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  • 1
    Electronic Resource
    Electronic Resource
    On the algebraic formulation of certain geometry statements and mechanical geometry theorem proving (1989)
    Springer
    Algorithmica 4 (1989), S. 237-262 
    Details
    ISSN: 1432-0541
    Keywords: Geometry theorem proving ; Provers ; Nondegenerate conditions ; Ritt's algorithms ; Wu's method ; The Gröbner basis method ; Algebraically (or real) closed field ; Algebraic geometry ; Irreducible variety ; Nondegenerate component ; Generally true ; Simson's theorem ; Pappus' theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we analyze the algebraic formulations of certain geometry statements appearing in recent literature related to mechanical geometry theorem proving and give several examples to show that one of these formulations can cause serious problems. We clarify a formulation which is essentially due to W. T. Wu and, in our opinion, is the most satisfactory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01553889
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An algorithm for constructing gröbner bases from characteristic sets and its application to geometry (1990)
    Springer
    Algorithmica 5 (1990), S. 147-154 
    Details
    ISSN: 1432-0541
    Keywords: Polynomial, (Prime) ideal ; Generators ; (Irreducible) ascending chain ; (Irreducible) algebraic set ; Decomposition of an algebraic set ; Geometric configuration ; Nondegenerate component ; Geometry theorem proving
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In Ritt's method, a prime ideal is given by a characteristic set. A characteristic set of a prime ideal is generally not a set of generators of this ideal. In this paper we present a simple algorithm for constructing Gröbner bases of a prime ideal from its characteristic set. We give a method for finding new theorems in geometry as an application of this algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840382
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    Paper (German National Licenses)
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