Let
$K$ be a
field,
$V$ a
$K$vector space
with basis
${e}_{1},\dots ,{e}_{n}$, and
$E$ the exterior
algebra of
$V$.
We introduce a
Macaulay2 package that allows one to deal with classes of monomial
ideals in
$E$.
More precisely, we implement in
Macaulay2 some algorithms in order
to easily compute stable, strongly stable and lexsegment ideals in
$E$. Moreover, an algorithm
to check whether an
$\left(n+1\right)$tuple
$\left(1,{h}_{1},\dots ,{h}_{n}\right)$
(${h}_{1}\le n={dim}_{K}V$)
of nonnegative integers is the Hilbert function of a graded
$K$algebra of
the form
$E\u2215I$, with
$I$ a graded ideal of
$E$, is given. In particular,
if
${H}_{E\u2215I}$ is the Hilbert function
of a graded
$K$algebra
$E\u2215I$,
the package is able to construct the unique lexsegment ideal
${I}^{lex}$ such
that
${H}_{E\u2215I}={H}_{E\u2215{I}^{lex}}$.
