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# isAlmostLexModule -- whether a monomial module over an exterior algebra is almost lex

- Usage:
    `isAlmostLexModule M`
- Inputs:
  - M, a monomial module over an exterior algebra
- Outputs:
  - a Boolean value, whether the module M is almost lex

## Description

Let $\{g_1,g_2,\ldots,g_r\}$ be a graded basis of F. A monomial submodule $M=\oplus_{i=1} ^{r}{I_ig_i}$ of F is almost lex if $I_i$ is a lex ideal of E for each $i.$

Example:

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

    o1 = E

    o1 : PolynomialRing, 4 skew commutative variable(s)

    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_2,e_1*e_3,e_2*e_3)

    o4 = ideal (e e , e e , e e )
                 1 2   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      0      e_2e_3 e_1e_3 e_1e_2 |

                                 2
    o5 : E-module, submodule of E

    i6 : isAlmostLexModule M

    o6 = false

    i7 : I_3=ideal(e_1*e_2,e_1*e_3, e_1*e_4)

    o7 = ideal (e e , e e , e e )
                 1 2   1 3   1 4

    o7 : Ideal of E

    i8 : isAlmostLexModule createModule({I_1,I_3},F)

    o8 = true

## See also

- almostLexModule -- compute an almost lex module with the same Hilbert sequence of the module in input

## Ways to use isAlmostLexModule:

- `isAlmostLexModule(Module)`

## For the programmer

The object isAlmostLexModule is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ExteriorModules.m2:614:0.