Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 With the right functions and a list comprehension, custom names can be easier. A multiplication table for hex digits (without carries): sage: from sage.matrix.operation_table import OperationTable sage: R=Integers(16) sage: names=[hex(Integer(a)) for a in R] sage: OperationTable(R, operation=operator.mul, names=names) * 0 1 2 3 4 5 6 7 8 9 a b c d e f +-------------------------------- 0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1| 0 1 2 3 4 5 6 7 8 9 a b c d e f 2| 0 2 4 6 8 a c e 0 2 4 6 8 a c e 3| 0 3 6 9 c f 2 5 8 b e 1 4 7 a d 4| 0 4 8 c 0 4 8 c 0 4 8 c 0 4 8 c 5| 0 5 a f 4 9 e 3 8 d 2 7 c 1 6 b 6| 0 6 c 2 8 e 4 a 0 6 c 2 8 e 4 a 7| 0 7 e 5 c 3 a 1 8 f 6 d 4 b 2 9 8| 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 9| 0 9 2 b 4 d 6 f 8 1 a 3 c 5 e 7 a| 0 a 4 e 8 2 c 6 0 a 4 e 8 2 c 6 b| 0 b 6 1 c 7 2 d 8 3 e 9 4 f a 5 c| 0 c 8 4 0 c 8 4 0 c 8 4 0 c 8 4 d| 0 d a 7 4 1 e b 8 5 2 f c 9 6 3 e| 0 e c a 8 6 4 2 0 e c a 8 6 4 2 f| 0 f e d c b a 9 8 7 6 5 4 3 2 1 This should be flexible enough to create a variety of such tables. sage: from sage.matrix.operation_table import OperationTable sage: from operator import xor sage: T=OperationTable(ZZ, xor, elements=range(8)) sage: T . a b c d e f g h +---------------- a| a b c d e f g h b| b a d c f e h g c| c d a b g h e f d| d c b a h g f e e| e f g h a b c d f| f e h g b a d c g| g h e f c d a b h| h g f e d c b a sage: names=[’000’, ’001’,’010’,’011’,’100’,’101’,’110’,’111’] sage: T.change_names(names) sage: T.set_print_symbols(’^’, ’\\land’) sage: T ^ 000 001 010 011 100 101 110 111 +-------------------------------- 000| 000 001 010 011 100 101 110 111 001| 001 000 011 010 101 100 111 110 010| 010 011 000 001 110 111 100 101 011| 011 010 001 000 111 110 101 100 100| 100 101 110 111 000 001 010 011 101| 101 100 111 110 001 000 011 010 110| 110 111 100 101 010 011 000 001 111| 111 110 101 100 011 010 001 000 sage: T = OperationTable([False, True], operator.or_, names = ’elements’) sage: T 406 Chapter 23. Operation Tables
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
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Sage Reference Manual: Matrices and
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Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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