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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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