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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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  • 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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  • 3
    Electronic Resource
    Electronic Resource
    On the parameterization of algebraic curves (1992)
    Springer
    Applicable algebra in engineering, communication and computing 3 (1992), S. 27-38 
    Details
    ISSN: 1432-0622
    Keywords: Geometric modeling ; Parameterization ; Algebraic curves ; Resolvents ; Ritt-Wu's decomposition algorithm ; Gröbner bases
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract In this paper, by using the concept of resolvents of a prime ideal introduced by Ritt, we give methods for constructing a hypersurface which is birational to a given irreducible variety and birational transformations between the hypersurface and the variety. In the case of algebraic curves, this implies that for an irreducible algebraic curveC, we can construct a plane curve which is birational toC. We also present a method to find rational parametric equations for a plane curve if it exists. Hence we have a complete method of parameterization for rational algebraic curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189021
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  • 4
    Electronic Resource
    Electronic Resource
    A method for the mechanical derivation of formulas in elementary geometry (1987)
    Springer
    Journal of automated reasoning 3 (1987), S. 291-299 
    Details
    ISSN: 1573-0670
    Keywords: Wu's method for geometry theorem proving ; Ritt's decomposition algorithm ; Gröbner bases ; Heron's formula for the area of a triangle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A method for mechanical derivation of formulas and calculation of quantities in geometry is given with several examples to illustrate its applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00243793
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  • 5
    Electronic Resource
    Electronic Resource
    Proving geometry theorems with rewrite rules (1986)
    Springer
    Journal of automated reasoning 2 (1986), S. 253-273 
    Details
    ISSN: 1573-0670
    Keywords: Rewrite rules ; Gröbner bases ; geometry theorem proving
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We investigate the application of rewrite rules to proving theorems from elementary geometry. We have proven 80 theorems, some of them quite difficult. There is a discussion of the formulation of the problem and degenerate conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02328448
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