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Mechanical theorem proving in the surfaces using the characteristic set method and Wronskian determinant

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Abstract

In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result onWronskian determinant, which can be used to decide whether the elements in a partial differential field are linearly dependent over its constant field. Based on Wronskian determinant, we can describe the geometry statements in the surfaces by an algebraic language and then prove them by the characteristic set method.

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Authors and Affiliations

  1. Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Beijing, 100190, China

    RuYong Feng

  2. Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing, 100083, China

    JianPing Yu

Authors
  1. RuYong Feng
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  2. JianPing Yu
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Correspondence to RuYong Feng.

Additional information

This work was partially supported by the National Key Basic Research Project of China (Grant No. 2004CB318000)

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Feng, R., Yu, J. Mechanical theorem proving in the surfaces using the characteristic set method and Wronskian determinant. Sci. China Ser. A-Math. 51, 1763–1774 (2008). https://doi.org/10.1007/s11425-008-0053-8

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  • DOI: https://doi.org/10.1007/s11425-008-0053-8

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