# 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:
• , 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