Search Results

You are looking at 1 - 4 of 4 items for :

  • "Gröbner basis" x
Clear All

The closed form solution of 7 parameter 3D transformation.The Gauss-Jacobi combinatorial adjustment is applied to solve the 3D transformation problem with 7 parameters, and it is also demonstrated that the combinatorial algorithm gives the same solution as the conventional linear Gauss-Markov model.

Restricted access

Summary  

Let F be a field, and α0,...,αk-1 be k distinct elements of F. Let λ =(λ1,...,λk) be a partition of n and Vλ be the set of all vectors v=(v1,...,vn)∈ Fn such that  |{j ∈ [n] : vji}|=λi+1  for 0≦ i ≦\ k-1. We describe the lexicographic standard monomials of the ideal of polynomials from  F[x1,...,xn] which vanish on the set Vλ. In the proof we give a new description of the orthogonal complement (Sλ) (with respect to the James scalar product) of the Specht module Sλ. As applications, a basis of (Sλ) is exhibited, and we obtain a combinatorial description of the Hilbert function of Vλ..  Our approach gives also the deglex standard monomials of Vλ, and hence provides a new proof of a result of A. M. Garsia and C. Procesi [10].

Restricted access

Farr, J and Gao, S. , Computing Gröbner basis for vanishing ideal of -nite set of points, in: Applied algebra, algebraic algorithms and error-correcting codes , LNCS 3857, 118–127, Springer, Berlin, 2006. MR 2007c :13039

Restricted access

A theory of “subalgebra basis” analogous to standard basis (the generalization of Gröbner bases to monomial orderings which are not necessarily well orderings [1]) for ideals in polynomial rings over a field is developed. We call these bases “SASBI Basis” for “Subalgebra Analogue to Standard Basis for Ideals”. The case of global orderings, here they are called “SAGBI Basis” for “Subalgebra Analogue to Gröbner Basis for Ideals”, is treated in [6]. Sasbi bases may be infinite. In this paper we consider subalgebras admitting a finite Sasbi basis and give algorithms to compute them.

Restricted access