Wiki source code of sum
Last modified by Administrator on 2020/08/13 18:57
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1.1 | 1 | h1. Notations of sum |
| 2 | |||
| 3 | Sum represents the n-ary addition operator. | ||
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| 6 | h3. Descriptions of this symbol | ||
| 7 | |||
| 8 | - OpenMath's [arith1/sum|http://www.openmath.org/cd/arith1.xhtml#sum] | ||
| 9 | - Sum in [MathML3|http://www.w3.org/TR/MathML3/chapter4.html#contm.sum] | ||
| 10 | - Sum in [MathWorld|http://mathworld.wolfram.com/Sum.html] | ||
| 11 | |||
| 12 | ---- | ||
| 13 | |||
| 14 | h3. Observations of sum | ||
| 15 | |||
| 16 | !sum-ar1.png|align=right! | ||
| 17 | h4. Arabic | ||
| 18 | The math book for high school in Saudi Arabia, Kuwait and some provinces represents summation symbol in Arabic context. | ||
| 19 | [Download the book and find the example in page 156|http://www2.moe.gov.sa/ebooks/11/????%20??????%20???????%20-%20????/????%20??????%20???????%20-%20?????%20???????%20??????%20-%20?????????.pdf]. | ||
| 20 | |||
| 21 | !sum-ar2.png|align=right! | ||
| 22 | In Jordan and some other provinces we find the Arabic book [Union Councils Of Scientific Arabic Language|Census.Bibliography#UnionCouncilsOfScientificArabicLanguage-Jordan] | ||
| 23 | also represents summation as we see in the example on the right. | ||
| 24 | The big two letters '???' means sum symbol, '?' for the upper bound of summation and '?' is the index of summation. | ||
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| 26 | \\ | ||
| 27 | |||
| 28 | h4. Dutch !sum-du1.png|align=right! | ||
| 29 | In Dutch book [Basisboek Wiskunde|Census.Bibliography#BasisboekWiskunde-JanvandeCraats] we see the summation symbol shown in page 69. [Download the book and find the example|http://staff.science.uva.nl/~craats/BasisboekWiskunde2HP.pdf]. | ||
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| 31 | \\ | ||
| 32 | |||
| 33 | h4. German !sum-de1.png|align=right! | ||
| 34 | We see in the German book [Höhere Mathematik mit Mathematica|Census.Bibliography#MathematikmitMathematica] the example represents summation symbol in german context. | ||
| 35 | [Download the scanned pages and find the example in page 11|http://wiki.math-bridge.org/download/attachments/1212431/hohereMathematik-Strampp-de.pdf]. | ||
| 36 | |||
| 37 | \\ | ||
| 38 | |||
| 39 | h4. French !sum-fr1.png|align=right! | ||
| 40 | The french book [Introduction aux mathématiques discrètes|Census.Bibliography#intro-math-discretes] shows the summation symbol in page 10. | ||
| 41 | [Go Directly to the example|http://books.google.com/books?id=NZlcnzvTxAwC&lpg=PA14&vq=Somme&pg=PA10#v=onepage&q=&f=false]. | ||
| 42 | |||
| 43 | \\ | ||
| 44 | |||
| 45 | h4. English !sum-en1.png|align=right! | ||
| 46 | The example in the American book [The Art of Combinatorial Proof |Census.Bibliography#combinatorialProof-BenjaminAndQuinn] represents the binomial summation in page 68. | ||
| 47 | [Find the example in google books link|http://books.google.com/books?id=VyMp9xIANp8C&lpg=PA93&dq=Stirling%20numbers%20of%20the%20first%20kind&pg=PA68#v=onepage&q=&f=false]. | ||
| 48 | |||
| 49 | \\ | ||
| 50 | |||
| 51 | h4. Finnish !sum-fi1.png|align=right! | ||
| 52 | We find the Finnish book [MAOL-taulukot|Census.Bibliography#MAOL-taulukot-Otava2005] shows sum symbol with the example in page 11. and it is called 'Summa' in Finnish context. | ||
| 53 | [Download and preview the book|http://matriisi.ee.tut.fi/~miilumak/material/]. | ||
| 54 | |||
| 55 | \\ | ||
| 56 | |||
| 57 | ---- | ||
| 58 | |||
| 59 | h3. Encoding the observations of sum | ||
| 60 | [See encodings|http://devdemo.activemath.org/mathbridge/tools/symbolpresentation.cmd?order=by+Theory&lang=x-all&fmt=html&clipCoordinate=2&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%22sum%22+xref%3D%22mbase%3A%2F%2Fopenmath-cds%2Farith1%2Fsum%22+%2F%3E%0D%0A++++%3COMV+name%3D%22I%22+%2F%3E%0D%0A++++%3COMBIND%3E%0D%0A++++++%3COMS+cd%3D%22fns1%22+name%3D%22lambda%22+xref%3D%22mbase%3A%2F%2Fopenmath-cds%2Ffns1%2Flambda%22+%2F%3E%0D%0A++++++%3COMBVAR%3E%0D%0A++++++++%3COMV+name%3D%22x%22+%2F%3E%0D%0A++++++%3C%2FOMBVAR%3E%0D%0A++++++%3COMV+name%3D%22f%22+%2F%3E%0D%0A++++%3C%2FOMBIND%3E%0D%0A++%3C%2FOMA%3E%0D%0A%3C%2FOMOBJ%3E&submit=View] | ||
| 61 | [See encodings|http://devdemo.activemath.org/mathbridge/tools/symbolpresentation.cmd?order=by+Theory&lang=x-all&fmt=html&clipCoordinate=11&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%22sum%22+xref%3D%22mbase%3A%2F%2Fopenmath-cds%2Farith1%2Fsum%22+%2F%3E%0D%0A++++%3COMA%3E%0D%0A++++++%3COMS+cd%3D%22interval1%22+name%3D%22integer_interval%22+xref%3D%22mbase%3A%2F%2Fopenmath-cds%2Finterval1%2Finteger_interval%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++++%3COMBIND%3E%0D%0A++++++%3COMS+cd%3D%22fns1%22+name%3D%22lambda%22+xref%3D%22mbase%3A%2F%2Fopenmath-cds%2Ffns1%2Flambda%22+%2F%3E%0D%0A++++++%3COMBVAR%3E%0D%0A++++++++%3COMV+name%3D%22x%22+%2F%3E%0D%0A++++++%3C%2FOMBVAR%3E%0D%0A++++++%3COMV+name%3D%22f%22+%2F%3E%0D%0A++++%3C%2FOMBIND%3E%0D%0A++%3C%2FOMA%3E%0D%0A%3C%2FOMOBJ%3E&submit=View] | ||
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| 63 | \\ | ||
| 64 | |||
| 65 | ---- | ||
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