treatment adequacy

### Physics

[edit]- Dimensional reduction, the limit of a compactified theory where the size of the compact dimension goes to zero
- Reduction criterion, in quantum information theory, a necessary condition a mixed state must satisfy in order for it to be separable
- Reduced 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

[edit]- Lithic reduction, in Stone Age toolmaking, to detach lithic flakes from a lump of tool stone
- Noise reduction, in acoustic or signal processing
- Reduction drive, a mechanical device to shift rotational speed

## Arts and media

[edit]*Reducing*(film), a 1931 American film- Reduction (music), music arranged for smaller resources (piano) for easier analysis or performance

## Linguistics

[edit]- Accent reduction, modifying one's foreign accent towards that of a native speaker
- Vowel reduction, any change in vowel quality perceived as "weakening"
- Relaxed pronunciation, slurring of syllables of common words
- Definite article reduction, use of vowel-less forms of the English definite article in Northern England

## Philosophy

[edit]- Reductionism, a range of philosophical systems
- Reductio ad absurdum, a form of argument in which a proposition is disproven by following its implications to an absurd consequence
- Eidetic reduction, 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, one theory makes predictions that perfectly or almost perfectly match the predictions of a second theory

## Settlements

[edit]- Reductions, settlements in Spanish America intended to control and Christianize Indians
- Indian reductions in the Andes, settlements in the Andes to control and Christianize Indians

## Other uses

[edit]- Reduction (cooking), 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), a return to the Crown of fiefs that had been granted to the Swedish nobility
- Reduce (waste), practices of minimizing waste
- Reduction, Pennsylvania, unincorporated community, United States
- Reduction in rank, in military law
- Reduction to practice, 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
- Reductions, resettlement of indigenous peoples during the Spanish colonization of the Americas