Module

Module -- the class of all modules which are handled by the engine.

The most general module M is represented as a submodule of a quotient module of a free module F. The matrix of relations used to produce the quotient module is stored as M.relations and the matrix of generators is stored as M.generators.

Functions which create modules:

Ring ^ ZZ

Tests:

Operations on modules:

Module == Module

Module _ ZZ -- get a generator of a module

Module + Module

Module ** Ring -- tensor product, base change.

Module ++ Module -- direct sum

Module ** Module -- tensor product

Module : Module -- the submodule quotient M : N

Module / Module -- the quotient module (M+N)/N

Module / Ideal -- the quotient module M/IM

Ideal / Ideal -- the quotient module (I+J)/J

ambient

annihilator -- the annihilator of a module

codim -- codimension of the support of a module

dim

End

fittingIdeal(i,m) -- the i-th Fitting ideal of the module M

Ext^i(M,N) -- Ext of two modules

gcdDegree

genera

generators

poincare(M,t) -- the numerator of the Hilbert series of M.

hilbertFunction(d,M) -- the Hilbert function of a module.

hilbertPolynomial(M) -- the Hilbert polynomial of a module

hilbertSeries(M) -- the Hilbert series of a module.

Hom(M,N) -- the module of homomorphisms

intersect(I,J) -- intersection of modules or ideals

presentation M -- a presentation matrix for M

prune M -- a minimal presentation for M

quotient

rank

relations

removeLowestDimension

resolution M -- a finite free resolution of M

super

tensorAssociativity -- associativity isomorphisms for tensor products

top

Tor_i(M,N) -- Tor of two modules

trim -- replace generators and relations by minimal sets

truncate

Operations on elements of modules (vectors):

Vector _ ZZ -- get a component of a vector

components

leadCoefficient

leadMonomial