class ARTIN_FORM
****
Artin's normal form for braid word.c.f. Artin,E. "Braid groups, generators and relations,solution of word problem" Theorie der Zopfe, Abh.Math.Sem.Univ.Hamburg 4(1926),47-72c.f. Artin,E. Theory of braids, Ann. of Math.(2)48(1947),101-126.

This code is "GPL"ed. 2006.02.14 K.Kodama bug fix in ARTIN_FORM 1998.7.2 K.Kodama


Flattened version is here



Public


Features
GArtinNormalForm(word:BRAID, reduce:BOOL):BRAID
PureArtinNormalForm(word:BRAID, reduce:BOOL):BRAID


Private

CnvReducedNormalForm(i:INT, inout Ai:BRAID, inout Di:BRAID)
**** Assume that Ai is pure braid.
GArtinNormalForm_work(word:BRAID, reduce:BOOL):BRAID
**** Generalized Artin Normal form. For braid w, w/E is pure braid, A be Normal form of w/E, A E is Gen. A. form.
checkD(D:BRAID, j:INT):BOOL
**** check j(=position of i-th string) in the word D.
cnvRA2A(i:INT, inout di:BRAID)
**** Convert from "Reduced Normal" form to "Normal" form.
twistN(inout Di:BRAID,k0:INT, inout j:INT)
**** negative twist "k0" and "k0+1"th string
twistP(inout Di:BRAID,k0:INT, inout j:INT)
**** positive twist "k0" and "k0+1"th string

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