Open AccessReal space quadrics and μ-bases
Author(s) -
J. William Hoffman,
Haohao Wang
Publication year - 2013
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.04.004
Subject(s) - quadric , mathematics , parametrization (atmospheric modeling) , surface (topology) , closure (psychology) , quadratic equation , image (mathematics) , projective space , euclidean space , space (punctuation) , pure mathematics , ambient space , combinatorics , mathematical analysis , projective test , geometry , physics , quantum mechanics , artificial intelligence , computer science , economics , market economy , radiative transfer , linguistics , philosophy
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