class BRAID |
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WORD |
attr index:CARD; |
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attr w:ARRAY{INT}; .. Included as w |
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attr index:CARD; |
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attr w:ARRAY{INT}; .. Included as w |
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aget(i:CARD):INT .. Included as aget |
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append(b:SAME) |
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append(b:SAME):SAME |
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append(s:INT) |
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append(s:INT):SAME |
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aset(i:CARD, g:INT) .. Included as aset |
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cancel:SAME .. Included as cancel |
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check:BOOL |
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clone:SAME |
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create(ind:CARD):SAME |
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create(p:PERM):SAME |
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**** | For permutation p, create standard braid w, s.t. w.perm=p. |
create(s:STR):SAME |
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**** | convert STR to BRAID. format: "4 : 2 -1 3 -2 -3 2 1 endcode"
_____index^___^^^^^^^^^^^^^^^^braid_word |
create:SAME |
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crossingNumTbl:ARRAY{INT} |
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**** | [g] is total_appearance for g-th generator. [0], [index] as guards. |
delete(pos:CARD) .. Included as delete |
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delete(pos:CARD):SAME .. Included as delete |
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div(b:SAME):SAME .. Included as div |
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div(s:INT):SAME .. Included as div |
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gstr(g:INT, b:INT):STR .. Included as gstr |
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**** | b: base for coverings. x_{g.b} or x_{g.b}^{-1} |
gstr(g:INT,b:INT, s1,s2,s3:STR):STR .. Included as gstr |
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**** | b: base for coverings s1(s2 resp.) is pre(post resp.) str for generator name "g". |
insert(pos:CARD,b:SAME):SAME |
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insert(pos:CARD, s:INT) |
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insert(pos:CARD, s:INT):SAME |
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inverse:SAME |
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**** | inverse as group |
is_PureBraid:BOOL |
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is_trivial:BOOL .. Included as is_trivial |
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lastPositionTbl:ARRAY{INT} |
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**** | [g] is where g-th generator is appear at last. [0], [index] as guards. |
maxGen:CARD .. Included as maxGen |
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**** | m= max index of generator |
perm:PERM |
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**** | get permutation [1..index] |
pow(n:CARD):SAME .. Included as pow |
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pow(n:INT):SAME .. Included as pow |
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printD |
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**** | print for debug/check |
reach(s:CARD):CARD |
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**** | where s-th string reach. |
reverse:SAME |
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**** | reverse order of elements |
size:CARD .. Included as size |
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str:STR |
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**** | convert BRAID to STR format: "4 : 2 -1 3 -2 -3 2 1 endcode"
_____index^___^^^^^^^^^^^^^^^^braid_word |
str_n(nl:CARD):STR .. Included as str_n |
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**** | convert WORD to STR as a sequence of number "\n" can be included. format: "1 2 3 -2 -1 -2" |
times(b:SAME):SAME .. Included as times |
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times(s:INT):SAME .. Included as times |
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total_appearance(g:INT):INT .. Included as total_appearance |
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**** | total appearance for g-th generator. |
total_negative_power:INT .. Included as total_negative_power |
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total_positive_power:INT .. Included as total_positive_power |
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total_power(g:INT):INT .. Included as total_power |
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**** | total power for g-th generator. |
total_power:INT .. Included as total_power |
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trackString(s:CARD):ARRAY{CARD} |
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**** | [i]: where s-th string arrives before w[i]. i.e. [i+1]: where s-th string arrives after w[i]. |
append(b:SAME) .. Included as word_append |
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append(b:SAME):SAME .. Included as word_append |
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append(s:INT) .. Included as word_append |
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append(s:INT):SAME .. Included as word_append |
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check:BOOL .. Included as word_check |
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clone:SAME .. Included as word_clone |
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create(s:STR):SAME .. Included as word_create |
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**** | convert STR to WORD. format: "2 -1 3 -2 -3 2 1"
__________^^^^^^^^^^^^^^^^word |
create:SAME .. Included as word_create |
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insert(pos:CARD,b:SAME):SAME .. Included as word_insert |
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insert(pos:CARD, s:INT) .. Included as word_insert |
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insert(pos:CARD, s:INT):SAME .. Included as word_insert |
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inverse:SAME .. Included as word_inverse |
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**** | inverse as group |
printD .. Included as word_printD |
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**** | print for debug/check |
reverse:SAME .. Included as word_reverse |
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**** | reverse order of elements |
str:STR .. Included as word_str |
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writheTbl:ARRAY{INT} |
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**** | [g] is total_power for g-th generator. [0], [index] as guards. |
wstr(s1,s2,s3:STR):STR .. Included as wstr |
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**** | convert WORD to STR s1(s2 resp.) is pre(post resp.) str for generator name "g". |
wstr:STR .. Included as wstr |
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**** | convert WORD to STR in TeX like format as "x_{1} x_{2} x_{1}^{-1} x_{2}^{-1}" |
ind!:CARD .. Included as ind! |
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