Real space quadrics and μ-bases
In Euclidean 3-space, a quadric surface is the zero set of a quadratic equation in three variables. Its projective closure can be given as the closure of the image of a rational parametrization P:R2→R4 where P maps the parameters (s,t)∈R2 to the tuple (a,b,c,d)∈R4 and a, b, c, d are linearly indepen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2013-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X13000485 |
| _version_ | 1811334025142337536 |
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| author | J. William Hoffman Haohao Wang |
| author_facet | J. William Hoffman Haohao Wang |
| author_sort | J. William Hoffman |
| collection | DOAJ |
| description | In Euclidean 3-space, a quadric surface is the zero set of a quadratic equation in three variables. Its projective closure can be given as the closure of the image of a rational parametrization P:R2→R4 where P maps the parameters (s,t)∈R2 to the tuple (a,b,c,d)∈R4 and a, b, c, d are linearly independent quadratic polynomials, with gcd(a, b, c, d) = 1. This paper provides an algorithm to classify the type of quadric surface, and identify the normal forms solely based on the parametrization of the quadric surface. |
| first_indexed | 2024-04-13T17:01:36Z |
| format | Article |
| id | doaj.art-a88485ec273142c7b83cb98c07de0412 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-04-13T17:01:36Z |
| publishDate | 2013-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-a88485ec273142c7b83cb98c07de04122022-12-22T02:38:37ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2013-10-0121316917410.1016/j.joems.2013.04.004Real space quadrics and μ-basesJ. William Hoffman0Haohao Wang1Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, United StatesDepartment of Mathematics, Southeast Missouri State University, Cape Girardeau, MO 63701, United StatesIn Euclidean 3-space, a quadric surface is the zero set of a quadratic equation in three variables. Its projective closure can be given as the closure of the image of a rational parametrization P:R2→R4 where P maps the parameters (s,t)∈R2 to the tuple (a,b,c,d)∈R4 and a, b, c, d are linearly independent quadratic polynomials, with gcd(a, b, c, d) = 1. This paper provides an algorithm to classify the type of quadric surface, and identify the normal forms solely based on the parametrization of the quadric surface.http://www.sciencedirect.com/science/article/pii/S1110256X13000485Quadric surfacesParametrizationImplicit equations |
| spellingShingle | J. William Hoffman Haohao Wang Real space quadrics and μ-bases Journal of the Egyptian Mathematical Society Quadric surfaces Parametrization Implicit equations |
| title | Real space quadrics and μ-bases |
| title_full | Real space quadrics and μ-bases |
| title_fullStr | Real space quadrics and μ-bases |
| title_full_unstemmed | Real space quadrics and μ-bases |
| title_short | Real space quadrics and μ-bases |
| title_sort | real space quadrics and μ bases |
| topic | Quadric surfaces Parametrization Implicit equations |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X13000485 |
| work_keys_str_mv | AT jwilliamhoffman realspacequadricsandmbases AT haohaowang realspacequadricsandmbases |