### 7.5.20 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:

> 7.5.20.0. Gweights |  | compute weights for a compatible ordering in a G-algebra,
> 7.5.20.0. weightedRing |  | change the ordering of a ring to a weighted one,
> 7.5.20.0. ndcond |  | the ideal of non-degeneracy conditions in G-algebra,
> 7.5.20.0. Weyl |  | create Weyl algebra structure in a basering (two different realizations),
> 7.5.20.0. makeWeyl |  | return n-th Weyl algebra in (x(i),D(i)) presentation,
> 7.5.20.0. makeHeisenberg |  | return n-th Heisenberg algebra in (x(i),y(i),h) realization,
> 7.5.20.0. Exterior |  | return qring, the exterior algebra of a basering,
> 7.5.20.0. findimAlgebra |  | create finite dimensional algebra structure from the basering and the multiplication matrix M,
> 7.5.20.0. superCommutative |  | return qring, a super-commutative algebra over a basering,
> 7.5.20.0. rightStd |  | compute right Groebner basis of an ideal,
> 7.5.20.0. rightNF |  | compute right normal form wrt a submodule,
> 7.5.20.0. rightModulo |  | compute kernel of a homomorphism of right modules,
> 7.5.20.0. moduloSlim |  | compute modulo command via slimgb
> 7.5.20.0. ncRelations |  | recover the non-commutative relations of a G-algebra,
> 7.5.20.0. isCentral |  | check for the commutativity of a polynomial in the G-algebra,
> 7.5.20.0. isNC |  | check whether basering is noncommutative,
> 7.5.20.0. isCommutative |  | check whether basering is commutative
> 7.5.20.0. isWeyl |  | check whether basering is a Weyl algebra
> 7.5.20.0. UpOneMatrix |  | return NxN matrix with 1's in the whole upper triagle,
> 7.5.20.0. AltVarStart |  | return first alternating variable of a super-commutative algebra,
> 7.5.20.0. AltVarEnd |  | return last alternating variable of a super-commutative algebra,
> 7.5.20.0. IsSCA |  | check whether current ring is a super-commutative algebra,
> 7.5.20.0. makeModElimRing |  | equip a ring with module elimination ordering,
> 7.5.20.0. embedMat |  | embeds matrix M in a left upper corner of m times n matrix

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