Reduction
Reduction, reduced, or reduce may refer to:
Science
Chemistry
- Organic redox reaction, a redox reaction that takes place with organic compounds
- Reduced gas, a gas with a low oxidation number
- Reducing agent, element or compound in a redox reaction that donates an electron to another species
- Reducing atmosphere, an oxygen-poor gaseous environment that inhibits oxidation
- Reductase, an enzyme that catalyzes a reduction reaction
- Reduction potential, a measure of the tendency of a chemical species to acquire electrons
- Ore reduction: see smelting
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 have contributed to its development under his direction.
Reduce is written entirely in its own LISP dialect called Portable Standard LISP, expressed in an Algol-like syntax called RLISP. The latter is used as a basis for Reduce's user-level language.
Implementations of Reduce are available on most variants of Unix, Linux, Microsoft Windows, or Apple Macintosh systems by using an underlying Portable Standard LISP or Codemist Standard LISP implementation.
Reduce was open sourced on December 2008 and is available for free under a modified BSD license on SourceForge. Previously it had cost $695.
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Reduction (complexity)
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A reduction from one problem to another may be used to show that the second problem is at least as difficult as the first.
Intuitively, problem A is reducible to problem B if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, solving A cannot be harder than solving B. "Harder" means having a higher estimate of the required computational resources in a given context (e.g., higher time complexity, etc.).
We write A ≤m B, usually with a subscript on the ≤ to indicate the type of reduction being used (m : mapping reduction, p : polynomial reduction).
The mathematical structure generated on a set of problems by the reductions of a particular type generally forms a preorder, whose equivalence classes may be used to define degrees of unsolvability and complexity classes.
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