### Abstract

Original language | English |
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Title of host publication | Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 40-54 |

ISBN (Print) | 9783540525318 |

DOIs | |

Publication status | Published - 1990 |

Event | Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 - Capri, Italy Duration: 9 Apr 1990 → 11 Apr 1990 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 429/1990 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 |
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Country | Italy |

City | Capri |

Period | 9/04/90 → 11/04/90 |

### Fingerprint

### Cite this

*Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings*(pp. 40-54). (Lecture Notes in Computer Science; Vol. 429/1990). Berlin: Springer. https://doi.org/10.1007/3-540-52531-9_122

**Scratchpad's view of algebra I: Basic commutative algebra.** / Davenport, James H; Trager, B. M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings.*Lecture Notes in Computer Science, vol. 429/1990, Springer, Berlin, pp. 40-54, Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 , Capri, Italy, 9/04/90. https://doi.org/10.1007/3-540-52531-9_122

}

TY - GEN

T1 - Scratchpad's view of algebra I: Basic commutative algebra

AU - Davenport, James H

AU - Trager, B. M.

PY - 1990

Y1 - 1990

N2 - While computer algebra systems have dealt with polynomials and rational functions with integer coefficients for many years, dealing with more general constructs from commutative algebra is a more recent problem. In this paper we explain how one system solves this problem, what types and operators it is necessary to introduce and, in short, how one can construct a computational theory of commutative algebra. Of necessity, such a theory is rather different from the conventional, non-constructive, theory. It is also somewhat different from the theories of Seidenberg [1974] and his school, who are not particularly concerned with practical questions of efficiency.

AB - While computer algebra systems have dealt with polynomials and rational functions with integer coefficients for many years, dealing with more general constructs from commutative algebra is a more recent problem. In this paper we explain how one system solves this problem, what types and operators it is necessary to introduce and, in short, how one can construct a computational theory of commutative algebra. Of necessity, such a theory is rather different from the conventional, non-constructive, theory. It is also somewhat different from the theories of Seidenberg [1974] and his school, who are not particularly concerned with practical questions of efficiency.

UR - http://dx.doi.org/10.1007/3-540-52531-9_122

U2 - 10.1007/3-540-52531-9_122

DO - 10.1007/3-540-52531-9_122

M3 - Conference contribution

SN - 9783540525318

T3 - Lecture Notes in Computer Science

SP - 40

EP - 54

BT - Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings

PB - Springer

CY - Berlin

ER -