Singular

7.5.14 nctools_lib

Library:

nctools.lib

Purpose:

General tools for noncommutative algebras

Authors:

Levandovskyy V., levandov@mathematik.uni-kl.de,
Lobillo, F.J., jlobillo@ugr.es,
Rabelo, C., crabelo@ugr.es,
Motsak, O., U@D, where U={motsak}, D={mathematik.uni-kl.de}

Overview:

Support: DFG (Deutsche Forschungsgesellschaft) and Metodos algebraicos y efectivos en grupos cuanticos, BFM2001-3141, MCYT, Jose Gomez-Torrecillas (Main researcher).

Procedures:

7.5.14.0. Gweights		compute weights for a compatible ordering in a G-algebra,
7.5.14.0. weightedRing		change the ordering of a ring to a weighted one,
7.5.14.0. ndcond		the ideal of non-degeneracy conditions in G-algebra,
7.5.14.0. Weyl		create Weyl algebra structure in a basering (two different realizations),
7.5.14.0. makeWeyl		return n-th Weyl algebra in (x(i),D(i)) presentation,
7.5.14.0. makeHeisenberg		return n-th Heisenberg algebra in (x(i),y(i),h) realization,
7.5.14.0. Exterior		return qring, the exterior algebra of a basering,
7.5.14.0. findimAlgebra		create finite dimensional algebra structure from the basering and the multiplication matrix M,
7.5.14.0. superCommutative		return qring, a super-commutative algebra over a basering,
7.5.14.0. rightStd		compute right Groebner basis of an ideal,
7.5.14.0. rightNF		compute right normal form wrt a submodule,
7.5.14.0. rightModulo		compute kernel of a homomorphism of right modules,
7.5.14.0. moduloSlim		compute modulo command via slimgb
7.5.14.0. ncRelations		recover the non-commutative relations of a G-algebra,
7.5.14.0. isCentral		check for the commutativity of a polynomial in the G-algebra,
7.5.14.0. isNC		check whether basering is noncommutative,
7.5.14.0. isCommutative		check whether basering is commutative
7.5.14.0. isWeyl		check whether basering is a Weyl algebra
7.5.14.0. UpOneMatrix		return NxN matrix with 1's in the whole upper triagle,
7.5.14.0. AltVarStart		return first alternating variable of a super-commutative algebra,
7.5.14.0. AltVarEnd		return last alternating variable of a super-commutative algebra,
7.5.14.0. IsSCA		check whether current ring is a super-commutative algebra,
7.5.14.0. makeModElimRing		equip a ring with module elimination ordering,
7.5.14.0. embedMat		embeds matrix M in a left upper corner of m times n matrix