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ExteriorModules :: almostStableModule

almostStableModule -- compute the smallest almost stable module containing a given monomial module

Synopsis

Description

Let $\{g_1,g_2,\ldots,g_r\}$ be a graded basis of F and let $M=\oplus_{i=1}^{r}{I_ig_i}$ a monomial submodule of F. The almost stable module associated to M is the monomial module $M_{s}=\oplus_{i=1}^{r}{J_ig_i}$ with $J_i=\mathrm{stableIdeal}\ I_i$ for each $i$, i.e., the stable ideal associated to $I_i$ for each $i.$

Example:

i1 : E = QQ[e_1..e_4, SkewCommutative => true]

o1 = E

o1 : PolynomialRing, 4 skew commutative variables
 
i2 : F=E^{0,0}

      2
o2 = E

o2 : E-module, free
 
i3 : I_1=ideal(e_1*e_2,e_1*e_3)

o3 = ideal (e e , e e )
             1 2   1 3

o3 : Ideal of E
 
i4 : I_2=ideal(e_1*e_3,e_2*e_3)

o4 = ideal (e e , e e )
             1 3   2 3

o4 : Ideal of E
 
i5 : M=createModule({I_1,I_2},F)

o5 = image | e_1e_3 e_1e_2 0      0      |
           | 0      0      e_2e_3 e_1e_3 |

                             2
o5 : E-module, submodule of E
 
i6 : N=almostStableModule M

o6 = image | e_1e_3 e_1e_2 0      0      0      |
           | 0      0      e_2e_3 e_1e_3 e_1e_2 |

                             2
o6 : E-module, submodule of E

See also

Ways to use almostStableModule :

For the programmer

The object almostStableModule is a method function.