### D.4.2 algebra_lib

Library:
  algebra.lib
Purpose:
  Compute with Algbras and Algebra Maps
Authors:
  Gert-Martin Greuel, greuel@mathematik.uni-kl.de,
  Agnes Eileen Heydtmann, agnes@math.uni-sb.de,
  Gerhard Pfister, pfister@mathematik.uni-kl.de

Procedures:

> D.4.2.1 algebra_containment |  | query of algebra containment
> D.4.2.2 module_containment |  | query of module containment over a subalgebra
> D.4.2.3 inSubring |  | test whether polynomial p is in subring generated by I
> D.4.2.4 algDependent |  | computes algebraic relations between generators of I
> D.4.2.5 alg_kernel |  | computes the kernel of the ringmap phi
> D.4.2.6 is_injective |  | test for injectivity of ringmap phi
> D.4.2.7 is_surjective |  | test for surjectivity of ringmap phi
> D.4.2.8 is_bijective |  | test for bijectivity of ring map phi
> D.4.2.9 noetherNormal |  | noether normalization of ideal id
> D.4.2.10 mapIsFinite |  | query for finiteness of map phi:R --> basering/I
> D.4.2.11 finitenessTest |  | find variables which occur as pure power in lead(i)
> D.4.2.12 nonZeroEntry |  | list describing non-zero entries of an identifier

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