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A New Approach for Automatic Theorem Proving in Real Geometry (1998)

Dolzmann, Andreas ; Sturm, Thomas ; Weispfenning, Volker

Springer

Journal of automated reasoning 21 (1998), S. 357-380

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ISSN: 1573-0670

Keywords: real quantifier elimination ; real geometry ; automatic theorem proving over the reals

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Abstract We present a new method for proving geometric theorems in the real plane or higher dimension. The method is derived from elimination set ideas for quantifier elimination in linear and quadratic formulas over the reals. In contrast to other approaches, our method can also prove theorems whose complex analogues fail. Moreover, the problem formulation may involve order inequalities. After specification of independent variables, nondegeneracy conditions are generated automatically. Moreover, when trying to prove conjectures that – apart from nondegeneracy conditions – do not hold in the claimed generality, missing premises are found automatically. We demonstrate the applicability of our method to nontrivial examples.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1006031329384

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Reactions of 2-(Organylseleno)propenenitriles with Dimethyl EthynedicarboxylateDedicated to Professor Peter Sartori on the occasion of his 65th birthday.Parts of this work were taken from the doctoral dissertation of Thomas Sturm, Gerhard-Mercator University Duisburg, 1996. (1997)

Döpp, Dietrich ; Sturm, Thomas

Weinheim : Wiley-Blackwell

Liebigs Annalen 1997 (1997), S. 541-546

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ISSN: 0947-3440

Keywords: [3 + 2] Cycloadditions ; Organylseleno group transfer ; 2,3-Dihydroselenophenes ; Polysubstituted butadienes ; Selenium ; Alkenes ; Chemistry ; Organic Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Notes: (2-tert-Butylseleno)propenenitrile (12a) has been prepared and treated with dimethyl ethynedicarboxylate (3) and methyl propiolate (18) to give the 2,3-dihydroselenophenes 16 and 21, respectively. In contrast, 2-(ethylseleno)-, 2-(methylseleno)- and 2-(phenylseleno)propenenitrile (12b-d) tend to form polysubstituted butadienes 17b-d with 3 by net organoylseleno group transfer from 12b-d to C-2 of 3 following attachment of C-3 of 17 to C-3 of 3. Five-membered selenonium ylides are proposed as intermediates.