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OrderedQQn -- The class of all ordered modules $\QQ^n$

Description

For an introduction see Ordered modules. Every element of an ordered $\QQ^n$ module is an instance of the type OrderedQQVector. A new ordered $\QQ^n$ module is created with the function orderedQQn.

i1 : R = QQ[x_1 .. x_4, MonomialOrder => Lex]

o1 = R

o1 : PolynomialRing
 
i2 : M = orderedQQn R

       4
o2 = QQ

o2 : Ordered QQ^4 module
 
i3 : M_0, M_1, M_2, M_3

o3 = (| 1 |, | 0 |, | 0 |, | 0 |)
      | 0 |  | 1 |  | 0 |  | 0 |
      | 0 |  | 0 |  | 1 |  | 0 |
      | 0 |  | 0 |  | 0 |  | 1 |

o3 : Sequence
 
i4 : M_0 < M_1

o4 = false
 
i5 : M_0 + M_3 < M_1 + M_2

o5 = false

See also

Methods that use an object of class OrderedQQn:

  • OrderedQQn == OrderedQQn -- see Ordered modules -- Overview of the ordered module $\QQ^n$
  • valuation(Function,LocalRing,OrderedQQn) -- see valuation -- User-defined valuation object
  • valuation(Function,Ring,OrderedQQn) -- see valuation -- User-defined valuation object
  • valuation(Function,RingOfInvariants,OrderedQQn) -- see valuation -- User-defined valuation object
  • valuation(Function,Subring,OrderedQQn) -- see valuation -- User-defined valuation object

For the programmer

The object OrderedQQn is a type, with ancestor classes Module < ImmutableType < HashTable < Thing.

The source of this document is in Valuations.m2:999:0.