| Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving |
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| 作者姓名： | Ning ZHANG~ |
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| 作者单位： | Ning ZHANG~(1 ) Hong-bo LI~2 1 China Institute for Actuarial Science (CIAS)，Central University of Finance and Economics，Beijing 100081，China; 2 Academy of Mathematics and Systems Science，Chinese Academy Sciences，Beijing 100080，China |
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| 摘 要： | This paper discusses two problems:one is some important theories and algorithms of affine bracket algebra;the other is about their applications in mechanical theorem proving.First we give some efficient algorithms including the boundary expanding algorithm which is a key feature in application.We analyze the characteristics of the boundary operator and this is the base for the implementation of the system.We also give some new theories or methods about the exact division,the representations and structure of affine geometry and so on.In practice,we implement the mechanical auto-proving system in Maple 10 based on the above algorithms and theories.Also we test about more than 100 examples and compare the results with the methods before.
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| 收稿时间： | 6 November 2006 |
| 修稿时间： | 28 February 2007 |
Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving |
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| Ning ZHANG.Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving[J].Science in China(Mathematics),2007,50(7):941-950. |
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| Authors: | Ning ZHANG Hong-bo LI |
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| Institution: | 1. China Institute for Actuarial Science (CIAS), Central University of Finance and Economics, Beijing 100081,China
2. Academy of Mathematics and Systems Science, Chinese Academy Sciences, Beijing 100080, China |
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| Abstract: | This paper discusses two problems:one is some important theories and algorithms of affine bracket algebra;the other is about their applications in mechanical theorem proving.First we give some efficient algorithms including the boundary expanding algorithm which is a key feature in application.We analyze the characteristics of the boundary operator and this is the base for the implementation of the system.We also give some new theories or methods about the exact division,the representations and structure of affine geometry and so on.In practice,we implement the mechanical auto-proving system in Maple 10 based on the above algorithms and theories.Also we test about more than 100 examples and compare the results with the methods before. |
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| Keywords: | mechanical theorem proving geometric invariance bracket algebra affine geometry affine bracket algebra |
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