Given a polynomial ring P over field K , an element g ∈ and -subalgebra S of we deal with the problem saturating respect to i.e. computing Sat ( ) = [ − 1 ] ∩ . In general case describe procedure/algorithm compute set generators for which terminates if only it is finitely generated. Then consider more interesting when graded. particular, graded by positive matrix W indeterminate, show that choo...

This special issue on Computer algebra and computer analysis was initiated by a session with the same title at the Third International ISAAC Congress, which took place in Berlin, 2001. The guest editors K. Gatermann and W. Koepf organized this session in order to stimulate the interaction between Computer Algebra and Analysis. In this special issue we have collected articles by participants of ...

Non-commutative calculations are considered from the molecular computing point of view. The main idea is that one can get more advantage in using molecular computing for noncommutative computer algebra compared with a commutative one. The restrictions, connected with the coefficient handling in Gröbner basis calculations are investigated. Semigroup and group cases are considered as more appropr...

Let K be a field, D a finite distributive lattice and P the set of all join-irreducible elements of D. We show that if {y ∈ P | y ≥ x} is pure for any x ∈ P , then the Hibi ring RK(D) is level. Using this result and the argument of sagbi basis theory, we show that the homogeneous coordinate rings of Schubert subvarieties of Grassmannians are level. MSC:13F50, 13H10, 13A02, 14M15, 13P10

Let Cp denote the cyclic group of order p where p ≥ 3 is prime. We denote by V3 the indecomposable three dimensional representation of Cp over a field F of characteristic p. We compute a set of generators, in fact a SAGBI basis, for the ring of invariants F[V3 ⊕ V3]p . Our main result confirms the conjecture of Shank[15], for this example, that all modular rings of invariants of Cp are generate...