# Towards the automated synthesis of a Gröbner bases algorithm.

RACSAM (2004)

• Volume: 98, Issue: 1, page 65-75
• ISSN: 1578-7303

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## Abstract

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We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with this approach, the automated synthesis of the author?s Gröbner bases algorithm is possible. Still, significant technical work will be necessary to improve the current theorem provers, in particular the ones in the Theorema system, so that the road map can be transformed into a completely computerized process.

## How to cite

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Buchberger, Bruno. "Towards the automated synthesis of a Gröbner bases algorithm.." RACSAM 98.1 (2004): 65-75. <http://eudml.org/doc/41036>.

@article{Buchberger2004,
abstract = {We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with this approach, the automated synthesis of the author?s Gröbner bases algorithm is possible. Still, significant technical work will be necessary to improve the current theorem provers, in particular the ones in the Theorema system, so that the road map can be transformed into a completely computerized process.},
author = {Buchberger, Bruno},
journal = {RACSAM},
keywords = {Gröbner basis; algorithm synthesis and analysis; symbolic computation; automated reasoning},
language = {eng},
number = {1},
pages = {65-75},
title = {Towards the automated synthesis of a Gröbner bases algorithm.},
url = {http://eudml.org/doc/41036},
volume = {98},
year = {2004},
}

TY - JOUR
AU - Buchberger, Bruno
TI - Towards the automated synthesis of a Gröbner bases algorithm.
JO - RACSAM
PY - 2004
VL - 98
IS - 1
SP - 65
EP - 75
AB - We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with this approach, the automated synthesis of the author?s Gröbner bases algorithm is possible. Still, significant technical work will be necessary to improve the current theorem provers, in particular the ones in the Theorema system, so that the road map can be transformed into a completely computerized process.
LA - eng
KW - Gröbner basis; algorithm synthesis and analysis; symbolic computation; automated reasoning
UR - http://eudml.org/doc/41036
ER -

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