We develop numerical homotopy algorithms for solving systems of polynomial equations arising from the classical Schubert calculus. These homotopies are optimal in that generically no paths diverge. For problems defined by hypersurface Schubert conditions we give two algorithms based on extrinsic deformations of the Grassmannian: one is derived from a Gröbner basis for the Plücker ideal of the G...

The notion of initial ideal for an a polynomial ring appears in the theory Gröbner basis. Similarly to ideals, we can define algebra subalgebra ring, or more generally Laurent which is used SAGBI (Subalgebra Analogue Bases Ideals) finitely generated not always generated, and no general criterion finite generation known. aim this paper present new class subalgebras having non-finitely algebras. ...

The theory of “subalgebra basis” analogous to standard basis (the generalization of Gröbner bases to monomial ordering which are not necessarily well ordering [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 Ana...

Let W be a finite-dimensional Z/p-module over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W ]Z/p, is called the Noether number of the representation, and is denoted by β(W ). A lower bound for β(W ) is derived, and it is shown that if U is a Z/p submodule of W , then β(U) 6 β(W ). A set of generators, in fact a SAGBI basis, is...