createModule -- create a module over an exterior algebra from a list of ideals in input

Synopsis

Usage:

createModule(L,F)
Inputs:
- L, a list of ideals
- F, a free module
Outputs:
- a module, the submodule of F which is a direct sum of submodules determined by the ideals in L

Description

Let $\{g_1,g_2,\ldots,g_r\}$ be a graded basis of F and let be $L=\{I_1,I_2,\ldots,I_r\}$. This method yields the following submodule of F: $I_1 g_1 \oplus I_2 g_2 \oplus \cdots \oplus I_r g_r$.

Example:

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

o1 = E

o1 : PolynomialRing, 4 skew commutative variables

i2 : F=E^{0,0,0}

      3
o2 = E

o2 : E-module, free

i3 : I_1=ideal {e_1*e_2,e_3*e_4};

o3 : Ideal of E

i4 : I_2=ideal {e_1*e_2,e_2*e_3*e_4};

o4 : Ideal of E

i5 : I_3=ideal {e_2*e_3*e_4};

o5 : Ideal of E

i6 : l={I_1,I_2,I_3};

i7 : M=createModule(l,F)

o7 = image | e_3e_4 e_1e_2 0      0         0         |
           | 0      0      e_1e_2 e_2e_3e_4 0         |
           | 0      0      0      0         e_2e_3e_4 |

                             3
o7 : E-module, submodule of E

Caveat

ideals and their number have to be compatible with ambient free module

Ways to use `createModule` :

"createModule(List,Module)"

For the programmer

The object createModule is a method function.