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Topic: Canonical equivalence

	Canonical XML
		The equivalence of the digests computed by the signing and relying parties (and hence the equivalence of the canonical forms over which they were computed) ensures that the information content of the document has not been altered since it was signed.
		The canonical form of an XML document may not be completely operational within the application context, though the circumstances under which this occurs are unusual.
		This problem may be of concern in certain applications since the canonical form of a document and the canonical form of the canonical form of the document are equivalent.
	www.w3.org /TR/2001/REC-xml-c14n-20010315 (6401 words)

	Canonical equivalence - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-03)
		Canonical equivalence refers to the state in which two things are in every significant respect identical.
		In Unicode, the canonical equivalence of two strings means that they can be reduced to identical strings by recursive application of canonical decomposition routines.
		(Compare compatibility equivalence.) Canonically equivalent strings always have the same meaning and behaviour; they should also look the same and be indistinguishable to the user.
	en.wikipedia.org /wiki/Canonical_equivalence (91 words)

	Compatibility equivalence - Wikipedia, the free encyclopedia
		Compatibility equivalence refers to a state in which two technically dissimilar things may be considered functionally identical.
		In Unicode, for instance, the compatibility equivalence of two strings (sequences of letters, numbers, or other characters) means that they can be reduced to identical strings by recursive application of both canonical decomposition and compatibility decomposition routines.
		Two Unicode strings that have the relation of compatibility equivalence may sometimes be considered identical, but generally they are not—the "micro sign" (µ) and "greek small letter mu" (μ) are similar, for example, but they are not considered strictly identical.
	en.wikipedia.org /wiki/Compatibility_equivalence (120 words)

	PlanetMath: equivalence class
		is sometimes referred to as the canonical projection.
		This is version 4 of equivalence class, born on 2001-10-23, modified 2004-11-30.
		Object id is 468, canonical name is EquivalenceClass.
	planetmath.org /encyclopedia/EquivalenceClass.html (72 words)

	[No title]
		Equivalently, a simplicial groupoid G is a groupoid enriched in simplicial sets such that the simplicial s* *et Mor (G) is the nerve of a groupoid.
		The morphism j is one of the canonical maps for an adjunction: the functor H 7!
		A morphism of 2-cocycles is a commutative diagram of functors ffppA OOOFO xxp'ppp
	hopf.math.purdue.edu /Jardine/gerbes6.txt (7536 words)

	webservices.xml.com: XML Canonicalization
		The purpose of finding the canonical (or simplified) form of an XML document is to determine logical equivalence between XML documents.
		If the two canonical forms contain the same sequence of octets, we will conclude that the two XML files are logically equivalent.
		The canonical form of XML requires that all line breaks (#xD or a combination of #xA and #xD) be replaced with #xA.
	webservices.xml.com /pub/a/ws/2002/09/18/c14n.html (1332 words)

	Proof Obligation : Canonical Terms (Forms) (Site not responding. Last check: 2007-11-03)
		If we now isolate one term from each of the different equivalence classes, (that is choose one member from each class as a ``representative'' of that class), then the collection of all such terms constitutes a set of canonical terms (forms).
		The importance of canonical forms is that every term which can be generated using the signature is equivalent to one of these canonical forms.
		The assertion that a set of terms constitutes a set of canonical forms must be proved by demonstrating that every (ground) term generated from the signature is equivalent to one and only one of the canonical forms.
	scom.hud.ac.uk /staff/scomtlm/book/node317.html (301 words)

	UAX #15: Unicode Normalization Forms
		Canonical equivalence is a basic equivalency between characters or sequences of characters.
		Canonical decomposition is the process of taking a string, recursively replacing composite characters using the Unicode canonical decomposition mappings (including the algorithmic Hangul canonical decomposition mappings; see Section 16, Hangul), and putting the result in canonical order.
		The canonically equivalent inputs or outputs are not just limited to strings, but are also relevant to the offsets within strings, because those play a fundamental role in Unicode string processing.
	www.unicode.org /reports/tr15 (9142 words)

	Canonical Term Algebra and Reduced Expressions
		It is often possible to identify a subset of the terms such that each term in the subset is a member of a different equivalence class and every term of the term algebra is equivalent to exactly one member of this subset.
		The individual terms which comprise such a subset are called canonical terms and algebras whose carrier sets consist of such a collection of canonical terms are referred to as canonical term algebras.
		Canonical terms can therefore be systematically generated using the atomic constructors and a canonical term algebra derived.
	scom.hud.ac.uk /scomtlm/book/node286.html (324 words)

	Department of Mathematics and Statistics
		A brief discussion of equivalence and canonical forms in the context of group theory will conclude the talk.
		The determination of a complete set of invariants of a given group action is of supreme importance for the study of equivalence and canonical forms.
		This thesis is committed to the construction of a global solution to the equivalence problem in differential geometry for a Lie group acting regularly on a smooth manifold.
	www.mathstat.dal.ca /~smirnov/invarianttheoryseminar05.html (1176 words)

	Normalizer (icu4j)
		It allows to work on strings that are not necessarily normalized with an algorithm (like in collation) that works under "canonical closure", i.e., it treats precomposed characters and their decomposed equivalents the same.
		Multiple strings may be canonically equivalent (their NFDs are identical) and may all conform to FCD without being identical themselves.
		Canonical equivalence between two strings is defined as their normalized forms (NFD or NFC) being identical.
	icu.sourceforge.net /apiref/icu4j/com/ibm/icu/text/Normalizer.html (4472 words)

	Canonical Equivalence in Applications
		This means that canonically equivalent strings should normally be displayed identically, sort identically, be case-mapped equivalently, and so on.
		Such data is called “canonically closed”, and the process of building such data from the original table is called “canonical closure”.
		In order to build canonically closed data one needs to enumerate all strings that are canonically equivalent to an input string and in FCD.
	www.unicode.org /notes/tn5 (1444 words)

	Character Equivalence
		Canonical equivalence is a fundamental equivalence between individual Unicode characters and sequences of Unicode characters.
		The composite character and the two-character sequence are canonical equivalents.
		Another example of canonical equivalence is that between Korean hangul syllables and the jamo characters that compose them.
	www.roguewave.com /support/docs/leif/sourcepro/html/i18nug/5-2.html (223 words)

	Formal Properties of Conditional Forms (Site not responding. Last check: 2007-11-03)
		We shall say that two gbfs are strongly equivalent if they have the same value for all values of the propositional variables in them including the case of undefined propositional variables.
		They are weakly equivalent if they have the same values for all values of the propositional variables when these are restricted to F and T. The equivalence of gbfs can be tested by a method of truth tables identical to that of propositional calculus.
		Two gbfs are equivalent (weakly or strongly) if and only if they have the same (weak or strong) canonical form.
	www-formal.stanford.edu /pub/jmc/basis1/node10.html (936 words)

	Internationalizing the Internet
		This transform of a Unicode string into a canonical format is based on the observation that in a number of languages there are a variety of ways to display the same text and a variety of ways to enter the same text.
		Is equivalence something as loose as the relationship between com and biz, namely being different abbreviations of words that reflect similar concepts with different name space populations that reflect market diversity and a competitive supply industry.
		One approach that could support of tight synchronization of equivalence is the use the DNAME record (RFC 2672) to create these top level domain name aliases for their ASCII equivalents, thereby allowing a single name registration to be resolveable using a root name expressed in any of the linguistic equivalents of the original tld name.
	www.circleid.com /posts/internationalizing_the_internet (10509 words)

	Re: U+0140
		There are to be sure, features of Unicode that are "embarassing", but I don't think this is one of them.
		These sorts of preferences can be taken into account in the tailoring of fonts to particular practices, and this issue doesn't not require that we let a thousand middle dots bloom.
		And canonical equivalence was the mechanism for saying that two variants of character really should never have been encoded (but we had to for compatibility reasons).
	www.mail-archive.com /unicode@unicode.org/msg23119.html (405 words)

	Pike Reference Manual - Unicode.normalize()
		C and D specifies whether to decompose (D) complex characters to their parts, or compose (C) single characters to complex ones.
		When K is present, compatibility transformations are performed as well as the canonical transformations.
		Because the characters are visually distinguished, replacing a character by a compatibility equivalent may lose formatting information unless supplemented by markup or styling.
	pike.oav.net /7.3/modref/ex/Unicode/normalize.html (238 words)

	Technical Report Changes
		Here, 'canonical' should be changed to 'composition', because that's what the C in NFC and NFKC stands for.
		For functions that map strings to strings, this is often called preserving canonical equivalence.
		"The canonically equivalent inputs or outputs are not just limited to strings, but are also relevant to the offsets within strings, since those play a fundamental role in Unicode string processing." is also a pocket definition, this time of 'canonically equivalent offset'.
	www.macchiato.com /utc/technical_report_recommendations.html?ch=0335 (1415 words)

	ICU 3.7.1: unorm.h File Reference
		It allows to work on strings that are not necessarily normalized with an algorithm (like in collation) that works under "canonical closure", i.e., it treats precomposed characters and their decomposed equivalents the same.
		Multiple strings may be canonically equivalent (their NFDs are identical) and may all conform to FCD without being identical themselves.
		Canonical equivalence between two strings is defined as their normalized forms (NFD or NFC) being identical.
	www.icu-project.org /apiref/icu4c/unorm_8h.html (2386 words)

	Understanding Unicode™ - II
		It was noted in Section 6 that some cases of equivalence involve one-to-one relationships, for example in the case of the exact character duplicates discussed in Section 6.1.
		Canonical equivalence is a transitive relationship, and so we intuitively know that all of the representations are canonically equivalent.
		In Sections 6.3 and 9, we saw various reasons why a given text element may be represented in Unicode in multiple ways: precomposed characters are canonically equivalent to their full or partial decompositions.
	scripts.sil.org /IWS-Chapter04b (12487 words)

	Unicode::Normalize - Unicode Normalization Forms (Site not responding. Last check: 2007-11-03)
		If the second parameter (a boolean) is omitted or false, the decomposition is canonical decomposition; if the second parameter (a boolean) is true, the decomposition is compatibility decomposition.
		If the character is canonically decomposable (including Hangul Syllables), it returns the (full) canonical decomposition as a string.
		Note: According to the Unicode standard, the canonical decomposition of the character that is not canonically decomposable is same as the character itself.
	cpan.uwinnipeg.ca /htdocs/Unicode-Normalize/Unicode/Normalize.html (1129 words)

	[I18n-sig] Re: [Python-Dev] Unicode debate (Site not responding. Last check: 2007-11-03)
		This is a semantic equivalence -- that is, they mean the same thing -- and doesn't depend on the display engine to be true.
		Specifically, in the Unicode 3.0 standard, rule D24 in section 3.6 (page 44) states that: "Two character sequences are said to be canonical equivalents if their full canonical decompositions are identical.
		For example, the sequences and <=F6> are canonical equivalents.
	mail.python.org /pipermail/python-dev/2000-May/003913.html (418 words)

	On Equivalence and Canonical Forms in the LF Type Theory - Harper, Pfenning (ResearchIndex) (Site not responding. Last check: 2007-11-03)
		Abstract: Decidability of definitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework.
		Coquand has considered a different approach, directly proving the correctness of a practical equivalence algorithm based on the shape of terms.
		On equivalence and canonical forms in the LF type theory.
	citeseer.ist.psu.edu /harper01equivalence.html (639 words)

	[No title]
		In the p-complete category, where a map (of spaces or spectra) is considered to be an equivalence if it induces an isomorphism on ordinary homology with Fp- coefficients, the local incarnations of finite loop spaces are the p-compact gr* *oups of Dwyer and Wilkerson [DW94].
		The Poincar'e duality equivalence and the inverse Poincar'e equivalence * pro- vide a chain of equivalences* S[G] ^ S-adG ^ SadG ' DG+ ^ S-adG ' S[G], which is equivariant with respect to the standard left action on both copies of S[G], the trivial action on S-adG and the standard left action on SadG.
		This condition is equivalent to asking th* at xy = 0 for each y 2 ker(ffl), i.e., x 2 H multiplies to zero with each eleme nt in the augmentation ideal of H. So PH (H) is the left annihilator ideal of the augmentation ideal of H. Eilenberg-Mac Lane spaces.
	hopf.math.purdue.edu /Rognes/dualizable.txt (5687 words)

	5 Linguistic Sorting and String Searching
		Canonical equivalence is a basic equivalence between characters or sequences of characters.
		Canonical equivalence is an attribute of a multilingual sort and describes how equivalent code point sequences are sorted.
		If canonical equivalence is applied in a particular linguistic sort, then canonically equivalent strings are treated as equal.
	www.stanford.edu /dept/itss/docs/oracle/10g/server.101/b10749/ch5lingsort.htm (4168 words)

	UTR #22: Character Mapping Tables
		id (required) is a canonical id which uniquely identifies this mapping table from all others.
		It allows the identification of the invocation sequences and state shifts that are associated with each particular mapping table (identified by its canonical names).
		It does not fully specify all of the elements and semantics of the particular ISO 2022 subset.
	www.mindspring.com /~markus.scherer/unicode/tr22-4-20040107.html (6419 words)

	Union-find sets
		) and the canonical equivalence class representative can be determined from any member (
		subclasses of union_find_set are expected to override this default method if they want to take action when two equivalence classes are merged.
		where its instances are known to always become the representative member of the equivalence class.
	www.cs.washington.edu /research/projects/cecil/cecil/www/Release/doc-diesel-stdlib/node23.html (127 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		\bigno \newsection Finite volume equivalence between canonical and grand canonical Gibbs measures In this section we assume that the apriori measures $\mu_0^{\{x\}}$ are all equal to a given positive probability measure $\mu_0$ on the state space $S$.
		\bigno {\it Remark.} Exactly the same result can be obtained if instead of comparing the finite volume canonical Gibbs measure with its grand canonical counterpart, we take the marginal on $\cF_\L$ of the infinite volume Gibbs state conditioned to $N_\L=N$ and compare it to the marginal on $\cF_\L$ of the unconditioned one.
		In this section we discuss the equivalence of multicanonical and multigrand canonical ensembles for a system where the assumption of {\it translation invariance} is removed and property $SMT(V,C,m,l)$ does no longer hold for all sets $V\in \bF_l$.
	www.ma.utexas.edu /mp_arc/papers/99-172 (5810 words)

	[No title]
		This is an unusual Boyer Informational [Page 5] RFC 3076 Canonical XML March 2001 case precisely because most XML processors currently discard the document type declaration, which discards the notation, the entity's binding to a URI, and the attribute type that binds the attribute value to an entity name.
		Boyer Informational [Page 6] RFC 3076 Canonical XML March 2001 The second parameter of input to the XML canonicalization method is a boolean flag indicating whether or not comments should be included in the canonical form output by the XML canonicalization method.
		Note: In the canonical form, the value of the attribute named attr in the element norm begins with a space, a single quote, then four spaces before the first character reference.
	www.ietf.org /rfc/rfc3076.txt (6039 words)

	Identifier “foo” is not in canonical form (tha canonical form would be “bar”) (Site not responding. Last check: 2007-11-03)
		URIs used as identifiers should be in canonical form, as described by section 6 of RFC 3986.
		All newly issued ids should be in canonical form.
		Use the canonical form given in the warning message for guidance.
	feedvalidator.org /docs/warning/NonCanonicalURI.html (193 words)

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