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In this paper we use Gröbner bases for the implicitization of rational parametric curves and surfaces in 3D-space. We prove that the implicit form of a curve or surface given by the rational parametrization x 1 := p 1 q 1 x 2 := p 2 q 2 x 3 := p 3 q 3 , where the p's and q's are univariate polynomials in y 1 or bivariate polynomials in y 1 , y 2 over a… (More)

Some canonical properties of nonlin-ear systems. 31] J.C. Willems. Input-output state-space representations of nite-dimensional linear time-invariant systems. 11 6] S. Diop. Diierential algebraic decision methods and some applications to system theory. Theoretical Comp. Sci., 1991. Special issue covering "Traitements Alg ebriques et Informatiques des S… (More)

- R Gebauer, M Kalkbrenner, B Wall, F Winkler, Casa, In M A Kaashoek +18 others
- 1992

A computer algebra package for constructive algebraic geometry. 27] A.J. van der Schaft. On realization of nonlin-ear systems described by higher-order diieren-tial equations. The inverse problem of the one discussed above (going from state space to input-output form) is simpler, but not trivial: it corresponds directly to implicitization. For an extensive… (More)

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