Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
. False True
+------------
False| False True
True| True True
TESTS:
Empty structures behave acceptably, though the ASCII table looks a bit odd. The LaTeX version works much
better.
sage: from sage.matrix.operation_table import OperationTable
sage: L=FiniteSemigroups().example(())
sage: L
An example of a finite semigroup: the left regular band generated by ()
sage: T=OperationTable(L, operation=operator.mul)
sage: T
*
+
sage: T._latex_()
’{\\setlength{\\arraycolsep}{2ex}\n\\begin{array}{r|*{0}{r}}\n\\multicolumn{1}{c|}{\\ast}\\\\\\h
If the algebraic structure cannot be listed (like when it is infinite) then there is no way to create a table.
sage: from sage.matrix.operation_table import OperationTable
sage: OperationTable(ZZ, operator.mul)
Traceback (most recent call last):
...
ValueError: Integer Ring is infinite
The value of elements must be a subset of the algebraic structure, in forms that can be coerced into the
structure. Here we demonstrate the proper use first:
sage: from sage.matrix.operation_table import OperationTable
sage: H=CyclicPermutationGroup(4)
sage: H.list()
[(), (1,2,3,4), (1,3)(2,4), (1,4,3,2)]
sage: elts = [’()’, ’(1,3)(2,4)’]
sage: OperationTable(H, operator.mul, elements=elts)
* a b
+----
a| a b
b| b a
This can be rewritten so as to pass the actual elements of the group H, using a simple for loop:
sage: L = H.list() #list of elements of the group H
sage: elts = [L[i] for i in {0, 2}]
sage: elts
[(), (1,3)(2,4)]
sage: OperationTable(H, operator.mul, elements=elts)
* a b
+----
a| a b
b| b a
Here are a couple of improper uses
sage: elts.append(5)
sage: OperationTable(H, operator.mul, elements=elts)
Traceback (most recent call last):
407