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7.3.20 opposite

Syntax:
opposite ( ring_name )
Type:
ring
Purpose:
creates an opposite algebra of a given algebra.
Note:
activate the ring with the setring command.
An opposite algebra of a given algebra ( ,#) is an algebra ( ,*) with the same vector space but with the opposite multiplication, i.e.

This is an identity functor on commutative algebras.

Remark:
Starting from the variables x_1,...,x_N and the ordering < of the given algebra, an opposite algebra will have variables X_N,...,X_1 (where the case and the position are reverted). Moreover, it is equipped with an opposed ordering <_opp (it is given by the matrix, obtained from the matrix ordering of < with the reverse order of columns).
Currently not implemented for non-global orderings.
 
See Matrix orderings; envelope; oppose.


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            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.