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# OrderedQQVector -- The class of all vectors of an ordered module $\QQ^n$

## Description

For an introduction see Ordered modules. Every ordered $\QQ^n$ vector belongs to an instance of the type OrderedQQn. The ordered $\QQ^n$ vectors are most easily accessed though the original module.

 i1 : M = orderedQQn(3, {Lex}) 3 o1 = QQ o1 : Ordered QQ^3 module i2 : M_0 + 2 * M_1 + 3 * M_2 o2 = | 1 | | 2 | | 3 | o2 : Ordered QQ^3 module

Any pair of vectors of a module of type OrderedQQn may be compared with <, >, and ==.

 i3 : M = orderedQQn(3, {GLex}) 3 o3 = QQ o3 : Ordered QQ^3 module i4 : 2*M_1 < M_0 + M_2 o4 = true i5 : 3*M_1 < M_0 + M_2 o5 = false

The image of $0$ under a valuation is $\infty$, so it may be necessary to test whether an element of an ordered module $\QQ^n$ is equal to the valuation of $0$.

 i6 : M = orderedQQn(3, {Lex}) 3 o6 = QQ o6 : Ordered QQ^3 module i7 : M_0 < infinity o7 = true i8 : M_0 == infinity o8 = false