A method for the mechanical derivation of formulas in elementary geometry (Q1099656)

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scientific article; zbMATH DE number 4041335
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A method for the mechanical derivation of formulas in elementary geometry
scientific article; zbMATH DE number 4041335

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    A method for the mechanical derivation of formulas in elementary geometry (English)
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    1987
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    The author gives a method for proving theorems in elementary geometry, which is in the spirit of \textit{Wu Wen-tsün}'s method [Sci. Sin. 21, 157-172 (1978; Zbl 0376.68057)]. The problem consists in calculating a polynomial g under conditions, represented by zero conditions on other polynomials. Ritt's decomposition algorithm is applied to get all components general in set of variables by which the solution is to be expressed. Afterwards, the polynomial g is normalized by a Gröbner basis of the ideal generated by the components. The author shows, how to apply the method to get unknown constants in geometrical problems, as for example the radius of an inscribed circle in a triangle in terms of the three sides. Unfortunately, many information needed in this paper only exists in unpublished form (as in the proof of a theorem).
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    geometry theorem proving
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    Ritt's decomposition algorithm
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    Gröbner basis
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