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Purpose
Substitute Lie Bracket Table relations in a Lie polynomial written
in terms of PHB elements.
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Syntax
e:=reduceLBT(x,B,lbt);
Description
This procedure is similar to reduceLB, it simplifies a Lie
polynomial given in to a expression in terms of elements in the
PHB in , but additionally substitutes the dependent brackets in the
PHB according to Lie bracket table relations passed to the procedure
in . The table defining the dependent brackets in terms of
independent ones is passed as a list. In the case that all elements
in the PHB are linearly independent, then should be an empty
set or list, and the result returned by reduceLBT will be
equal to that obtained by using reduceLB if there are no
brackets of order higher than the degree of nilpotency. To make this
clearer we stress the following characteristic of this procedure:
Unlike reduceLB, this procedure eliminates from the
expression all those Lie brackets of order higher than the
degree of nilpotency, i.e. sets them to zero.
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Arguments
The Philip Hall basis.
Examples
Consider the Lie polynomial x given by:
2
x := 1/2 dg3 g1 (f0 &* (f0 &* f2))
+ dg4 g2 (f1 &* (f0 &* f1))
and the Lie bracket table sr ,
> sr:={B[4]=B[1]+6*B[2]};
sr := {f0 &* f1 = f0 + 6 f1}
The function reduceLBT with the P. Hall basis given in the example for the phb function on page , yields
> reduceLBT(x,B,sr);
2
1/2 dg3 g1 (f0 &* (f0 &* f2)) - dg4 g2 f0 - 6 dg4 g2 f1
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Implementation Notes
This function basically relies only on reduceLB and Maple's
subs function. The algorithm is rather simple, the procedure
repeatedly tries to replace the dependent relations in using the
substitution relations in until there are no more dependent
terms (brackets) in . At every substitution iteration, the function
reduceLB is called to simplify the expression.
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Next: ad
Up: Function Reference
Previous: codeCBHcf
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Miguel Attilio Torres-Torriti
2004-05-31