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Topic: Associativity

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Note that the dual of an associative composition is associative.
Before going on to combine associativity and identifiability to obtain a category, pause to consider something associativity alone allows us to say about null identities in an arrow land.
Associativity is just the property needed to ensure that these are equal.
www.chaos.org.uk /~eddy/math/arrow/associate.html   (1289 words)

  PlanetMath: associative
Examples of associative operations are addition and multiplication over the integers (or reals), or addition or multiplication over
This is version 6 of associative, born on 2002-02-18, modified 2002-03-03.
Object id is 2150, canonical name is Associative.
planetmath.org /encyclopedia/Associative.html   (120 words)

It means that, within an expression containing two or more of the same associative operators in a row, the order of operations does not matter as long as the sequence of the operands is not changed.
Associativity is not to be confused with the commutativity.
is an example of associativity because the parentheses were changed (and consequently the order of operations during evaluatation) while the operands 5, 2, and 1 appeared in the exact same order from left to right in the expression.
www.buzznet.com /tags/associativity   (226 words)

 Running SICStus Prolog - 2.2.2. Associativity
Precedence and associativity are defined in Prolog with the built-in predicate
The first argument determines precedence, the second associativity and the third defines the operator symbol.
The associativity argument is also used to declare whether the operator is an infix operator (like the arithmetical ones), a prefix operator or a postfix operator.
www-users.york.ac.uk /~sjh1/courses/L333intro_to_prolog/complete/complete-2.2.2.html   (276 words)

 Power associativity - Wikipedia, the free encyclopedia
In abstract algebra, power associativity is a weak form of associativity.
An algebra (or more generally a magma) is said to be power-associative if the subalgebra generated by any element is associative.
Every associative algebra is obviously power-associative, but so are all other alternative algebras (like the octonions, which are non-associative) and even some non-alternative algebras like the sedenions.
en.wikipedia.org /wiki/Power_associativity   (284 words)

 Associativity - Wikipedia, the free encyclopedia
For associativity in central processor unit memory cache architecture see CPU cache.
However, many important and interesting operations are non-associative; one common example would be the vector cross product.
In short, composition of maps is always associative.
en.wikipedia.org /wiki/Associativity   (616 words)

 Associativity Encyclopedia   (Site not responding. Last check: )
Associative operations are abundant in mathematics, and in fact most algebraic structures explicitly require their binary operations to be associative.
Power associativity and alternativity are weak forms of associativity.
The modified nonverbal task and the associativity of length task investigated the qualitylogic on the modified nonverbal and associativity of length tasks, although there weredifferent tasks.
www.hallencyclopedia.com /topic/Associativity.html   (766 words)

 Re: RE-ASSOC: a question about the associativity of RE concatenation
It's significant that _none_ of the example regexps in the spec are sensative to the associativity issue.
So if you stated or assumed a definition of "subpattern", but didn't _explicitly_ consider associativity, then we can't look to your definition to answer any questions about associativity: your intent might have decided associativity simply by accident.
For the associativity question, I know of no answer that makes more sense than to give regexps the useful algebraic properties that follow from the left associativity of concatenation.
www.opengroup.org /austin/mailarchives/ag/msg03930.html   (920 words)

 Associativity Properties of the Symplectic Sum - McDuff, Symington (ResearchIndex)
Associativity Properties of the Symplectic Sum - McDuff, Symington (ResearchIndex)
Abstract: In this note we apply a 4-fold sum operation to develop an associativity rule for the pairwise symplectic sum.
The question of uniqueness of a symplectic structure (up to path equivalence in the space of symplectic forms) is quite delicate.
citeseer.ist.psu.edu /mcduff96associativity.html   (454 words)

 Associativity Summary
Thus, the associative property states that combining a with b first, and then combining the result with c, is equivalent to combining b with c first, and then combining a with that result.
Subtraction of real numbers is not associative since in general (a - b) -c not equal a - (b - c), for example (35 - 2) - 6 = 33 - 6 = 27, while 35 - (2 - 6) = 35 - (-4) = 39.
When the associative property holds for all the members of a set, every combination of elements must result in another element of the same set.
www.bookrags.com /Associativity   (817 words)

 A Discussion on Modern Design Optimization Tools: Full Associativity of CAD, FEA and Event Simulators   (Site not responding. Last check: )
Care is taken such that the FEA model is also updated using the principle of associativity, which implies that constraints and loads are preserved from the prior analysis.
Associativity between the CAD and FEA software should allow the engineer to alter the model in either application, and have the other automatically reflect these changes.
Thus, associativity is required in order to achieve this automatic communication between the CAD and FEA models.
www.algor.com /news_pub/tech_white_papers/design_optimization   (3065 words)

 CS 3411C - April 22, 1999
If an operator has left associativity, then the leftmost occurrence of that operator is evaluated first.
If the operator has right associativity, then the rightmost occurrence of that operator is evaluated first.
Usually, associativity is left to right (in imperative languages), except with exponentiation which is right to left.
www.cc.gatech.edu /computing/classes/cs3411c_99_spring/lec08.html   (1239 words)

 [No title]
If the associativity ticks are too big, it means that a MH stayed at a location for a long time, so it is likely to move soon.
The stability is determined using "associativity ticks" -- a count of "alive" messages from neighboring nodes greater than a set threshold (determined by the migration speed and transmission distance of the nodes) sets those nodes as active links, and not just a migratory node.
The degree of the association is proportional to the number of ticks (temporal association).
www.cs.cornell.edu /Courses/cs615/2001fa/615/fall01-paper10.txt   (7544 words)

 C++ Ripped Apart - Operator Precedence & Operator Associativity   (Site not responding. Last check: )
Operator precedence (determines which expressions are evaluated before others in a statement) and operator associativity are both very important to understand.
Associativity may be left associative (left to right) or right associative (right to left).
Now that we have covered the precedence of operators and operator associativity, we can move on to something that occurs during assignment statements, sometimes without the programmer asking for it and sometimes by the programmer specifically asking for it.
warebizprogramming.com /text/cpp/section1/part5.htm   (301 words)

 Nodesets and Sidesets
This functionality can be used either to associate a previously-generated mesh with a geometry (See Importing an Exodus II File), or to associate a field function with a geometry for adaptive surface meshing (See Adaptive Meshing).
Then, the name of each geometry entity is associated with the corresponding nodeset by writing a property name and designating the corresponding nodeset as having that property.
Nodeset numbers used for associativity nodesets are determined by adding a fixed base number (depending on the order of the geometric entity) to the geometric entity id number.
cubit.sandia.gov /help-version9.1/chapter_6/nodesets_and_sidesets.html   (1095 words)

 Table of C and C++ operator precedence and associativity
This table lists the C and C++ language operators in order of precedence and shows the direction of associativity for each operator.
The operator associativity rules define the order in which adjacent operators with the same precedence level are evaluated.
In this case we say that subtraction is left associative meaning that the left most subtraction must be done first.
web.ics.purdue.edu /~cs240/misc/operators.html   (174 words)

 2.6.2 Precedence and Associativity Declarations in Cecil
Cecil allows the precedence and associativity of infix operators to be specified by programmers through precedence declarations.
Expressions mixing operators of unrelated precedences or multiple sequential occurrences of an operator that is non-associative must be explicitly parenthesized.
The effect of a precedence declaration is to declare the relationship of the precedences of several binary operators and/or to specify the associativity of a binary operator.
www.cs.washington.edu /research/projects/cecil/www/Vortex-Two-Zero/doc-cecil-lang/cecil-spec-39.html   (503 words)

This term is of course derived from "associated" and "associative".
To be honest, I thought the word "associativity" was one of those words invented by some techno-marketeer in the late 1980s to describe an important attribute of solid modeling systems.
Associative Edits -- Assuming that we have conducted all the above work as one user at one workstation in one data workspace, we simply edit the industrial design part and voila, all the rest happens automatically without user intervention (or user approval).
www.wamware.com /primer/associativity.htm   (1551 words)

 Operator Precedence and Associativity
When we can't decide by operator precedence alone in which order to calculate an expression, we must use associativity.
If you don't use parentheses, Pike will use the precedences and the associativities of the operators to decide in which order to perform them.
This table shows the priority and associativity of each operator in Pike, with the highest priority at the top:
docs.roxen.com /pike/7.0/tutorial/expressions/operator_tables.xml   (200 words)

 Characterization of Fine-Grained Associativity Gaps
Drawing on over a decade of X-analysis integration (XAI) [1] research and development, it uses the XAI multi-representation architecture (MRA) as a means to decompose the problem and guide identification of potential key metrics.
One problem, denoted the fine-grained associativity gap, is highlighted in particular.
Other associativity gap costs have yet to be estimated, including over- and under-design, lack of knowledge capture, and inconsistencies.
eislab.gatech.edu /pubs/reports/EL004   (289 words)

 [C++] Overloaded Operator Associativity - Neowin.net
This leads me to believe that the associativity of my overloaded operators is based on the associativity of the default operators (or that the actual symbols used specify associativity, and not the function itself).
associativity and precedence of operators is always the same, regardless the type.
The names of, precedence of, associativity of, and arity of operators is fixed by the language.
www.neowin.net /forum/index.php?showtopic=447385&view=getnewpost   (413 words)

 Understanding CPU caching and performance: Page 7   (Site not responding. Last check: )
Any more than eight-way associativity and the cache's latency is increased so much that the decrease in miss rate isn't worth it.
Any less than two-way associativity and the number of collisions often increase the miss rate to the point that the decrease in latency isn't worth it.
First, though you've probably already figured it out, a direct-mapped cache is simply a one-way associative cache and a fully associative cache is an n-way associative cache where n is equal to the total number of blocks in the cache.
arstechnica.com /articles/paedia/cpu/caching.ars/7   (1078 words)

 Operators, Precedence and Associativity
Thus the associativity properties show that the expression is equivalent to the expression
Properties of the C operators of primary interest for our purposes are summarized in table 2.4 grouped in order of decreasing precedence, with their associativity properties.
While it is best to know in detail the precedence level of all the operators, when there is any doubt, it is best to use parentheses to force the interpretation that you, the programmer intends.
www.students.itu.edu.tr /~sekerc/c/6.html   (779 words)

 MuLE Static versus Dynamic Scoping Lab
Implicit rules for associativity are defined for a language so that evaluating expressions involving operations at the same level of precedence can determine the order of operation.
This lab requires you to examine two other possibilities and explain their implementation in terms of associativity and precedence with respect to expression evaluation This will neither affect the parsing of a SPoc program or the execution of SPoc programs.
After recording eight sets of output, explain the associativity and precedence rules for each of the three implementations.
math.holycross.edu /~mule/labs/RLvLR.htm   (440 words)

 Associativity and Commutativity   (Site not responding. Last check: )
Not all set operations are associative and/or commutative.
These concepts of associativity and commutativity are of fundamental importance in mathematics.
The familiar operations of addition and multiplication over the real numbers are both associative and commutative.
scom.hud.ac.uk /scomtlm/book/node27.html   (127 words)

 How much commutativity in associativity :)
Also, I don't think you mean to call G a group, since the group operation is associative by definition.
The two plus signs in each expression of the equation are the operations, and associativity is saying that the order of doing the operations don't matter, you can go left to right or right to left.
It says that we cannot say that "+" is associative without referring to commutativity, that is, an operation cannot said to be just associative but non-commutative.
www.physicsforums.com /showthread.php?p=575206#post575206   (1346 words)

 C++ Operators, with Precedence and Associativity
The associativity rules of a language specify which operator is evaluated first when two operators with the same precedence are adjacent in an expression.
Associativity information is given in the center column, in which LR=Left-to-Right associativity and RL=Right-to-Left associativity).
The example is, of course, somewhat artificial (since how often do we really want to output the value of a conditional expression?), but it makes the point.
cs.stmarys.ca /~porter/csc/ref/cpp_operators.html   (443 words)

 Associativity Based Routing   (Site not responding. Last check: )
The main idea of associativity is that there no point in choosing a route based on the shortest path when the route is going to be broken or invalidated due to node’s mobility.
Association in ABR takes up a few metrics such as link delay, signal strength, power life, route relaying load, period of presence or spatial and temporal characteristics.
The associativity ticks with its neighbours will also be appended together with other routing metrics/ qualities.
www.comp.brad.ac.uk /~sburuha1/abr.htm   (689 words)

 Syntax extensions and interpretation scopes
By default, a notation is considered non associative, but the precedence level is mandatory (except for special cases whose level is canonical).
To avoid giving the precedence and associativity every time, it is possible to declare a parsing rule in advance without giving its interpretation.
An abbreviation expects no precedence nor associativity, since it can always be put at the lower level of atomic expressions, and associativity is irrelevant.
pauillac.inria.fr /coq/doc/Reference-Manual013.html   (3928 words)

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