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.


Flattened version is here



Public


Readonly Shareds
shared Aw,Dw:BRAID;
****
shared Aw,Dw:BRAID;
****
shared j:INT;
shared p,p1:INT;
**** shared k0,g,gd:INT;
shared p,p1:INT;
**** shared k0,g,gd:INT;
shared spos:BRAID;
**** position of "i"-th string

Writable Shareds
shared Aw,Dw:BRAID;
****
shared Aw,Dw:BRAID;
****
shared j:INT;
shared p,p1:INT;
**** shared k0,g,gd:INT;
shared p,p1:INT;
**** shared k0,g,gd:INT;
shared spos:BRAID;
**** position of "i"-th string

Features
CnvReducedNormalForm(i:INT, inout Ai:BRAID, inout Di:BRAID)
GArtinNormalForm(inout word:BRAID, reduce:BOOL):BOOL
**** Generalized Normal form. For pure braid w, wE, A be Normal form of wE, 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)
**** negative twist "k0" and "k0+1"th string
twistP(inout Di:BRAID,k0:INT)
**** positive twist "k0" and "k0+1"th string


Private

PureArtinNormalForm(inout word:BRAID, reduce:BOOL):BOOL

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