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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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