class ARTIN_FORM |
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**** | 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. |
shared Aw,Dw:BRAID; |
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**** |
shared Aw,Dw:BRAID; |
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**** |
shared j:INT; |
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shared p,p1:INT; |
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**** | shared k0,g,gd:INT; |
shared p,p1:INT; |
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**** | shared k0,g,gd:INT; |
shared spos:BRAID; |
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**** | position of "i"-th string |
shared Aw,Dw:BRAID; |
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**** |
shared Aw,Dw:BRAID; |
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**** |
shared j:INT; |
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shared p,p1:INT; |
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**** | shared k0,g,gd:INT; |
shared p,p1:INT; |
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**** | shared k0,g,gd:INT; |
shared spos:BRAID; |
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**** | position of "i"-th string |
CnvReducedNormalForm(i:INT, inout Ai:BRAID, inout Di:BRAID) |
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GArtinNormalForm(inout word:BRAID, reduce:BOOL):BOOL |
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**** | 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 |
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**** | check j(=position of i-th string) in the word D. |
cnvRA2A(i:INT, inout di:BRAID) |
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**** | Convert from "Reduced Normal" form to "Normal" form. |
twistN(inout Di:BRAID,k0:INT) |
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**** | negative twist "k0" and "k0+1"th string |
twistP(inout Di:BRAID,k0:INT) |
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**** | positive twist "k0" and "k0+1"th string |
PureArtinNormalForm(inout word:BRAID, reduce:BOOL):BOOL |
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