orderedQQn -- Construct an ordered module $\QQ^n$

For an overview see Ordered modules. Let $R$ be a polynomial ring with $n$ variables $x_1 \dots x_n$. Then the corresponding ordered $\QQ^n$ module has the following ordering. Suppose that $v, w \in \QQ^n$. Let $d \in \ZZ$ be a positive integer and $c \in \ZZ^n_{\ge 0}$ be a vector such that $dv + c$ and $dw + c$ have non-negative entries. Then $v < w$ if and only if $x^{dv + c} > x^{dw + c}$ in $R$. Note that this property does not depend on the choices of $c$ and $d$, so we obtain a well-defined order on $\QQ^n$.

Instead of supplying a polynomial ring, we may supply the rank $n$ of the module along with a monomial order. The constructor creates the ring $R$ with $n$ variables and the given monomial order to construct the OrderedQQn module

$N$ and $N'$ are the same module because they are built from the same ring. See OrderedQQn == OrderedQQn.