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Topic: Idempotent function

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	Idempotence - Wikipedia, the free encyclopedia
		For example, the greatest integer function is idempotent as a function from the set of real numbers to the set of integers.
		An idempotent element of a ring is by definition an element that's idempotent with respect to the ring's multiplication.
		The central idempotents of R are closely related to the decompositions of R as a direct sum of rings.
	en.wikipedia.org /wiki/Idempotent (809 words)

	Floor function - Wikipedia, the free encyclopedia
		Being a piecewise constant function, its derivative is zero where it exists, that is, at all points which are not integers.
		In fancy language: the floor function is part of a Galois connection; it is the upper adjoint of the function that embeds the integers into the reals.
		The floor and ceiling function are usually typeset with left and right square brackets where the upper (for floor function) or lower (for ceiling function) horizontal bars are missing, and, e.g., in the LaTeX typesetting system these symbols can be constructed with the \lfloor, \rfloor, \lceil and \rceil commands.
	en.wikipedia.org /wiki/Floor_function (716 words)

	Idempotent (Site not responding. Last check: 2007-11-01)
		In mathematics an idempotent element, or an idempotent for short, is anything that, when multiplied by itself, gives itself as result.
		A function f from a set M to itself is called idempotent if f o f = f, that is, f(f(x)) = f(x) for all x in M.
		Less trivial examples are the absolute value function of a real or complex argument, and the closure operator for a topological space X, which is an idempotent function on the power set of X.
	bopedia.com /en/wikipedia/i/id/idempotent.html (460 words)

	PlanetMath: idempotency
		For example, every identity element is idempotent, and in a group this is the only idempotent element.
		An idempotent linear transformation from a vector space to itself is called a projection.
		This is version 18 of idempotency, born on 2002-02-24, modified 2006-07-12.
	planetmath.org /encyclopedia/Idempotent.html (150 words)

	Fabulous Adventures In Coding : Five-Dollar Words for Programmers, Part One: Idempotence
		A function is "idempotent" if the result of doing it twice (feeding the output of the first call into the second call) is exactly the same as the result of doing it once.
		Idempotent (in my experience) is rarely applied to functions from R to R. It's usually reserved for functions that operate on "more complex" domains.
		Fixed points and idempotency are related; in the subspace projection example, half of the reason that it's idempotent is that every vector in the subspace is a fixed point (the other half is that the operator maps every point into the subspace).
	blogs.msdn.com /ericlippert/archive/2005/10/26/483900.aspx (1205 words)

	Wikinfo \| Functional programming (Site not responding. Last check: 2007-11-01)
		For example, if a function is known to be idempotent, then a call to a function which has itself as its argument, and which is known to have no side-effects, may be efficiently computed without multiple calls.
		Functions are treated as first-class values, which is to say that functions can be parameters or inputs to other functions and can be the return values or outputs of a function.
		Functional languages have remained largely the domain of academics and hobbyists, and what little inroads have been made are due to impure functional languages such as Erlang and Common Lisp.
	www.wikinfo.org /wiki.php?title=Functional_programming (1666 words)

	[No title]
		Idempotent Function: The property that applying a function to its return value returns an identical value.
		Referential Transparency: The property of a function or block construct such that it will produce the same value every time it is called with the same arguments.
		Mathematical functions are referentially transparent, by definition, but functions whose results depend on global state, external context, or local mutable values are -referentially opaque-.
	gnosis.cx /TPiP/glossary.txt (1144 words)

	[No title]
		The derivation shows that the expressions in the first line and the last line denote the same function, or that the function in the first line is identical with the function in the last line.
		Both functions are defined for all stacks, and both return a stack which is like the argument stack except that two copies of the number 42 have been pushed.
		In these the unary function is replaced by a new binary function, and for each element in the domain a unary function can be defined from the new binary function by letting one parameter be the given element.
	www.latrobe.edu.au /philosophy/phimvt/joy/j04alg.html (6035 words)

	SSL Functions
		This function changes the default values for all subsequently opened sockets as long as the current application program is running.
		The client application's certificate authentication callback function needs to compare the domain name in the server's certificate against the domain name of the server the client was attempting to contact.
		Several functions in the NSS libraries use the password callback function to obtain the password before performing operations that involve the protected information.
	www.mozilla.org /projects/security/pki/nss/ref/ssl/sslfnc.html (8670 words)

	XQuery 1.0 and XPath 2.0 Functions and Operators
		Most of the functions in the core library have the property that calling the same function twice within an ·execution scope· with the same arguments returns the same result: these functions are said to be stable.
		If the argument to a constructor function is a literal, the result of the function may be evaluated statically; if an error is found during such evaluation, it may be reported as a static error.
		Summary: This function backs up the "idiv" operator and performs an integer division: that is, it divides the first argument by the second, and returns the integer obtained by truncating the fractional part of the result.
	www.w3.org /TR/2005/CR-xpath-functions-20051103 (5787 words)

	Know it all Inc. (I) (Site not responding. Last check: 2007-11-01)
		There are standard functions to provided the sort of support provided by the standard I/O and the C libraries, as well as additional types and functions to support common needs such as simple non-indexed {database}s; character based screen handling; direct access to many {system call}s; {safe pointer}s and {floating-point}.
		Function definitions can have a {guard} condition (introduced by ":-") which is a conjunction of equalities between arbitrary terms, including functions.
		The opposite of an injection function is a {projection} function which extracts a component of a constructed object, e.g.
	artikbre.synchro.net /docs/I.html (17821 words)

	UTR #23: Character Property Model
		Given a string S, and offsets a and b, a context-dependent string function is any string function F for which F(S,a,b) depends on the content of S before a and after b.
		A context-independent string function is a string function that is not context-dependent.
		A string function F whose output F(S) is itself a string, with the property that repeated applications of the same function F produce the same output: F(F(S)) = F(S) for all input strings S.
	www.macchiato.com /utc/prop_model_changes.html (1285 words)

	Epsilon-Delta » Time-Local Idempotent Operations
		There is a definition of the term “locally idempotent” from abstract algebra which does not have much to do with this construction, so there is no need for confusion.
		Time-local idempotent operations present a problem because the caching method used in one instance may be a spectacular failure in another.
		A time-local idempotent operation is a generalization of an idempotent operation.
	epsilondelta.net /2006/05/14/time-local-idempotent-operations (1227 words)

	Re: [ebxml-msg] Proposed "idempotent" parameter and attribute and CPAele
		Typically, it is the function that is idempotent, not the input.
		OTOH, the receiving MSH may know, through some similarly unspecified means, that the application/service's function is NOT idempotent as in the case of a message debiting some account, in which case the MSH MUST assume responsibility to ensure that any duplicate message is filtered and prevented from being received by the application/service.
		Furthermore, if the "idempotent" element is present in >the MessageHeader, it must agree with the parameter value, or else the >To party MSH reports an error with errorCode set to Inconsistent and >severity set to Error.
	www.oasis-open.org /archives/ebxml-msg/200111/msg00198.html (750 words)

	Orðasafn: I (Site not responding. Last check: 2007-11-01)
		indicator function 1 kennifall, = characteristic function 2.
		inverse function andhverfa, andhverft fall, -> inverse 1,, -> inverse 1,.
		inverse trigonometric function arkarfall, bogafall, = antitrigonometric function, = arc-trigonometric function, = cyclometric function, = inverse circular function.
	www.hi.is /~mmh/ord/safn/safnI.html (2408 words)

	HTTP/1.1: Method Definitions
		Methods can also have the property of "idempotence" in that (aside from error or expiration issues) the side-effects of N > 0 identical requests is the same as for a single request.
		(A sequence is idempotent if a single execution of the entire sequence always yields a result that is not changed by a reexecution of all, or part, of that sequence.) For example, a sequence is non-idempotent if its result depends on a value that is later modified in the same sequence.
		The actual function performed by the POST method is determined by the server and is usually dependent on the Request-URI.
	www.w3.org /Protocols/rfc2616/rfc2616-sec9.html (2241 words)

	UTR #23: Character Property Model
		A string function is a function whose input is a string S and two offsets a and b, with a ≤ b.
		A string function whose result is a string containing the same number of code points as its input, is a count preserving string function.
		A string function whose result is a string containing the same number of code units as its input, is a buffer length preserving string function.
	www.unicode.org /reports/tr23 (6540 words)

	idempotent - FOLDOC Definition
		Any value in the image of an idempotent function is a fixed point of the function.
		This term can be used to describe C header files, which contain common definitions and declarations to be included by several source files.
		The term can also be used to describe an initialisation subroutine that is arranged to perform some critical action exactly once, even if the routine is called several times.
	www.nightflight.com /foldoc-bin/foldoc.cgi?idempotent (187 words)

	Transit Note #107 Guaranteeing Idempotence for Tightly-Coupled, Fault-Tolerant Networks
		We argue that the placement of functionality which ensures idempotent network operation must be balanced by between requirements of simplicity and efficiency.
		Remote function invocation is very similar to writes in that they perform side effects into the destination's memory, or into a network messages to be sent back to the source.
		This can be assumed if we know that all the data values accessed by the function and the operations on that data will be invariant between duplicate calls, then the function reduces to the case of a simple, deterministic write, and is consequently idempotent.
	www.cs.caltech.edu /research/ic/transit/tn107/tn107.html (4270 words)

	pamfunc (Site not responding. Last check: 2007-11-01)
		This is the same function as you would get with -multiplier, specifying the multiplicative inverse of realnum.
		This is the same function as you would get with -multiplier, specifying the negative of integer.
		If wholenum is greater than the maxval, the function is idempotent -- the output is identical to the input.
	gd.tuwien.ac.at /.vhost/linuxcommand.org/man_pages/pamfunc1.html (530 words)

	Digital Logic Gates Part-III
		To achieve, first the logic function has to be written in Sum of Product (SOP) form.
		Once logic function is converted to SOP, then is very easy to implement using NAND gate.
		Once logic function is converted to POS, then is very easy to implement using NOR gate.
	www.asic-world.com /digital/gates3.html (353 words)

	[No title]
		Summary comments are large comments at the start of the function they are describing.
		These should be descriptive - an explanation in English of what the function is trying to do and how it is doing it.
		It does mean that the code can become deeply indented, but if this becomes a problem, you probably should break the function into a number of sub-functions.
	www.chris-lott.org /resources/cstyle/cstyle-ESA-OZ-v2.txt (902 words)

	Jerry Muir - Research Goals (Site not responding. Last check: 2007-11-01)
		Using the identities proven for holomorphic idempotents, I proved necessary and sufficient conditions for a set R in B to be a holomorphic retract of B.
		The area of geometric function theory originated with the study of analytic mappings of the open unit disk in the complex plane whose images have certain geometric properties such as convexity, starlikeness, close-to-convexity, etc.
		For example, it is known that a holomorphic automorphism of the unit ball in a commutative C*-algebra with identity can be written as the composition of an isometric linear automorphism of the algebra and a Lorch analytic automorphism of the ball.
	www.ms.uky.edu /~jmuir/research.html (880 words)

	QNX Developer Support
		The snmp_select_info() function is used to return information about what SNMP requires from a select() call.
		To have SNMP transactions occur asynchronously, you can invoke the functions snmp_select_info(), snmp_timeout(), and snmp_read() in conjunction with the system call select().
		The snmp_select_info() function modifies the information, which is subsequently passed to select().
	www.qnx.com /developers/docs/6.3.0/neutrino/lib_ref/s/snmp_select_info.html (327 words)

	5 - C H A P T E R -
		To accommodate templates, make sure your header file is tolerant of multiple inclusions (idempotent).
		This macro is most useful for separating prototyped from nonprototyped function definitions.
		You can best accomplish idempotency by setting preprocessor conditions that prevent the body of your header file from appearing more than once.
	docs.sun.com /source/816-2460/Program_Org.html (587 words)

	CISC181 Midterm 2, 06S, Post-Exam Notes
		Get functions don't need any parameters—they are invoked on an object that already has the data members inside of it.
		A get function cannot be void—its return type needs to match that of the value being returned.
		This is not acceptable because declaring temp as a local variable hides the private data member, which will remain unassigned.
	www.udel.edu /CIS/181/pconrad/06S/examInfo/E02/E02_181_06S_postExamNotes.html (605 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		We showed that the unification problem for the theory of one associative and idempotent binary function symbol (AI-unification), i.e.
		We also described the complexity of the unification problems for all equational theories of a binary function symbol that consist of associativity and idempotency together with any set of additional identities.
		We showed that the unification problem for such a theory is decidable in polynomial time if the function symbol satisfies the identity $xyzx=xzyx$ and it is NP-complete otherwise.
	www.math.muni.cz /~klima/Math/profile.html (354 words)

	Fabulous Adventures In Coding
		Worse still, we have a function that is essentially used as a composition operator that only makes sense to use on functions that have side effects and no arguments or returns.
		prototype, so that it is of general use on all functions of one argument, not just functions of no arguments and no returns that have side effects.
		Rather, it is a member of the outer function's execution context.
	blogs.msdn.com /ericlippert/Default.aspx?p=3 (6261 words)

	Easy Questions Are Boring
		The functions in the above links are functionally perfect, but I don't get why the XMLNS is hard-coded and not passed as an argument, since FF can grok SVG and MathML now.
		My solution was to write my own event queue for which the "add" function was idempotent.
		This means that adding the same function three times (as above) has no effect on the second and third time.
	ianso.blogspot.com (3524 words)

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