Wiki source code of gcd
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1 | h1. Greatest Common Divisor Notations | ||
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3 | In mathematics, The greatest common divisor of two positive integers {html}\\(a\\){html} and {html}\\(b\\){html}, denoted {html}\\(GCD(a,b)\\){html}. | ||
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6 | h3. Semantic | ||
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8 | - OpenMath's [combinat1/gcd|http://www.openmath.org/cd/arith1.xhtml#gcd] | ||
9 | - [MathML's gcd element|http://www.w3.org/TR/MathML3/chapter4.html#contm.gcd] | ||
10 | - [MathWorld's Greatest common divisor|http://mathworld.wolfram.com/GreatestCommonDivisor.html] | ||
11 | - [Wikipedia's Greatest common divisor|http://en.wikipedia.org/wiki/Greatest_common_divisor] | ||
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13 | ---- | ||
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15 | h3. Observations of GCD | ||
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19 | h4. Arabic | ||
20 | In [Saudi math book for grad VII|Census.Bibliography#arMath-gradeVII] we find in page number 75 the example shows gcd as '?.?.?' for 63 and 42 in Arabic language. | ||
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22 | !gcd-ar1.png|align=right! | ||
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26 | h4. English | ||
27 | In [Bibliography|Census.Bibliography#discrete-math-ThomasKoshy] we find in page 191 this book shows the greatest common divisor in English. | ||
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29 | !gcd-en.png|align=right! | ||
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34 | h4. German | ||
35 | As found in [Bibliography|Census.Bibliography#lineareAlgebra-KowalskyMichler] the German book shows the greatest common divisor in page 307. | ||
36 | |||
37 | !ggt-de.png|align=right! | ||
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43 | h4. Dutch | ||
44 | In [Bibliography|Census.Bibliography#InzienEnBewijzen-EijckVisser] the Dutch book shows the greatest common divisor in page 81. | ||
45 | See also the symbol in the Dutch book [Basisboek Wiskunde|Census.Bibliography#BasisboekWiskunde-JanvandeCraats] page 21. | ||
46 | Also used is !gcd-du-lc.png!, as seen in [Relaties en Structuren|Census.Bibliography#relensfrankdeclerck] (page 48). | ||
47 | |||
48 | !ggd81-du.png|align=right! | ||
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52 | h4. Spanish | ||
53 | In page 271 in the Spanish book represents the greatest common divisor as found in [Bibliography|Census.Bibliography#matematicaDiscreta-SpanishEdition]. | ||
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55 | !mcd-sp.png|align=right! | ||
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59 | h4. French | ||
60 | On page 101 of [Intro-math-discrètes|Census.Bibliography#intromathdiscretes], the notation and name of the gcd is described ([goto page|http://books.google.com/books?id=NZlcnzvTxAwC&lpg=PP1&hl=fr&pg=PA101#v=onepage&q=&f=false]). | ||
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62 | !pgcd-intro-math-discretes.png|align=right! | ||
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66 | h4. Finnish | ||
67 | On the Helsinki University of Technology, [Department of Mathematics website|https://matta.hut.fi/matta2/isom/html/alkutekj3.html], we find that they use _syt_ instead of gcd, and it is called 'Suurin yhteinen tekijä' in Finnish context. | ||
68 | Also find _syt_ in [wekipedia|http://fi.wikipedia.org/wiki/Suurin_yhteinen_tekij%C3%A4]. Usually at university level notation (_a,b_) is used for greatest common divisor of numbers _a_ and _b_ instead of letter combination _syt_. For example see [Lecture notes by Pentti Haukkanen at University of Tampere|http://mtl.uta.fi/Opetus/Algebra/algI04.pdf]. | ||
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70 | !syt1-fi.png|align=right!!sin-fin.png|thumbnail,align=right! | ||
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73 | |||
74 | ---- | ||
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76 | h3. Encoding GCD observations | ||
77 | [See encodings|http://devdemo.activemath.org/mathbridge/tools/symbolpresentation.cmd?order=by+Theory&lang=x-all&fmt=html&clipCoordinate=0&noApplet=true&omsource=%3COMOBJ+xmlns%3D%22http%3A%2F%2Fwww.openmath.org%2FOpenMath%22%3E%0D%0A++%3COMA%3E%0D%0A++++%3COMS+cd%3D%22arith1%22+name%3D%22gcd%22+xref%3D%22mbase%3A%2F%2Fopenmath-cds%2Farith1%2Fgcd%22+%2F%3E%0D%0A++++%3COMV+name%3D%22a%22+%2F%3E%0D%0A++++%3COMV+name%3D%22b%22+%2F%3E%0D%0A++%3C%2FOMA%3E%0D%0A%3C%2FOMOBJ%3E&submit=View] | ||
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79 | \\ | ||
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81 | ---- | ||
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