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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

See also

Methods that use an object of class OrderedQQVector:

For the programmer

The object OrderedQQVector is a type, with ancestor classes Vector < BasicList < Thing.