The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application
We give an overview of how a huge class of multisum identities can be proven and discovered with the summation package Sigma implemented in the computer algebra system Mathematica. General principles of symbolic summation are discussed. We illustrate the usage of Sigma by showing how one can fi...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2004-12-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/195 |
| _version_ | 1811293659378745344 |
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| author | Carsten Schneider |
| author_facet | Carsten Schneider |
| author_sort | Carsten Schneider |
| collection | DOAJ |
| description | We give an overview of how a huge class of multisum identities can be proven and discovered with the summation package Sigma implemented in the computer algebra system Mathematica. General principles of symbolic summation are discussed. We illustrate the usage of Sigma by showing how one can find and prove a multisum identity that arose in the enumeration of rhombus tilings of a symmetric hexagon. Whereas this identity has been derived alternatively with the help of highly involved transformations of special functions, our tools enable to find and prove this identity completely automatically with the computer. |
| first_indexed | 2024-04-13T05:04:46Z |
| format | Article |
| id | doaj.art-babb649c0eda44d6b6e4c43bbf23a145 |
| institution | Directory Open Access Journal |
| issn | 1462-7264 1365-8050 |
| language | English |
| last_indexed | 2024-04-13T05:04:46Z |
| publishDate | 2004-12-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-babb649c0eda44d6b6e4c43bbf23a1452022-12-22T03:01:12ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80502004-12-0162The Summation Package Sigma: Underlying Principles and a Rhombus Tiling ApplicationCarsten SchneiderWe give an overview of how a huge class of multisum identities can be proven and discovered with the summation package Sigma implemented in the computer algebra system Mathematica. General principles of symbolic summation are discussed. We illustrate the usage of Sigma by showing how one can find and prove a multisum identity that arose in the enumeration of rhombus tilings of a symmetric hexagon. Whereas this identity has been derived alternatively with the help of highly involved transformations of special functions, our tools enable to find and prove this identity completely automatically with the computer.http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/195 |
| spellingShingle | Carsten Schneider The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application Discrete Mathematics & Theoretical Computer Science |
| title | The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application |
| title_full | The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application |
| title_fullStr | The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application |
| title_full_unstemmed | The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application |
| title_short | The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application |
| title_sort | summation package sigma underlying principles and a rhombus tiling application |
| url | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/195 |
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