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Fixed crash on disconnected braid and possible loss of orientation

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information when building braids.  knot parser supports disjoint union
(juxtaposition).  Minor documentation changes.
This commit is contained in:
Cotton Seed 2013-03-26 12:44:40 -04:00
parent dc11fd082c
commit 36e0303fca
8 changed files with 271 additions and 181 deletions
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11
README
View File

@ -106,13 +106,17 @@ usage: kk <invariant> [options...] <link>
<invariant> can be one of: <invariant> can be one of:
kh: Khovanov homology kh: Khovanov homology
gss: Szabo's geometric spectral sequence gss: Szabo's geometric spectral sequence
ls: Batson-Seed link splitting spectral sequence lsss: Batson-Seed link splitting spectral sequence
component weights are 0, 1, ..., m component weights are 0, 1, ..., m
sq2: Lipshitz-Sarkar Steenrod square on Z/2 Kh sq2: Lipshitz-Sarkar Steenrod square on Z/2 Kh
output suitable for Sage output suitable for Sage
leess: spectral sequence coming from Bar-Natan analogue of Lee's leess: spectral sequence coming from Bar-Natan analogue of Lee's
deformation of Khovanov's complex (whew!) deformation of Khovanov's complex (whew!)
s: Rasmussen's s-invariant coming from lee s: Rasmussen's s-invariant coming from lee
output:
kh, gss, lsss, leess: .tex file
sq2: text in Sage format
s: text
options: options:
-r : compute reduced theory -r : compute reduced theory
-h : print this message -h : print this message
@ -128,7 +132,7 @@ options:
- a torus knot, e.g. T(2,3) - a torus knot, e.g. T(2,3)
- a Rolfsen table knot, e.g. 10_124 - a Rolfsen table knot, e.g. 10_124
- a Hoste-Thistlethwaite-Weeks knot, e.g. 11a12 or 12n214 - a Hoste-Thistlethwaite-Weeks knot, e.g. 11a12 or 12n214
- a Morwen Thistlethwaite link, e.g. L9a21 or L14n7631 - a Morwen Thistlethwaite link, e.g. L8n9 or L13n8862
- a planar diagram, e.g. - a planar diagram, e.g.
PD[X[1, 4, 2, 5], X[3, 6, 4, 1], X[5, 2, 6, 3]] or PD[X[1, 4, 2, 5], X[3, 6, 4, 1], X[5, 2, 6, 3]] or
PD[[1, 4, 2, 5], [3, 6, 4, 1], [5, 2, 6, 3]] PD[[1, 4, 2, 5], [3, 6, 4, 1], [5, 2, 6, 3]]
@ -137,6 +141,7 @@ options:
DT[dadbcda] or DT[dadbcda] or
DT[{6, -8}, {-10, 12, -14, 2, -4}] DT[{6, -8}, {-10, 12, -14, 2, -4}]
- a braid, e.g. BR[2, {-1, -1, -1}] - a braid, e.g. BR[2, {-1, -1, -1}]
- disjoint union (juxtaposition), e.g. T(2,3) U
4. UPCOMING CHANGES 4. UPCOMING CHANGES
@ -145,7 +150,7 @@ The following changes are currently planned:
* support for Z/p, p arbitrary prime and F(x) field of rational functions * support for Z/p, p arbitrary prime and F(x) field of rational functions
* Roberts' totally twisted Khovanov homology * Roberts' totally twisted Khovanov homology
* the E^3 page of the twisted spectral sequence Kh(L) => \widehat{HF}(\Sigma_L) * the E^3 page of the twisted spectral sequence Kh(L) => \widehat{HF}(\Sigma_L)
* spectral sequences of PIDs: ls over F[x], gss over Z * spectral sequences of PIDs: lsss over F[x], gss over Z
* maps induced by cobordisms * maps induced by cobordisms
5. FOR DEVELOPERS 5. FOR DEVELOPERS

12
kk.cpp
View File

@ -11,13 +11,17 @@ usage ()
printf ("<invariant> can be one of:\n"); printf ("<invariant> can be one of:\n");
printf (" kh: Khovanov homology\n"); printf (" kh: Khovanov homology\n");
printf (" gss: Szabo's geometric spectral sequence\n"); printf (" gss: Szabo's geometric spectral sequence\n");
printf (" ls: Batson-Seed link splitting spectral sequence\n"); printf (" lsss: Batson-Seed link splitting spectral sequence\n");
printf (" component weights are 0, 1, ..., m\n"); printf (" component weights are 0, 1, ..., m\n");
printf (" sq2: Lipshitz-Sarkar Steenrod square on Z/2 Kh\n"); printf (" sq2: Lipshitz-Sarkar Steenrod square on Z/2 Kh\n");
printf (" output suitable for Sage\n"); printf (" output suitable for Sage\n");
printf (" leess: spectral sequence coming from Bar-Natan analogue of Lee's\n"); printf (" leess: spectral sequence coming from Bar-Natan analogue of Lee's\n");
printf (" deformation of Khovanov's complex (whew!)\n"); printf (" deformation of Khovanov's complex (whew!)\n");
printf (" s: Rasmussen's s-invariant coming from lee\n"); printf (" s: Rasmussen's s-invariant coming from lee\n");
printf ("output:\n");
printf (" kh, gss, lsss, leess: .tex file\n");
printf (" sq2: text in Sage format\n");
printf (" s: text\n");
printf ("options:\n"); printf ("options:\n");
printf (" -r : compute reduced theory\n"); printf (" -r : compute reduced theory\n");
printf (" -h : print this message\n"); printf (" -h : print this message\n");
@ -33,7 +37,7 @@ usage ()
printf (" - a torus knot, e.g. T(2,3)\n"); printf (" - a torus knot, e.g. T(2,3)\n");
printf (" - a Rolfsen table knot, e.g. 10_124\n"); printf (" - a Rolfsen table knot, e.g. 10_124\n");
printf (" - a Hoste-Thistlethwaite-Weeks knot, e.g. 11a12 or 12n214\n"); printf (" - a Hoste-Thistlethwaite-Weeks knot, e.g. 11a12 or 12n214\n");
printf (" - a Morwen Thistlethwaite link, e.g. L9a21 or L14n7631\n"); printf (" - a Morwen Thistlethwaite link, e.g. L8n9 or L13n8862\n");
printf (" - a planar diagram, e.g.\n"); printf (" - a planar diagram, e.g.\n");
printf (" PD[X[1, 4, 2, 5], X[3, 6, 4, 1], X[5, 2, 6, 3]] or\n"); printf (" PD[X[1, 4, 2, 5], X[3, 6, 4, 1], X[5, 2, 6, 3]] or\n");
printf (" PD[[1, 4, 2, 5], [3, 6, 4, 1], [5, 2, 6, 3]]\n"); printf (" PD[[1, 4, 2, 5], [3, 6, 4, 1], [5, 2, 6, 3]]\n");
@ -42,6 +46,7 @@ usage ()
printf (" DT[dadbcda] or\n"); printf (" DT[dadbcda] or\n");
printf (" DT[{6, -8}, {-10, 12, -14, 2, -4}]\n"); printf (" DT[{6, -8}, {-10, 12, -14, 2, -4}]\n");
printf (" - a braid, e.g. BR[2, {-1, -1, -1}]\n"); printf (" - a braid, e.g. BR[2, {-1, -1, -1}]\n");
printf (" - disjoint union (juxtaposition), e.g. T(2,3) U\n");
} }
FILE *outfp = stdout; FILE *outfp = stdout;
@ -317,10 +322,11 @@ compute_invariant ()
sseq ss (b, pages); sseq ss (b, pages);
tex_header (); tex_header ();
fprintf (outfp, "$E_k = %s^{BS}_k(\\verb~%s~; \\verb~%s~)$:\\\\\n", fprintf (outfp, "$E_k = %s^{BS}_k({}^{%d}\\verb~%s~; \\verb~%s~)$:\\\\\n",
(reduced (reduced
? "\\widetilde{E}" ? "\\widetilde{E}"
: "E"), : "E"),
m,
knot, knot,
field); field);
ss.texshow (outfp, mapper); ss.texshow (outfp, mapper);

10
knot_diagram.h
View File

@ -1,4 +1,14 @@
// for building knot_diagram
inline unsigned edge_from_ept (unsigned e)
{
return e * 2 - 1;
}
inline unsigned edge_to_ept (unsigned e)
{
return e * 2;
}
static inline unsigned static inline unsigned
add_base1_mod4 (unsigned x, unsigned y) add_base1_mod4 (unsigned x, unsigned y)
{ {

302
knot_parser/knot_parser.cc
View File

@ -52,7 +52,7 @@
YY_DECL; YY_DECL;
/* Line 285 of lalr1.cc */ /* Line 285 of lalr1.cc */
#line 29 "knot_parser/knot_parser.yy" #line 30 "knot_parser/knot_parser.yy"
#define yylex knot_yylex #define yylex knot_yylex
@ -416,16 +416,35 @@ namespace yy {
YY_REDUCE_PRINT (yyn); YY_REDUCE_PRINT (yyn);
switch (yyn) switch (yyn)
{ {
case 10: case 2:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 67 "knot_parser/knot_parser.yy" #line 60 "knot_parser/knot_parser.yy"
{
parsed_knot = *(yysemantic_stack_[(1) - (1)].kd);
delete (yysemantic_stack_[(1) - (1)].kd);
}
break;
case 4:
/* Line 661 of lalr1.cc */
#line 69 "knot_parser/knot_parser.yy"
{
(yyval.kd) = new knot_diagram (DISJOINT_UNION, *(yysemantic_stack_[(2) - (1)].kd), *(yysemantic_stack_[(2) - (2)].kd));
delete (yysemantic_stack_[(2) - (1)].kd);
delete (yysemantic_stack_[(2) - (2)].kd);
}
break;
case 13:
/* Line 661 of lalr1.cc */
#line 89 "knot_parser/knot_parser.yy"
{ {
unsigned n = (yysemantic_stack_[(3) - (1)].integer), unsigned n = (yysemantic_stack_[(3) - (1)].integer),
k = (yysemantic_stack_[(3) - (3)].integer); k = (yysemantic_stack_[(3) - (3)].integer);
if (n >= 1 && n <= 10 if (n >= 1 && n <= 10
&& k >= 1 && k <= rolfsen_crossing_knots (n)) && k >= 1 && k <= rolfsen_crossing_knots (n))
parsed_knot = knot_diagram (rolfsen_knot (n, k)); (yyval.kd) = new knot_diagram (rolfsen_knot (n, k));
else else
{ {
fprintf (stderr, "knot_parser: no such Rolfsen knot `%d_%d'\n", fprintf (stderr, "knot_parser: no such Rolfsen knot `%d_%d'\n",
@ -435,9 +454,9 @@ namespace yy {
} }
break; break;
case 11: case 14:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 85 "knot_parser/knot_parser.yy" #line 107 "knot_parser/knot_parser.yy"
{ {
unsigned n = (yysemantic_stack_[(3) - (1)].integer), unsigned n = (yysemantic_stack_[(3) - (1)].integer),
k = (yysemantic_stack_[(3) - (3)].integer); k = (yysemantic_stack_[(3) - (3)].integer);
@ -445,7 +464,7 @@ namespace yy {
if (n >= 1 && n <= 16 if (n >= 1 && n <= 16
&& k >= 1 && k <= htw_knots (n, alt)) && k >= 1 && k <= htw_knots (n, alt))
parsed_knot = knot_diagram (htw_knot (n, alt, k)); (yyval.kd) = new knot_diagram (htw_knot (n, alt, k));
else else
{ {
fprintf (stderr, "knot_parser: no such HTW knot `%d%c%d'\n", fprintf (stderr, "knot_parser: no such HTW knot `%d%c%d'\n",
@ -455,9 +474,9 @@ namespace yy {
} }
break; break;
case 12: case 15:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 104 "knot_parser/knot_parser.yy" #line 126 "knot_parser/knot_parser.yy"
{ {
unsigned n = (yysemantic_stack_[(4) - (2)].integer), unsigned n = (yysemantic_stack_[(4) - (2)].integer),
k = (yysemantic_stack_[(4) - (4)].integer); k = (yysemantic_stack_[(4) - (4)].integer);
@ -465,7 +484,7 @@ namespace yy {
if (n >= 1 && n <= 14 if (n >= 1 && n <= 14
&& k >= 1 && k <= mt_links (n, alt)) && k >= 1 && k <= mt_links (n, alt))
parsed_knot = knot_diagram (mt_link (n, alt, k)); (yyval.kd) = new knot_diagram (mt_link (n, alt, k));
else else
{ {
fprintf (stderr, "knot_parser: no such MT link `%d%c%d'\n", fprintf (stderr, "knot_parser: no such MT link `%d%c%d'\n",
@ -475,66 +494,66 @@ namespace yy {
} }
break; break;
case 13:
/* Line 661 of lalr1.cc */
#line 123 "knot_parser/knot_parser.yy"
{ parsed_knot = knot_diagram (planar_diagram ("<parsed>", *(yysemantic_stack_[(4) - (3)].int_vec2))); }
break;
case 14:
/* Line 661 of lalr1.cc */
#line 125 "knot_parser/knot_parser.yy"
{ parsed_knot = knot_diagram (planar_diagram ("<parsed>", *(yysemantic_stack_[(4) - (3)].int_vec2))); }
break;
case 15:
/* Line 661 of lalr1.cc */
#line 130 "knot_parser/knot_parser.yy"
{
basedvector<basedvector<int, 1>, 1> even_labels (1);
even_labels[1] = *(yysemantic_stack_[(4) - (3)].int_vec);
parsed_knot = knot_diagram (dt_code ("<parsed>", even_labels));
}
break;
case 16: case 16:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 136 "knot_parser/knot_parser.yy" #line 145 "knot_parser/knot_parser.yy"
{ parsed_knot = knot_diagram (dt_code ("<parsed>", *(yysemantic_stack_[(4) - (3)].int_vec2))); } { (yyval.kd) = new knot_diagram (planar_diagram ("<parsed>", *(yysemantic_stack_[(4) - (3)].int_vec2))); }
break; break;
case 17: case 17:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 138 "knot_parser/knot_parser.yy" #line 147 "knot_parser/knot_parser.yy"
{ parsed_knot = knot_diagram (dt_code ("<parsed>", (yysemantic_stack_[(4) - (3)].string))); } { (yyval.kd) = new knot_diagram (planar_diagram ("<parsed>", *(yysemantic_stack_[(4) - (3)].int_vec2))); }
break; break;
case 18: case 18:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 143 "knot_parser/knot_parser.yy" #line 152 "knot_parser/knot_parser.yy"
{ parsed_knot = knot_diagram (torus_knot ((yysemantic_stack_[(6) - (3)].integer), (yysemantic_stack_[(6) - (5)].integer))); } {
basedvector<basedvector<int, 1>, 1> even_labels (1);
even_labels[1] = *(yysemantic_stack_[(4) - (3)].int_vec);
(yyval.kd) = new knot_diagram (dt_code ("<parsed>", even_labels));
}
break; break;
case 19: case 19:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 148 "knot_parser/knot_parser.yy" #line 158 "knot_parser/knot_parser.yy"
{ parsed_knot = knot_diagram (braid ((yysemantic_stack_[(6) - (3)].integer), *(yysemantic_stack_[(6) - (5)].int_vec))); } { (yyval.kd) = new knot_diagram (dt_code ("<parsed>", *(yysemantic_stack_[(4) - (3)].int_vec2))); }
break; break;
case 20: case 20:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 153 "knot_parser/knot_parser.yy" #line 160 "knot_parser/knot_parser.yy"
{ { (yyval.kd) = new knot_diagram (dt_code ("<parsed>", (yysemantic_stack_[(4) - (3)].string))); }
unsigned unknot_ar[1][4] = { break;
{ 2, 1, 3, 4, },
}; case 21:
parsed_knot = knot_diagram ("U", 1, unknot_ar); /* Line 661 of lalr1.cc */
} #line 165 "knot_parser/knot_parser.yy"
{ (yyval.kd) = new knot_diagram (torus_knot ((yysemantic_stack_[(6) - (3)].integer), (yysemantic_stack_[(6) - (5)].integer))); }
break;
case 22:
/* Line 661 of lalr1.cc */
#line 170 "knot_parser/knot_parser.yy"
{ (yyval.kd) = new knot_diagram (braid ((yysemantic_stack_[(6) - (3)].integer), *(yysemantic_stack_[(6) - (5)].int_vec))); }
break; break;
case 23: case 23:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 168 "knot_parser/knot_parser.yy" #line 175 "knot_parser/knot_parser.yy"
{
unsigned unknot_ar[1][4] = {
{ 2, 1, 3, 4, },
};
(yyval.kd) = new knot_diagram ("U", 1, unknot_ar);
}
break;
case 26:
/* Line 661 of lalr1.cc */
#line 190 "knot_parser/knot_parser.yy"
{ {
basedvector<basedvector<int, 1>, 1> *v basedvector<basedvector<int, 1>, 1> *v
= new basedvector<basedvector<int, 1>, 1> (); = new basedvector<basedvector<int, 1>, 1> ();
@ -543,9 +562,9 @@ namespace yy {
} }
break; break;
case 24: case 27:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 175 "knot_parser/knot_parser.yy" #line 197 "knot_parser/knot_parser.yy"
{ {
basedvector<basedvector<int, 1>, 1> *v = (yysemantic_stack_[(3) - (1)].int_vec2); basedvector<basedvector<int, 1>, 1> *v = (yysemantic_stack_[(3) - (1)].int_vec2);
v->append (*(yysemantic_stack_[(3) - (3)].int_vec)); v->append (*(yysemantic_stack_[(3) - (3)].int_vec));
@ -553,21 +572,21 @@ namespace yy {
} }
break; break;
case 25: case 28:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 184 "knot_parser/knot_parser.yy" #line 206 "knot_parser/knot_parser.yy"
{ (yyval.int_vec) = (yysemantic_stack_[(3) - (2)].int_vec); } { (yyval.int_vec) = (yysemantic_stack_[(3) - (2)].int_vec); }
break; break;
case 26: case 29:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 186 "knot_parser/knot_parser.yy" #line 208 "knot_parser/knot_parser.yy"
{ (yyval.int_vec) = (yysemantic_stack_[(3) - (2)].int_vec); } { (yyval.int_vec) = (yysemantic_stack_[(3) - (2)].int_vec); }
break; break;
case 27: case 30:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 191 "knot_parser/knot_parser.yy" #line 213 "knot_parser/knot_parser.yy"
{ {
basedvector<int, 1> *v = basedvector<int, 1> *v =
new basedvector<int, 1> (); new basedvector<int, 1> ();
@ -576,9 +595,9 @@ namespace yy {
} }
break; break;
case 28: case 31:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 198 "knot_parser/knot_parser.yy" #line 220 "knot_parser/knot_parser.yy"
{ {
basedvector<int, 1> *v = (yysemantic_stack_[(3) - (1)].int_vec); basedvector<int, 1> *v = (yysemantic_stack_[(3) - (1)].int_vec);
v->append ((yysemantic_stack_[(3) - (3)].integer)); v->append ((yysemantic_stack_[(3) - (3)].integer));
@ -586,9 +605,9 @@ namespace yy {
} }
break; break;
case 29: case 32:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 207 "knot_parser/knot_parser.yy" #line 229 "knot_parser/knot_parser.yy"
{ {
basedvector<basedvector<int, 1>, 1> *v basedvector<basedvector<int, 1>, 1> *v
= new basedvector<basedvector<int, 1>, 1> (); = new basedvector<basedvector<int, 1>, 1> ();
@ -597,9 +616,9 @@ namespace yy {
} }
break; break;
case 30: case 33:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 214 "knot_parser/knot_parser.yy" #line 236 "knot_parser/knot_parser.yy"
{ {
basedvector<basedvector<int, 1>, 1> *v = (yysemantic_stack_[(3) - (1)].int_vec2); basedvector<basedvector<int, 1>, 1> *v = (yysemantic_stack_[(3) - (1)].int_vec2);
v->append (*(yysemantic_stack_[(3) - (3)].int_vec)); v->append (*(yysemantic_stack_[(3) - (3)].int_vec));
@ -607,9 +626,9 @@ namespace yy {
} }
break; break;
case 31: case 34:
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 223 "knot_parser/knot_parser.yy" #line 245 "knot_parser/knot_parser.yy"
{ {
basedvector<int, 1> *v basedvector<int, 1> *v
= new basedvector<int, 1> (); = new basedvector<int, 1> ();
@ -623,7 +642,7 @@ namespace yy {
/* Line 661 of lalr1.cc */ /* Line 661 of lalr1.cc */
#line 627 "knot_parser/knot_parser.cc" #line 646 "knot_parser/knot_parser.cc"
default: default:
break; break;
} }
@ -809,18 +828,18 @@ namespace yy {
/* YYPACT[STATE-NUM] -- Index in YYTABLE of the portion describing /* YYPACT[STATE-NUM] -- Index in YYTABLE of the portion describing
STATE-NUM. */ STATE-NUM. */
const signed char knot_parser::yypact_ninf_ = -36; const signed char knot_parser::yypact_ninf_ = -39;
const signed char const signed char
knot_parser::yypact_[] = knot_parser::yypact_[] =
{ {
-1, 10, -9, 25, 26, 37, 9, -36, 43, -36, -1, 10, -9, 25, 26, 37, 9, -39, 43, -1,
-36, -36, -36, -36, -36, -36, -36, -36, -36, 41, -39, -39, -39, -39, -39, -39, -39, -39, -39, -39,
42, -7, -3, 44, 24, 45, -36, -36, -36, 30, -39, 41, 42, -7, -3, 44, 24, 45, -39, -1,
46, 46, 7, -36, 11, -36, -36, 33, 12, 15, -39, -39, 30, 46, 46, 7, -39, 11, -39, -39,
-4, 48, 34, 49, 16, -2, -36, 0, -36, 47, 33, 12, 15, -4, 48, 34, 49, 16, -2, -39,
-36, -36, -36, 51, 0, -36, 53, 38, -36, -36, 0, -39, 47, -39, -39, -39, 51, 0, -39, 53,
-36, -36, -36, 50, 39, 55, -36, -36, 52, 57, 38, -39, -39, -39, -39, -39, 50, 39, 55, -39,
54, 58, 59, -36 -39, 52, 57, 54, 58, 59, -39
}; };
/* YYDEFACT[S] -- default reduction number in state S. Performed when /* YYDEFACT[S] -- default reduction number in state S. Performed when
@ -829,30 +848,30 @@ namespace yy {
const unsigned char const unsigned char
knot_parser::yydefact_[] = knot_parser::yydefact_[] =
{ {
0, 0, 0, 0, 0, 0, 0, 20, 0, 2, 0, 0, 0, 0, 0, 0, 0, 23, 0, 2,
3, 4, 5, 6, 7, 9, 8, 21, 22, 0, 3, 5, 6, 7, 8, 9, 10, 12, 11, 24,
0, 0, 0, 0, 0, 0, 1, 10, 11, 0, 25, 0, 0, 0, 0, 0, 0, 0, 1, 4,
0, 0, 0, 23, 0, 29, 27, 0, 0, 0, 13, 14, 0, 0, 0, 0, 26, 0, 32, 30,
0, 0, 0, 0, 0, 0, 13, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16,
17, 16, 15, 0, 0, 12, 0, 0, 26, 25, 0, 17, 0, 20, 19, 18, 0, 0, 15, 0,
24, 30, 28, 0, 0, 0, 19, 18, 0, 0, 0, 29, 28, 27, 33, 31, 0, 0, 0, 22,
0, 0, 0, 31 21, 0, 0, 0, 0, 0, 34
}; };
/* YYPGOTO[NTERM-NUM]. */ /* YYPGOTO[NTERM-NUM]. */
const signed char const signed char
knot_parser::yypgoto_[] = knot_parser::yypgoto_[] =
{ {
-36, -36, -36, -36, -36, -36, -36, -36, -36, -36, -39, -39, 62, -39, -39, -39, -39, -39, -39, -39,
40, 56, -35, 8, -36, 13 -39, -39, 40, 56, -38, 5, -39, 13
}; };
/* YYDEFGOTO[NTERM-NUM]. */ /* YYDEFGOTO[NTERM-NUM]. */
const signed char const signed char
knot_parser::yydefgoto_[] = knot_parser::yydefgoto_[] =
{ {
-1, 8, 9, 10, 11, 12, 13, 14, 15, 16, -1, 8, 29, 10, 11, 12, 13, 14, 15, 16,
20, 32, 33, 39, 34, 35 17, 18, 22, 35, 36, 42, 37, 38
}; };
/* YYTABLE[YYPACT[STATE-NUM]]. What to do in state STATE-NUM. If /* YYTABLE[YYPACT[STATE-NUM]]. What to do in state STATE-NUM. If
@ -862,14 +881,15 @@ namespace yy {
const unsigned char const unsigned char
knot_parser::yytable_[] = knot_parser::yytable_[] =
{ {
36, 29, 1, 2, 3, 4, 5, 21, 6, 30, 39, 32, 1, 2, 3, 4, 5, 23, 6, 33,
7, 37, 60, 30, 31, 54, 30, 53, 31, 63, 7, 40, 63, 33, 34, 57, 33, 56, 34, 66,
59, 31, 17, 18, 46, 19, 47, 25, 48, 51, 62, 34, 19, 20, 49, 21, 50, 27, 51, 54,
49, 47, 52, 58, 53, 53, 17, 18, 44, 45, 52, 50, 55, 61, 56, 56, 19, 20, 47, 48,
24, 22, 23, 26, 27, 28, 43, 40, 42, 36, 26, 24, 25, 28, 30, 31, 46, 43, 45, 39,
50, 55, 57, 56, 62, 29, 64, 65, 68, 67, 53, 58, 60, 59, 65, 32, 67, 68, 71, 70,
70, 72, 61, 0, 41, 0, 0, 66, 0, 0, 73, 75, 9, 0, 0, 64, 44, 69, 0, 0,
0, 69, 0, 71, 0, 0, 73, 0, 38 0, 72, 0, 74, 0, 0, 76, 0, 0, 0,
41
}; };
/* YYCHECK. */ /* YYCHECK. */
@ -877,13 +897,14 @@ namespace yy {
knot_parser::yycheck_[] = knot_parser::yycheck_[] =
{ {
3, 8, 3, 4, 5, 6, 7, 16, 9, 16, 3, 8, 3, 4, 5, 6, 7, 16, 9, 16,
11, 14, 47, 16, 21, 19, 16, 19, 21, 54, 11, 14, 50, 16, 21, 19, 16, 19, 21, 57,
22, 21, 12, 13, 17, 15, 19, 18, 17, 17, 22, 21, 12, 13, 17, 15, 19, 18, 17, 17,
19, 19, 17, 17, 19, 19, 12, 13, 30, 31, 19, 19, 17, 17, 19, 19, 12, 13, 33, 34,
3, 16, 16, 0, 3, 3, 16, 3, 3, 3, 3, 16, 16, 0, 3, 3, 16, 3, 3, 3,
17, 3, 3, 19, 3, 8, 3, 19, 3, 20, 17, 3, 3, 19, 3, 8, 3, 19, 3, 20,
3, 3, 49, -1, 24, -1, -1, 17, -1, -1, 3, 3, 0, -1, -1, 52, 26, 17, -1, -1,
-1, 19, -1, 19, -1, -1, 17, -1, 22 -1, 19, -1, 19, -1, -1, 17, -1, -1, -1,
24
}; };
/* STOS_[STATE-NUM] -- The (internal number of the) accessing /* STOS_[STATE-NUM] -- The (internal number of the) accessing
@ -892,13 +913,13 @@ namespace yy {
knot_parser::yystos_[] = knot_parser::yystos_[] =
{ {
0, 3, 4, 5, 6, 7, 9, 11, 24, 25, 0, 3, 4, 5, 6, 7, 9, 11, 24, 25,
26, 27, 28, 29, 30, 31, 32, 12, 13, 15, 26, 27, 28, 29, 30, 31, 32, 33, 34, 12,
33, 16, 16, 16, 3, 18, 0, 3, 3, 8, 13, 15, 35, 16, 16, 16, 3, 18, 0, 25,
16, 21, 34, 35, 37, 38, 3, 14, 34, 36, 3, 3, 8, 16, 21, 36, 37, 39, 40, 3,
3, 33, 3, 16, 36, 36, 17, 19, 17, 19, 14, 36, 38, 3, 35, 3, 16, 38, 38, 17,
17, 17, 17, 19, 19, 3, 19, 3, 17, 22, 19, 17, 19, 17, 17, 17, 19, 19, 3, 19,
35, 38, 3, 35, 3, 19, 17, 20, 3, 19, 3, 17, 22, 37, 40, 3, 37, 3, 19, 17,
3, 19, 3, 17 20, 3, 19, 3, 19, 3, 17
}; };
#if YYDEBUG #if YYDEBUG
@ -917,20 +938,20 @@ namespace yy {
const unsigned char const unsigned char
knot_parser::yyr1_[] = knot_parser::yyr1_[] =
{ {
0, 23, 24, 24, 24, 24, 24, 24, 24, 24, 0, 23, 24, 25, 25, 26, 26, 26, 26, 26,
25, 26, 27, 28, 28, 29, 29, 29, 30, 31, 26, 26, 26, 27, 28, 29, 30, 30, 31, 31,
32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 31, 32, 33, 34, 35, 35, 36, 36, 37, 37,
37, 38 38, 38, 39, 39, 40
}; };
/* YYR2[YYN] -- Number of symbols composing right hand side of rule YYN. */ /* YYR2[YYN] -- Number of symbols composing right hand side of rule YYN. */
const unsigned char const unsigned char
knot_parser::yyr2_[] = knot_parser::yyr2_[] =
{ {
0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 1, 1, 1,
3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 1, 1, 1, 3, 3, 4, 4, 4, 4, 4,
1, 1, 1, 1, 3, 3, 3, 1, 3, 1, 4, 6, 6, 1, 1, 1, 1, 3, 3, 3,
3, 10 1, 3, 1, 3, 10
}; };
#if YYDEBUG #if YYDEBUG
@ -941,8 +962,8 @@ namespace yy {
{ {
"\"end of file\"", "error", "$undefined", "INT", "PD", "DT", "BR", "\"end of file\"", "error", "$undefined", "INT", "PD", "DT", "BR",
"LINK", "X", "T", "U", "UNKNOT", "ALT", "NONALT", "STRING", "'_'", "'['", "LINK", "X", "T", "U", "UNKNOT", "ALT", "NONALT", "STRING", "'_'", "'['",
"']'", "'('", "','", "')'", "'{'", "'}'", "$accept", "knot", "']'", "'('", "','", "')'", "'{'", "'}'", "$accept", "entry", "knot",
"rolfsen_knot", "htw_knot", "mt_link", "planar_diagram", "dt", "knot_1", "rolfsen_knot", "htw_knot", "mt_link", "planar_diagram", "dt",
"torus_link", "braid", "unknot", "alt_spec", "int_vec2", "int_vec", "torus_link", "braid", "unknot", "alt_spec", "int_vec2", "int_vec",
"int_vec_1", "crossing_vec", "crossing", YY_NULL "int_vec_1", "crossing_vec", "crossing", YY_NULL
}; };
@ -952,18 +973,19 @@ namespace yy {
const knot_parser::rhs_number_type const knot_parser::rhs_number_type
knot_parser::yyrhs_[] = knot_parser::yyrhs_[] =
{ {
24, 0, -1, 25, -1, 26, -1, 27, -1, 28, 24, 0, -1, 25, -1, 26, -1, 25, 25, -1,
-1, 29, -1, 30, -1, 32, -1, 31, -1, 3, 27, -1, 28, -1, 29, -1, 30, -1, 31, -1,
15, 3, -1, 3, 33, 3, -1, 7, 3, 33, 32, -1, 34, -1, 33, -1, 3, 15, 3, -1,
3, -1, 4, 16, 34, 17, -1, 4, 16, 37, 3, 35, 3, -1, 7, 3, 35, 3, -1, 4,
17, -1, 5, 16, 36, 17, -1, 5, 16, 34, 16, 36, 17, -1, 4, 16, 39, 17, -1, 5,
17, -1, 5, 16, 14, 17, -1, 9, 18, 3, 16, 38, 17, -1, 5, 16, 36, 17, -1, 5,
19, 3, 20, -1, 6, 16, 3, 19, 35, 17, 16, 14, 17, -1, 9, 18, 3, 19, 3, 20,
-1, 11, -1, 12, -1, 13, -1, 35, -1, 34, -1, 6, 16, 3, 19, 37, 17, -1, 11, -1,
19, 35, -1, 21, 36, 22, -1, 16, 36, 17, 12, -1, 13, -1, 37, -1, 36, 19, 37, -1,
-1, 3, -1, 36, 19, 3, -1, 38, -1, 37, 21, 38, 22, -1, 16, 38, 17, -1, 3, -1,
19, 38, -1, 8, 16, 3, 19, 3, 19, 3, 38, 19, 3, -1, 40, -1, 39, 19, 40, -1,
19, 3, 17, -1 8, 16, 3, 19, 3, 19, 3, 19, 3, 17,
-1
}; };
/* YYPRHS[YYN] -- Index of the first RHS symbol of rule number YYN in /* YYPRHS[YYN] -- Index of the first RHS symbol of rule number YYN in
@ -971,20 +993,20 @@ namespace yy {
const unsigned char const unsigned char
knot_parser::yyprhs_[] = knot_parser::yyprhs_[] =
{ {
0, 0, 3, 5, 7, 9, 11, 13, 15, 17, 0, 0, 3, 5, 7, 10, 12, 14, 16, 18,
19, 23, 27, 32, 37, 42, 47, 52, 57, 64, 20, 22, 24, 26, 30, 34, 39, 44, 49, 54,
71, 73, 75, 77, 79, 83, 87, 91, 93, 97, 59, 64, 71, 78, 80, 82, 84, 86, 90, 94,
99, 103 98, 100, 104, 106, 110
}; };
/* YYRLINE[YYN] -- Source line where rule number YYN was defined. */ /* YYRLINE[YYN] -- Source line where rule number YYN was defined. */
const unsigned char const unsigned char
knot_parser::yyrline_[] = knot_parser::yyrline_[] =
{ {
0, 55, 55, 56, 57, 58, 59, 60, 61, 62, 0, 59, 59, 67, 68, 77, 78, 79, 80, 81,
66, 84, 103, 122, 124, 129, 135, 137, 142, 147, 82, 83, 84, 88, 106, 125, 144, 146, 151, 157,
152, 162, 163, 167, 174, 183, 185, 190, 197, 206, 159, 164, 169, 174, 184, 185, 189, 196, 205, 207,
213, 222 212, 219, 228, 235, 244
}; };
// Print the state stack on the debug stream. // Print the state stack on the debug stream.
@ -1059,10 +1081,10 @@ namespace yy {
} }
const int knot_parser::yyeof_ = 0; const int knot_parser::yyeof_ = 0;
const int knot_parser::yylast_ = 78; const int knot_parser::yylast_ = 80;
const int knot_parser::yynnts_ = 16; const int knot_parser::yynnts_ = 18;
const int knot_parser::yyempty_ = -2; const int knot_parser::yyempty_ = -2;
const int knot_parser::yyfinal_ = 26; const int knot_parser::yyfinal_ = 28;
const int knot_parser::yyterror_ = 1; const int knot_parser::yyterror_ = 1;
const int knot_parser::yyerrcode_ = 256; const int knot_parser::yyerrcode_ = 256;
const int knot_parser::yyntokens_ = 23; const int knot_parser::yyntokens_ = 23;
@ -1073,9 +1095,9 @@ namespace yy {
} // yy } // yy
/* Line 1106 of lalr1.cc */ /* Line 1106 of lalr1.cc */
#line 1077 "knot_parser/knot_parser.cc" #line 1099 "knot_parser/knot_parser.cc"
/* Line 1107 of lalr1.cc */ /* Line 1107 of lalr1.cc */
#line 233 "knot_parser/knot_parser.yy" #line 255 "knot_parser/knot_parser.yy"
void void

5
knot_parser/knot_parser.hh
View File

@ -82,10 +82,11 @@ namespace yy {
basedvector<int, 1> *int_vec; basedvector<int, 1> *int_vec;
basedvector<basedvector<int, 1>, 1> *int_vec2; basedvector<basedvector<int, 1>, 1> *int_vec2;
const char *string; const char *string;
knot_diagram *kd;
/* Line 36 of lalr1.cc */ /* Line 36 of lalr1.cc */
#line 89 "knot_parser/knot_parser.hh" #line 90 "knot_parser/knot_parser.hh"
}; };
#else #else
typedef YYSTYPE semantic_type; typedef YYSTYPE semantic_type;
@ -283,7 +284,7 @@ namespace yy {
} // yy } // yy
/* Line 36 of lalr1.cc */ /* Line 36 of lalr1.cc */
#line 287 "knot_parser/knot_parser.hh" #line 288 "knot_parser/knot_parser.hh"

46
knot_parser/knot_parser.yy
View File

@ -24,6 +24,7 @@ YY_DECL;
basedvector<int, 1> *int_vec; basedvector<int, 1> *int_vec;
basedvector<basedvector<int, 1>, 1> *int_vec2; basedvector<basedvector<int, 1>, 1> *int_vec2;
const char *string; const char *string;
knot_diagram *kd;
} }
%code { %code {
@ -36,9 +37,12 @@ YY_DECL;
%token PD DT BR LINK X T %token PD DT BR LINK X T
%token U UNKNOT %token U UNKNOT
%token <alternating> ALT NONALT %token <alternating> ALT NONALT
%token <string> STRING %token <string> STRING
%type <kd> knot knot_1
%type <kd> rolfsen_knot htw_knot mt_link planar_diagram dt torus_link unknot braid
%type <alternating> alt_spec %type <alternating> alt_spec
%type <int_vec> int_vec int_vec_1 %type <int_vec> int_vec int_vec_1
@ -49,9 +53,27 @@ YY_DECL;
%% %%
%start knot; %start entry;
entry:
knot
{
parsed_knot = *$1;
delete $1;
}
;
knot: knot:
knot_1
| knot knot
{
$$ = new knot_diagram (DISJOINT_UNION, *$1, *$2);
delete $1;
delete $2;
}
;
knot_1:
rolfsen_knot rolfsen_knot
| htw_knot | htw_knot
| mt_link | mt_link
@ -70,7 +92,7 @@ rolfsen_knot:
if (n >= 1 && n <= 10 if (n >= 1 && n <= 10
&& k >= 1 && k <= rolfsen_crossing_knots (n)) && k >= 1 && k <= rolfsen_crossing_knots (n))
parsed_knot = knot_diagram (rolfsen_knot (n, k)); $$ = new knot_diagram (rolfsen_knot (n, k));
else else
{ {
fprintf (stderr, "knot_parser: no such Rolfsen knot `%d_%d'\n", fprintf (stderr, "knot_parser: no such Rolfsen knot `%d_%d'\n",
@ -89,7 +111,7 @@ htw_knot:
if (n >= 1 && n <= 16 if (n >= 1 && n <= 16
&& k >= 1 && k <= htw_knots (n, alt)) && k >= 1 && k <= htw_knots (n, alt))
parsed_knot = knot_diagram (htw_knot (n, alt, k)); $$ = new knot_diagram (htw_knot (n, alt, k));
else else
{ {
fprintf (stderr, "knot_parser: no such HTW knot `%d%c%d'\n", fprintf (stderr, "knot_parser: no such HTW knot `%d%c%d'\n",
@ -108,7 +130,7 @@ mt_link:
if (n >= 1 && n <= 14 if (n >= 1 && n <= 14
&& k >= 1 && k <= mt_links (n, alt)) && k >= 1 && k <= mt_links (n, alt))
parsed_knot = knot_diagram (mt_link (n, alt, k)); $$ = new knot_diagram (mt_link (n, alt, k));
else else
{ {
fprintf (stderr, "knot_parser: no such MT link `%d%c%d'\n", fprintf (stderr, "knot_parser: no such MT link `%d%c%d'\n",
@ -120,9 +142,9 @@ mt_link:
planar_diagram: planar_diagram:
PD '[' int_vec2 ']' PD '[' int_vec2 ']'
{ parsed_knot = knot_diagram (planar_diagram ("<parsed>", *$3)); } { $$ = new knot_diagram (planar_diagram ("<parsed>", *$3)); }
| PD '[' crossing_vec ']' | PD '[' crossing_vec ']'
{ parsed_knot = knot_diagram (planar_diagram ("<parsed>", *$3)); } { $$ = new knot_diagram (planar_diagram ("<parsed>", *$3)); }
; ;
dt: dt:
@ -130,22 +152,22 @@ dt:
{ {
basedvector<basedvector<int, 1>, 1> even_labels (1); basedvector<basedvector<int, 1>, 1> even_labels (1);
even_labels[1] = *$3; even_labels[1] = *$3;
parsed_knot = knot_diagram (dt_code ("<parsed>", even_labels)); $$ = new knot_diagram (dt_code ("<parsed>", even_labels));
} }
| DT '[' int_vec2 ']' | DT '[' int_vec2 ']'
{ parsed_knot = knot_diagram (dt_code ("<parsed>", *$3)); } { $$ = new knot_diagram (dt_code ("<parsed>", *$3)); }
| DT '[' STRING ']' | DT '[' STRING ']'
{ parsed_knot = knot_diagram (dt_code ("<parsed>", $3)); } { $$ = new knot_diagram (dt_code ("<parsed>", $3)); }
; ;
torus_link: torus_link:
T '(' INT ',' INT ')' T '(' INT ',' INT ')'
{ parsed_knot = knot_diagram (torus_knot ($3, $5)); } { $$ = new knot_diagram (torus_knot ($3, $5)); }
; ;
braid: braid:
BR '[' INT ',' int_vec ']' BR '[' INT ',' int_vec ']'
{ parsed_knot = knot_diagram (braid ($3, *$5)); } { $$ = new knot_diagram (braid ($3, *$5)); }
; ;
unknot: unknot:
@ -154,7 +176,7 @@ unknot:
unsigned unknot_ar[1][4] = { unsigned unknot_ar[1][4] = {
{ 2, 1, 3, 4, }, { 2, 1, 3, 4, },
}; };
parsed_knot = knot_diagram ("U", 1, unknot_ar); $$ = new knot_diagram ("U", 1, unknot_ar);
} }
; ;

62
knot_tables.cpp
View File

@ -612,7 +612,7 @@ torus_knot (unsigned n_strands, unsigned n_shifts)
return planar_diagram (std::string (buf), crossings); return planar_diagram (std::string (buf), crossings);
} }
planar_diagram knot_diagram
braid (unsigned n_strands, unsigned n_twists, int twists_ar[]) braid (unsigned n_strands, unsigned n_twists, int twists_ar[])
{ {
basedvector<int, 1> twists (n_twists); basedvector<int, 1> twists (n_twists);
@ -621,10 +621,9 @@ braid (unsigned n_strands, unsigned n_twists, int twists_ar[])
return braid (n_strands, twists); return braid (n_strands, twists);
} }
planar_diagram knot_diagram
braid (unsigned n_strands, const basedvector<int, 1> &twists) braid (unsigned n_strands, const basedvector<int, 1> &twists)
{ {
unsigned n_crossings = twists.size ();
unsigned e = 0; unsigned e = 0;
basedvector<unsigned, 1> final_strands (n_strands); basedvector<unsigned, 1> final_strands (n_strands);
@ -644,14 +643,36 @@ braid (unsigned n_strands, const basedvector<int, 1> &twists)
last_twist[t] = i; last_twist[t] = i;
last_twist[t + 1] = i; last_twist[t + 1] = i;
} }
#ifndef NDEBUG
for (unsigned i = 1; i <= n_strands; i ++)
assert (last_twist[i] != 0);
#endif
basedvector<basedvector<int, 1>, 1> crossings (n_crossings); unsigned n_crossings = twists.size ();
for (unsigned i = 1; i <= n_strands; i ++)
{
if (last_twist[i] == 0)
n_crossings ++;
}
basedvector<basedvector<unsigned, 1>, 1> crossings (n_crossings);
for (unsigned i = 1; i <= n_crossings; i ++) for (unsigned i = 1; i <= n_crossings; i ++)
crossings[i] = basedvector<int, 1> (4); crossings[i] = basedvector<unsigned, 1> (4);
unsigned c = twists.size ();
for (unsigned i = 1; i <= n_strands; i ++)
{
if (last_twist[i] == 0)
{
++ c;
unsigned e1 = strands[i];
unsigned e2 = ++ e;
strands[i] = final_strands[i] = 0;
crossings[c][1] = edge_from_ept (e1);
crossings[c][2] = edge_to_ept (e2);
crossings[c][3] = edge_from_ept (e2);
crossings[c][4] = edge_to_ept (e1);
}
}
assert (c == n_crossings);
for (unsigned i = 1; i <= twists.size (); i ++) for (unsigned i = 1; i <= twists.size (); i ++)
{ {
@ -686,27 +707,30 @@ braid (unsigned n_strands, const basedvector<int, 1> &twists)
if (twists[i] > 0) if (twists[i] > 0)
{ {
crossings[i][1] = e1; crossings[i][1] = edge_to_ept (e1);
crossings[i][2] = e2; crossings[i][2] = edge_from_ept (e2);
crossings[i][3] = e3; crossings[i][3] = edge_from_ept (e3);
crossings[i][4] = e4; crossings[i][4] = edge_to_ept (e4);
} }
else else
{ {
crossings[i][1] = e2; crossings[i][1] = edge_from_ept (e2);
crossings[i][2] = e3; crossings[i][2] = edge_from_ept (e3);
crossings[i][3] = e4; crossings[i][3] = edge_to_ept (e4);
crossings[i][4] = e1; crossings[i][4] = edge_to_ept (e1);
} }
} }
assert (e == n_crossings * 2); assert (e == n_crossings * 2);
#ifndef NDEBUG #ifndef NDEBUG
for (unsigned i = 1; i <= n_strands; i ++) for (unsigned i = 1; i <= n_strands; i ++)
assert (final_strands[i] == 0); {
assert (strands[i] == 0);
assert (final_strands[i] == 0);
}
#endif #endif
return planar_diagram ("abraid", crossings); return knot_diagram ("abraid", crossings);
} }
basedvector<basedvector<unsigned, 1>, 1> basedvector<basedvector<unsigned, 1>, 1>

4
knotkit.h
View File

@ -115,8 +115,8 @@ dt_code mt_link (unsigned n, unsigned k);
planar_diagram torus_knot (unsigned n_strands, unsigned n_shifts); planar_diagram torus_knot (unsigned n_strands, unsigned n_shifts);
planar_diagram braid (unsigned n_strands, const basedvector<int, 1> &twists); knot_diagram braid (unsigned n_strands, const basedvector<int, 1> &twists);
planar_diagram braid (unsigned n_strands, unsigned n_twists, int twists_ar[]); knot_diagram braid (unsigned n_strands, unsigned n_twists, int twists_ar[]);
knot_diagram parse_knot (const char *s); knot_diagram parse_knot (const char *s);
resolution_diagram parse_resolution_diagram (const char *s); resolution_diagram parse_resolution_diagram (const char *s);