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Floating point Gröbner bases
Bracket coefficients for polynomials are introduced. These are like specific precision floating point numbers together with error terms. Working in terms of bracket coefficients, an algorithm that computes a Gröbner basis with floating point coefficients is presented, and a new criterion for determi...
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| Published in: | Mathematics and computers in simulation 1996, Vol.42 (4), p.509-528 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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| Online Access: | Get full text |
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| cited_by | cdi_FETCH-LOGICAL-c338t-e262b27132454e95ab58e992d23f1abdc4899bd6f2d1220bc96b5e587b5838d43 |
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| cites | cdi_FETCH-LOGICAL-c338t-e262b27132454e95ab58e992d23f1abdc4899bd6f2d1220bc96b5e587b5838d43 |
| container_end_page | 528 |
| container_issue | 4 |
| container_start_page | 509 |
| container_title | Mathematics and computers in simulation |
| container_volume | 42 |
| creator | Shirayanagi, Kiyoshi |
| description | Bracket coefficients for polynomials are introduced. These are like specific precision floating point numbers together with error terms. Working in terms of bracket coefficients, an algorithm that computes a Gröbner basis with floating point coefficients is presented, and a new criterion for determining whether a bracket coefficient is zero is proposed. Given a finite set
F of polynomials with real coefficients, let
G
μ
be the result of the algorithm for
F and a precision value μ, and
G be a true Gröbner basis of
F. Then, as μ approaches infinity,
G
μ
converges to
G coefficientwise. Moreover, there is a precision
M such that if
μ ≥
M, then the sets of monomials with non-zero coefficients of
G
μ
and
G are exactly the same. The practical usefulness of the algorithm is suggested by experimental results. |
| doi_str_mv | 10.1016/S0378-4754(96)00027-4 |
| format | article |
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F of polynomials with real coefficients, let
G
μ
be the result of the algorithm for
F and a precision value μ, and
G be a true Gröbner basis of
F. Then, as μ approaches infinity,
G
μ
converges to
G coefficientwise. Moreover, there is a precision
M such that if
μ ≥
M, then the sets of monomials with non-zero coefficients of
G
μ
and
G are exactly the same. The practical usefulness of the algorithm is suggested by experimental results.</description><identifier>ISSN: 0378-4754</identifier><identifier>EISSN: 1872-7166</identifier><identifier>DOI: 10.1016/S0378-4754(96)00027-4</identifier><language>eng</language><publisher>Elsevier B.V</publisher><ispartof>Mathematics and computers in simulation, 1996, Vol.42 (4), p.509-528</ispartof><rights>1996</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c338t-e262b27132454e95ab58e992d23f1abdc4899bd6f2d1220bc96b5e587b5838d43</citedby><cites>FETCH-LOGICAL-c338t-e262b27132454e95ab58e992d23f1abdc4899bd6f2d1220bc96b5e587b5838d43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0378475496000274$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3415,3550,4009,27902,27903,27904,45951,45981</link.rule.ids></links><search><creatorcontrib>Shirayanagi, Kiyoshi</creatorcontrib><title>Floating point Gröbner bases</title><title>Mathematics and computers in simulation</title><description>Bracket coefficients for polynomials are introduced. These are like specific precision floating point numbers together with error terms. Working in terms of bracket coefficients, an algorithm that computes a Gröbner basis with floating point coefficients is presented, and a new criterion for determining whether a bracket coefficient is zero is proposed. Given a finite set
F of polynomials with real coefficients, let
G
μ
be the result of the algorithm for
F and a precision value μ, and
G be a true Gröbner basis of
F. Then, as μ approaches infinity,
G
μ
converges to
G coefficientwise. Moreover, there is a precision
M such that if
μ ≥
M, then the sets of monomials with non-zero coefficients of
G
μ
and
G are exactly the same. The practical usefulness of the algorithm is suggested by experimental results.</description><issn>0378-4754</issn><issn>1872-7166</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><recordid>eNqFkMtKA0EQRRtRMEY_IZCV6GK034-VSDBRCLhQ100_aqRlMhO7J4I_5g_4Y04SceuqanHqFvcgNCH4imAir58wU7riSvALIy8xxlRV_ACNiFa0UkTKQzT6Q47RSSlvAzTsYoQm86ZzfWpfp-sutf10kb-_fAt56l2BcoqOatcUOPudY_Qyv3ue3VfLx8XD7HZZBcZ0XwGV1FNFGOWCgxHOCw3G0EhZTZyPgWtjfJQ1jYRS7IORXoDQauCYjpyN0fk-d5279w2U3q5SCdA0roVuUyxlQlNO2QCKPRhyV0qG2q5zWrn8aQm2Wxl2J8Num1oj7U6G3T642d_B0OIjQbYlJGgDxJQh9DZ26Z-EH1mMZSY</recordid><startdate>1996</startdate><enddate>1996</enddate><creator>Shirayanagi, Kiyoshi</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>1996</creationdate><title>Floating point Gröbner bases</title><author>Shirayanagi, Kiyoshi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c338t-e262b27132454e95ab58e992d23f1abdc4899bd6f2d1220bc96b5e587b5838d43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shirayanagi, Kiyoshi</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Mathematics and computers in simulation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shirayanagi, Kiyoshi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Floating point Gröbner bases</atitle><jtitle>Mathematics and computers in simulation</jtitle><date>1996</date><risdate>1996</risdate><volume>42</volume><issue>4</issue><spage>509</spage><epage>528</epage><pages>509-528</pages><issn>0378-4754</issn><eissn>1872-7166</eissn><abstract>Bracket coefficients for polynomials are introduced. These are like specific precision floating point numbers together with error terms. Working in terms of bracket coefficients, an algorithm that computes a Gröbner basis with floating point coefficients is presented, and a new criterion for determining whether a bracket coefficient is zero is proposed. Given a finite set
F of polynomials with real coefficients, let
G
μ
be the result of the algorithm for
F and a precision value μ, and
G be a true Gröbner basis of
F. Then, as μ approaches infinity,
G
μ
converges to
G coefficientwise. Moreover, there is a precision
M such that if
μ ≥
M, then the sets of monomials with non-zero coefficients of
G
μ
and
G are exactly the same. The practical usefulness of the algorithm is suggested by experimental results.</abstract><pub>Elsevier B.V</pub><doi>10.1016/S0378-4754(96)00027-4</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0378-4754 |
| ispartof | Mathematics and computers in simulation, 1996, Vol.42 (4), p.509-528 |
| issn | 0378-4754 1872-7166 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_23582423 |
| source | ScienceDirect Freedom Collection; Backfile Package - Computer Science (Legacy) [YCS]; Backfile Package - Mathematics (Legacy) [YMT] |
| title | Floating point Gröbner bases |
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