By Ladislav NebeskyÌ
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Additional info for Algebraic properties of trees (Acta Universitatis Carolinae : Philologica monographia)
The admissible derivations assigned to w are denoted by ΔW (w) ⊆ Δ and we call the cone w ΔW (w) the Janet cone of w with respect to W . This construction ensures disjointness of cones but not necessarily that the union of cones equals W Δ . For the Janet completion a ﬁnite set W ⊃ W is successively created by adding any w ˜ = ∂i wj ∈ w∈W w ΔW (w) to W , where wj ∈ W and ∂i ∈ Δ \ ΔW (wj ). This leads to the disjoint Janet decomposition W Δ= w ΔW (w) w∈W that separates a Δ-closed set W into ﬁnitely many cones w ΔW (w) after ﬁnitely many steps.
Algorithm: 1: x ← ld(p) 2: while exists q= ∈ (ST )= and i1 , . .
Moreover, the matrix formalism and symbolic formulae for some matrix operations lead us to more eﬃcient computational procedures for the distributed and parallel computational process. Additional computational ﬂows are connected with the next two procedures. The ﬁrst of them is devoted to visualization of all necessary information including auxiliary procedures (for example, analysis of images using diﬀerential geometry methods) and space-charge force computing. Here we can use the methods proposed in our previous publications (see, for example, [16,17,18]).