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B.7 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.

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

Procedures:

B.7.0.1 Gweights  computes weights for a compatible ordering in a G-algebra,
B.7.0.2 weightedRing  changes the ordering of a ring to a weighted one,
B.7.0.3 ndc  the ideal of non-degeneracy conditions in G-algebra,
B.7.0.4 RootOfUnity  the minimal polynomial for the n-th primitive root of unity,
B.7.0.5 Weyl  creates Weyl algebra structure in a basering (two different realizations),
B.7.0.6 CreateWeyl  returns n-th Weyl algebra in (x(i),D(i)) presentation; in char p, if an integer p is given,
B.7.0.7 Heisenberg  returns N-th Heisenberg algebra in (x(i),y(i),h) realization,
B.7.0.8 Exterior  returns qring, the exterior algebra of a basering,
B.7.0.9 Fin_dim_algebra  creates finite dimensional algebra structure from the basering and the multiplication matrix M,
Auxiliary procedures:
B.7.0.10 Newton  Newton diagram of a polynomial f,
B.7.0.11 NCRelations  recovers the non-commutative relations of a G-algebra,
B.7.0.12 IsCentral  check for the commutativity of polynomial p with the G-algebra,
B.7.0.13 Is_NC  checks whether basering is noncommutative,
B.7.0.14 UpOneMatrix  returns NxN matrix with 1's in the whole upper triagle,
Alias procedures:
B.7.0.15 wRing  alias to weightedRing,


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