AUTOMATED PROVING OF TRIGONOMETRIC FUNCTION INEQUALITIES USING TAYLOR EXPANSION

CHEN Shiping,LIU Zhong

Journal of Systems Science and Mathematical Sciences ›› 2016, Vol. 36 ›› Issue (8) : 1339-1348.

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Journal of Systems Science and Mathematical Sciences ›› 2016, Vol. 36 ›› Issue (8) : 1339-1348. DOI: 10.12341/jssms12871

AUTOMATED PROVING OF TRIGONOMETRIC FUNCTION INEQUALITIES USING TAYLOR EXPANSION

  • CHEN Shiping1 ,LIU Zhong2
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Abstract

The problem of mechanical proving of transcendental inequalities is discussed with the trigonometric function inequalities in accordance with the model of f(x,tan(x2))>0 as the research object. Using Taylor expansion, the proving of the target inequality is transformed to the verification of a series of polynomial inequalities with only one variable, and then completed by algebraic inequality-proving package such as BOTTEMA. The above algorithms are implemented on Maple, and experiments show that they are very effective for most trigonometric function inequalities, furthermore the procedure is ``readable".

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CHEN Shiping , LIU Zhong. AUTOMATED PROVING OF TRIGONOMETRIC FUNCTION INEQUALITIES USING TAYLOR EXPANSION. Journal of Systems Science and Mathematical Sciences, 2016, 36(8): 1339-1348 https://doi.org/10.12341/jssms12871
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