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7.5.14 nctools_lib

General tools for noncommutative algebras
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}

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

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