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Magma[Nucleus] - compute the nucleus of a magma
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Calling Sequence
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Nucleus( m )
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Parameters
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m
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Array representing the Cayley table of a finite magma
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Description
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The nucleus of a magma is the set of its members that associate with every member of the magma. That is, an element x is in the nucleus if all of the equations (xy)z = x(yz), (yx)z = y(xz) and (yz)x = y(zx) are satisfied, for all y and z from the magma.
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The Nucleus command returns the nucleus of the magma m as a set.
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Compatibility
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The Magma[Nucleus] command was introduced in Maple 15.
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Examples
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![m := Matrix([[1, 2, 3], [2, 3, 1], [3, 1, 2]])](/support/helpjp/helpview.aspx?si=8606/file02161/math75.png)
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![m := Matrix([[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 2, 4], [1, 2, 2, 4, 5]])](/support/helpjp/helpview.aspx?si=8606/file02161/math89.png)
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![m := Matrix([[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 2, 4], [1, 2, 1, 4, 5]])](/support/helpjp/helpview.aspx?si=8606/file02161/math103.png)
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