class BRAID


Ancestors
WORD



Public


Readable Attributes
attr index:CARD;
attr w:ARRAY{INT}; .. Included as w

Writable Attributes
attr index:CARD;
attr w:ARRAY{INT}; .. Included as w

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

Iters
ind!:CARD .. Included as ind!

The Sather Home Page