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Fl(\)\()p Fj(\034)909 1213 y Fe(\000)p Fd(1)964 1231 y Ff(\012)g Fl(1)1034 1238 y Fg(N)1068 1231 y Fl(\)\(1)1130 1238 y Fg(A)1166 1231 y Ff(\012)g Fj(\026)1241 1238 y Fg(M)1288 1231 y Ff(\012)g Fl(1)1358 1238 y Fg(N)1392 1231 y Fl(\)\()p Ff(r)1472 1238 y Fg(A)1508 1231 y Ff(\012)g Fl(1)1578 1238 y Fg(M)1625 1231 y Ff(\012)g Fl(1)1695 1238 y Fg(N)1729 1231 y Fl(\))14 b(=)0 1289 y Fj(\034)27 1271 y Fe(\000)p Fd(1)74 1289 y Fl(\()p Fj(\026)122 1296 y Fg(N)163 1289 y Ff(\012)7 b Fj(\026)238 1296 y Fg(M)278 1289 y Fl(\)\(1)340 1296 y Fg(A)376 1289 y Ff(\012)g Fj(\034)13 b Ff(\012)7 b Fl(1)526 1296 y Fg(M)566 1289 y Fl(\)\()p Ff(r)646 1296 y Fg(A)681 1289 y Ff(\012)g Fj(\034)f Fl(\).)20 b(Cut)15 b(eac)o(h)e(side)h(of)h(the)f(graphical)h (equation)f(up)g(in)o(to)0 1347 y(single)i(lines)f(e.g.)p 800 1442 V 832 1425 a Fj(A)30 b(M)7 b(N)p 800 1442 V 824 1455 a Fi(\013)p 824 1491 2 13 v(\010)p 874 1491 V 849 1454 V 924 1491 2 50 v 974 1591 2 150 v 800 1492 200 2 v 825 1492 2 2 v 825 1492 V 825 1493 V 825 1494 V 825 1494 V 825 1495 V 826 1495 V 826 1496 V 826 1496 V 826 1497 V 826 1497 V 826 1498 V 826 1498 V 826 1499 V 827 1499 V 827 1500 V 827 1500 V 827 1501 V 828 1501 V 828 1502 V 828 1502 V 828 1503 V 829 1503 V 829 1503 V 829 1504 V 830 1504 V 830 1505 V 830 1505 V 831 1506 V 831 1506 V 832 1506 V 832 1507 V 832 1507 V 833 1508 V 833 1508 V 834 1508 V 834 1509 V 835 1509 V 835 1510 V 836 1510 V 836 1510 V 837 1511 V 837 1511 V 838 1511 V 839 1512 V 839 1512 V 840 1513 V 841 1513 V 841 1513 V 842 1514 V 843 1514 V 843 1514 V 844 1514 V 845 1515 V 845 1515 V 846 1515 V 847 1516 V 848 1516 V 849 1516 V 849 1517 V 850 1517 V 850 1517 V 851 1517 V 852 1517 V 853 1518 V 853 1518 V 854 1518 V 855 1519 V 856 1519 V 856 1519 V 857 1520 V 858 1520 V 858 1520 V 859 1520 V 860 1521 V 860 1521 V 861 1522 V 862 1522 V 862 1522 V 863 1523 V 863 1523 V 864 1523 V 865 1524 V 865 1524 V 866 1524 V 866 1525 V 867 1525 V 867 1526 V 868 1526 V 868 1526 V 868 1527 V 869 1527 V 869 1528 V 870 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933 1893 V 933 1843 V 931 1892 4 50 v 956 1856 a Fi(\013)p 956 1892 2 13 v(\010)p 1006 1892 V 982 1854 V 1031 1892 4 50 v 1057 1892 2 50 v 1081 1892 4 50 v 1106 1892 2 50 v 1130 1892 4 50 v 933 1893 200 2 v 933 1843 V 0 1988 a Fl(represen)o(ting)e Ff(r)315 1995 y Fg(A)349 1988 y Ff(\012)6 b Fl(1)418 1995 y Fg(M)463 1988 y Ff(\012)g Fl(1)532 1995 y Fg(N)579 1988 y Fl(and)15 b(enco)q(de)e(these)h(maps)f (with)g(the)h(sym)o(b)q(ols)e(describ)q(ed)i(b)q(elo)o(w.)50 2046 y(All)19 b(commands)g(for)i(a)g(graphical)g(diagram)f(start)i (with)e Ff(n)p Fl(g)h Fj(:)8 b(:)g(:)16 b Fl(.)35 b(A)20 b(graphical)h(equation)0 2105 y(is)i(written)f(\(and)i(cen)o(tered\))d (with)i(the)g(mathematical)d(sym)o(b)q(ols)i($$)i Fj(:)8 b(:)g(:)30 b Fl($$.)42 b(Eac)o(h)24 b(single)0 2163 y(graphical)e (diagram)f(\(side)g(of)i(an)f(equation\))g(is)f(op)q(ened)h(b)o(y)g Ff(n)p Fl(gb)q(eg)g(and)h(closed)e(b)o(y)g Ff(n)p Fl(gend.)0 2221 y(Eac)o(h)16 b(graphical)f(sym)o(b)q(ol)g(in)g(a)h(graphical)g (diagram)f(is)h(con)o(tained)f(in)g(an)i(in)o(visible)c(b)q(o)o(x)j(of) g(size)0 2279 y(x-dim)j(b)o(y)h(y-dim.)33 b(It)21 b(can)g(ha)o(v)o(e)f (sev)o(eral)f(top)i(and)h(b)q(ottom)e(connectors.)35 b(T)l(o)22 b(in)o(terconnect)0 2337 y(the)d(connectors)g(of)h(one)f (sym)o(b)q(ol)f(with)h(the)g(connectors)g(of)h(another)f(sym)o(b)q(ol)f (the)h(command)0 2395 y Ff(n)p Fl(gcon)p Ff(f)p Fj(x)p Ff(gf)p Fj(y)r Ff(gf)p Fj(t)p Ff(gf)p Fj(b)p Ff(g)13 b Fl(is)i(used.)21 b(The)15 b(v)m(arious)h(a)o(v)m(ailable)e(graphical) h(sym)o(b)q(ols)f(are)h(describ)q(ed)f(in)0 2453 y(the)i(follo)o(wing)g (table:)p 0 2561 250 2 v 50 2608 a Fc(Date)s Fm(:)e(31.)j(Oct.)i(1998.) 890 2658 y Fb(1)p eop %%Page: 2 2 2 1 bop 0 118 a Fb(2)761 b(B.)17 b(P)m(AREIGIS)71 212 y Fl(name)68 b(sym)o(b.)39 b(b)q(o)o(xed)i(x)h(y)f(parameters)95 b(description)420 270 y(sym)o(b.)46 b(dim)p 50 289 1734 2 v 71 348 a Ff(n)p Fl(gb)q(eg)393 b(x)42 b(y)f Ff(f)p Fj(x)p Ff(gf)p Fj(y)r Ff(g)178 b Fl(\(gb)q(eg)18 b(=)e(graphic)h Fk(b)n(e)n(g)p Fl(in\))g(b)q(eginning)1054 406 y(of)c(graphical)f (diagram)g(-)g(parameters)1054 464 y Fj(x)k Fl(and)h Fj(y)h Fl(denote)e(the)g(o)o(v)o(erall)e(size)i(of)1054 522 y(the)g(diagram)71 591 y Ff(n)p Fl(gend)526 b(none)232 b(\(gend)38 b(=)f(graphic)g Fk(end)p Fl(\))h(end)f(of)1054 649 y(graphical)17 b(diagram)71 718 y Ff(n)p Fl(gnl)561 b(none)232 b(\(gnl)16 b(=)f(graphic)g Fk(n)p Fl(ew)h Fk(l)p Fl(ine\))f(new)g(line)1054 776 y(command)28 b(in)h(the)g (graphical)h(dia-)1054 834 y(gram)71 903 y Ff(n)p Fl(gv)m(ac)p 456 866 54 2 v 456 915 2 50 v 508 915 V 456 917 54 2 v 400 w(1)43 b(1)f Ff(f)p Fj(n)p Ff(g)253 b Fl(\(gv)m(ac)27 b(=)g(graphic)f Fk(vac)p Fl(uous)i(\014elds\))1054 961 y(empt)o(y)12 b(space)i(of)g(width)f Fj(n)h Fl(\(here)f Fj(n)h Fl(=)1054 1019 y(1\))71 1091 y Ff(n)p Fl(gcl)p 315 1103 2 50 v 456 1053 54 2 v 456 1103 2 50 v 508 1103 V 456 1105 54 2 v 482 1103 2 50 v 433 w(1)43 b(1)f Ff(f)p Fj(y)r Ff(g)256 b Fl(\(gcl)28 b(=)g(graphic)h Fk(c)p Fl(onnecting)f Fk(l)p Fl(ine\))1054 1149 y(connect)42 b(command)f(-)i(v)o(ertically)1054 1207 y(connects)13 b(one)h(b)q(ottom)f(connector)g(of)1054 1265 y(one)29 b(morphism)e(with)i(a)g(top)h(con-)1054 1323 y(nector)15 b(of)h(another)f(morphism)e(-)i(has)1054 1381 y(v)o(ertical)g(length)h Fj(y)71 1450 y Ff(n)p Fl(gcn)p 291 1413 2 2 v 291 1414 V 291 1415 V 291 1415 V 291 1416 V 291 1416 V 291 1417 V 291 1417 V 291 1418 V 292 1418 V 292 1419 V 292 1419 V 292 1420 V 292 1420 V 292 1421 V 293 1421 V 293 1422 V 293 1422 V 293 1423 V 294 1423 V 294 1424 V 294 1424 V 294 1425 V 295 1425 V 295 1425 V 295 1426 V 296 1426 V 296 1427 V 296 1427 V 297 1428 V 297 1428 V 298 1428 V 298 1429 V 299 1429 V 299 1430 V 300 1430 V 300 1430 V 301 1431 V 301 1431 V 302 1432 V 302 1432 V 303 1432 V 303 1433 V 304 1433 V 304 1433 V 305 1434 V 306 1434 V 306 1434 V 307 1435 V 308 1435 V 308 1435 V 309 1436 V 310 1436 V 310 1436 V 311 1437 V 312 1437 V 313 1437 V 314 1438 V 314 1438 V 315 1438 V 316 1438 V 316 1438 V 317 1439 V 318 1439 V 318 1439 V 319 1440 V 320 1440 V 321 1440 V 321 1440 V 322 1441 V 323 1441 V 324 1441 V 324 1442 V 325 1442 V 326 1442 V 326 1443 V 327 1443 V 327 1443 V 328 1444 V 329 1444 V 329 1444 V 330 1445 V 330 1445 V 331 1446 V 331 1446 V 332 1446 V 332 1447 V 333 1447 V 333 1448 V 334 1448 V 334 1448 V 335 1449 V 335 1449 V 335 1450 V 336 1450 V 336 1450 V 337 1451 V 337 1451 V 337 1452 V 338 1452 V 338 1453 V 338 1453 V 338 1454 V 339 1454 V 339 1455 V 339 1455 V 339 1455 V 340 1456 V 340 1456 V 340 1457 V 340 1457 V 340 1458 V 340 1458 V 340 1459 V 341 1459 V 341 1460 V 341 1460 V 341 1461 V 341 1461 V 341 1462 V 341 1462 V 341 1463 V 431 1413 103 2 v 431 1462 2 50 v 533 1462 V 431 1464 103 2 v 458 1413 2 2 v 458 1414 V 458 1415 V 458 1415 V 458 1416 V 458 1416 V 458 1417 V 458 1417 V 458 1418 V 459 1418 V 459 1419 V 459 1419 V 459 1420 V 459 1420 V 459 1421 V 460 1421 V 460 1422 V 460 1422 V 460 1423 V 461 1423 V 461 1424 V 461 1424 V 461 1425 V 462 1425 V 462 1425 V 462 1426 V 463 1426 V 463 1427 V 463 1427 V 464 1428 V 464 1428 V 465 1428 V 465 1429 V 466 1429 V 466 1430 V 467 1430 V 467 1430 V 467 1431 V 468 1431 V 469 1432 V 469 1432 V 470 1432 V 470 1433 V 471 1433 V 471 1433 V 472 1434 V 473 1434 V 473 1434 V 474 1435 V 475 1435 V 475 1435 V 476 1436 V 477 1436 V 477 1436 V 478 1437 V 479 1437 V 480 1437 V 481 1438 V 481 1438 V 482 1438 V 483 1438 V 483 1438 V 484 1439 V 485 1439 V 485 1439 V 486 1440 V 487 1440 V 488 1440 V 488 1440 V 489 1441 V 490 1441 V 491 1441 V 491 1442 V 492 1442 V 493 1442 V 493 1443 V 494 1443 V 494 1443 V 495 1444 V 496 1444 V 496 1444 V 497 1445 V 497 1445 V 498 1446 V 498 1446 V 499 1446 V 499 1447 V 500 1447 V 500 1448 V 501 1448 V 501 1448 V 502 1449 V 502 1449 V 502 1450 V 503 1450 V 503 1450 V 504 1451 V 504 1451 V 504 1452 V 504 1452 V 505 1453 V 505 1453 V 505 1454 V 506 1454 V 506 1455 V 506 1455 V 506 1455 V 506 1456 V 507 1456 V 507 1457 V 507 1457 V 507 1458 V 507 1458 V 507 1459 V 508 1459 V 508 1460 V 508 1460 V 508 1461 V 508 1461 V 508 1462 V 508 1462 V 508 1463 V 420 w(2)43 b(1)f Ff(f)p Fj(x)p Ff(gf)p Fj(y)r Ff(gf)p Fj(t)p Ff(gf)p Fj(b)p Ff(g)d Fl(\(gcn)27 b(=)f(graphic)h Fk(c)p Fl(o)p Fk(n)p Fl(nector\))h(con-) 1054 1508 y(nect)35 b(command)f(-)i(connects)f(one)1054 1566 y(b)q(ottom)f(connector)f(of)h(one)g(mor-)1054 1624 y(phism)12 b(with)h(a)g(top)h(connector)f(of)g(an-)1054 1682 y(other)24 b(morphism)d(\(see)j(description)1054 1741 y(b)q(elo)o(w\))71 1812 y Ff(n)p Fl(gnot)306 1808 y Fg(f)p 456 1775 54 2 v 456 1825 2 50 v 508 1825 V 456 1827 54 2 v 150 w(f)589 1812 y Fl(0)43 b(1)f Ff(f)p Fj(f)5 b Ff(g)253 b Fl(\(gnot)21 b(=)f(grphic)g Fk(not)p Fl(ation\))h(sp)q (eci\014-)1054 1870 y(cation)k(for)g(morphisms,)f(to)h(b)q(e)g(in-)1054 1928 y(serted)15 b(in)o(to)g(b)q(o)o(xed)g(morphisms)d(\(see)1054 1986 y(b)q(elo)o(w\))71 2058 y Ff(n)p Fl(got)137 b Fj(S)259 b Fl(2)43 b(1)f Ff(f)p Fj(n)p Ff(gf)p Fj(S)s Ff(g)170 b Fl(\(got)21 b(=)f(graphic)h Fk(o)p Fl(b)s(ject)e Fk(t)p Fl(op\))i(sp)q(ec-)1054 2116 y(i\014cation)i(for)g(the)g(domain)f(of)i (mor-)1054 2174 y(phisms,)13 b(to)i(b)q(e)f(used)h(at)f(the)g(top)h(of) g(a)1054 2232 y(graphical)d(diagram)e(-)i(1st)f(parameter)1054 2290 y(is)17 b(width)f Fj(n)h Fl(of)g(b)q(o)o(x,)f(2nd)h(parameter)1054 2349 y(is)f(sp)q(eci\014cation)g(for)h(the)f(ob)s(ject)g Fj(S)71 2417 y Ff(n)p Fl(gob)129 b Fj(S)259 b Fl(2)43 b(1)f Ff(f)p Fj(n)p Ff(gf)p Fj(S)s Ff(g)170 b Fl(\(gob)31 b(=)e(graphic)h Fk(o)p Fl(b)s(ject)e Fk(b)p Fl(ottom\))1054 2475 y(sp)q(eci\014cation)13 b(for)g(the)g(range)g(of)h(mor-)1054 2533 y(phisms,)g(to)i(b)q(e)g(used)f(at)h(the)f(b)q(ottom)1054 2592 y(of)i(a)g(graphical)f(diagram)p eop %%Page: 3 3 3 2 bop 557 118 a Fb(GRAPHICAL)16 b(CALCULUS)g(PR)o(OGRAM)538 b(3)71 212 y Fl(name)127 b(sym)o(b.)64 b(b)q(o)o(xed)53 b(x)41 b(y)g(parameters)g(description)504 270 y(sym)o(b.)58 b(dim)p 50 289 1775 2 v 71 348 a Ff(n)p Fl(gm)o(u)p 349 323 2 13 v 349 349 a Fi(\012)p 399 323 V(\011)p 375 360 V 515 311 103 2 v 515 360 2 50 v 616 360 V 515 362 103 2 v 540 323 2 13 v 91 w(\012)p 590 323 V(\011)p 566 360 V 684 348 a Fl(2)43 b(1)f(none)178 b(\(gm)o(u)28 b(=)i(graphic)f Fk(mu)p Fl(ltiplication\))1095 406 y(m)o(ultiplic)o(ation)14 b(*\))71 478 y Ff(n)p Fl(gcm)o(u)349 454 y Fi(\013)p 349 490 V(\010)p 399 490 V 375 453 V 515 440 103 2 v 515 490 2 50 v 616 490 V 515 492 103 2 v 91 w(\013)p 540 490 2 13 v(\010)p 590 490 V 566 453 V 684 478 a Fl(2)43 b(1)f(none)178 b(\(gcm)o(u)189 b(=)i(graphic)1095 536 y Fk(c)p Fl(o)p Fk(mu)p Fl(ltiplication\))117 b(com)o(ultipli)o(-)1095 594 y(cation)16 b(*\))71 665 y Ff(n)p Fl(glm)p 350 645 2 17 v 351 645 50 2 v 351 658 a Fh(P)359 661 y(P)p 400 678 2 50 v 515 628 103 2 v 515 678 2 50 v 616 678 V 515 680 103 2 v 541 645 2 17 v 542 645 50 2 v 542 658 a(P)550 661 y(P)p 591 678 2 50 v 684 665 a Fl(2)43 b(1)f(none)178 b(\(glm)19 b(=)i(graphic)g Fk(l)p Fl(eft)g Fk(m)p Fl(o)q(dule\))g(left) 1095 724 y(mo)q(dule)15 b(action)71 783 y Ff(n)p Fl(grm)p 400 762 2 17 v 351 763 50 2 v 359 776 a Fh(\020)351 778 y(\020)p 350 795 2 50 v 515 745 103 2 v 515 795 2 50 v 616 795 V 515 797 103 2 v 591 762 2 17 v 542 763 50 2 v 550 776 a(\020)542 778 y(\020)p 541 795 2 50 v 684 783 a Fl(2)43 b(1)f(none)178 b(\(grm)32 b(=)h(graphic)h Fk(r)p Fl(igh)o(t)f Fk(m)p Fl(o)q(dule\))1095 841 y(righ)o(t)16 b(mo)q(dule)f(action)71 909 y Ff(n)p Fl(glcm)p 350 922 2 17 v 351 906 50 2 v 351 905 a Fh(\020)359 903 y(\020)p 400 922 2 50 v 515 872 103 2 v 515 922 2 50 v 616 922 V 515 924 103 2 v 541 922 2 17 v 542 906 50 2 v 542 905 a(\020)550 903 y(\020)p 591 922 2 50 v 684 909 a Fl(2)43 b(1)f(none)178 b(\(glcm)20 b(=)j(graphic)f Fk(l)p Fl(eft)g Fk(c)p Fl(o-)p Fk(m)p Fl(o)q(dule\))1095 968 y(left)15 b(como)q(dule)g(coaction)71 1027 y Ff(n)p Fl(grcm)p 400 1039 2 17 v 351 1023 50 2 v 359 1022 a Fh(P)351 1020 y(P)p 350 1039 2 50 v 515 989 103 2 v 515 1039 2 50 v 616 1039 V 515 1041 103 2 v 591 1039 2 17 v 542 1023 50 2 v 550 1022 a(P)542 1020 y(P)p 541 1039 2 50 v 684 1027 a Fl(2)43 b(1)f(none)178 b(\(grcm)11 b(=)h(graphic)g Fk(r)p Fl(igh)o(t)f Fk(c)p Fl(o-)p Fk(m)p Fl(o)q(dule\))1095 1085 y(righ)o(t)16 b(como)q(dule)f(coaction)71 1153 y Ff(n)p Fl(gwm)o(u)p 325 1120 2 5 v 325 1155 a Fi(\016)p 424 1120 V 33 w(\015)p 359 1155 34 2 v 375 1166 2 13 v 490 1116 153 2 v 490 1166 2 50 v 641 1166 V 490 1168 153 2 v 516 1120 2 5 v 26 w(\016)p 615 1120 V 33 w(\015)p 550 1155 34 2 v 566 1166 2 13 v 684 1153 a Fl(3)43 b(1)f Ff(f)p Fj(n)p Ff(g)199 b Fl(\(gwm)o(u)90 b(=)h(graphic)h Fk(w)p Fl(ide)1095 1212 y Fk(mu)p Fl(ltiplication\))82 b(wide)h(m)o(ulti-)1095 1270 y(plication)19 b(-)h(width)g Fj(n)f Fl(\(here)h Fj(n)f Fl(=)h(3\))1095 1328 y(is)c(giv)o(en)f(b)o(y) h(the)g(parameter)f(*\))71 1399 y Ff(n)p Fl(gw)o(cm)325 1376 y Fi(\017)p 325 1412 2 5 v 33 w(\014)p 424 1412 V 359 1376 34 2 v 375 1374 2 13 v 490 1362 153 2 v 490 1412 2 50 v 641 1412 V 490 1414 153 2 v 26 w(\017)p 516 1412 2 5 v 33 w(\014)p 615 1412 V 550 1376 34 2 v 566 1374 2 13 v 684 1399 a Fl(3)43 b(1)f Ff(f)p Fj(n)p Ff(g)199 b Fl(\(gw)o(cm)52 b(=)i(graphic)h Fk(w)p Fl(ide)e Fk(c)p Fl(o-)1095 1457 y Fk(mu)p Fl(ltiplication\))32 b(wide)h(com)o(ultipli)o (-)1095 1516 y(cation)16 b(*\))71 1587 y Ff(n)p Fl(gwm)o(uc)p 326 1551 100 2 v 325 1554 2 5 v 325 1588 a Fi(\016)p 424 1554 V 33 w(\015)p 359 1588 34 2 v 375 1599 2 13 v 490 1550 153 2 v 490 1599 2 50 v 641 1599 V 490 1601 153 2 v 517 1551 100 2 v 516 1554 2 5 v 26 w(\016)p 615 1554 V 33 w(\015)p 550 1588 34 2 v 566 1599 2 13 v 684 1587 a Fl(3)43 b(1)f Ff(f)p Fj(n)p Ff(g)199 b Fl(\(gwm)o(uc)83 b(=)h(graphic)g Fk(w)p Fl(ide)1095 1645 y Fk(mu)p Fl(ltiplication)e Fk(c)p Fl(losed\))i(wide)1095 1703 y(closed)16 b(m)o(ultipli)o(cation)e (sym)o(b)q(ol)h(*\))71 1775 y Ff(n)p Fl(gw)o(cmc)p 326 1788 100 2 v 325 1751 a Fi(\017)p 325 1787 2 5 v 33 w(\014)p 424 1787 V 359 1751 34 2 v 375 1750 2 13 v 490 1737 153 2 v 490 1787 2 50 v 641 1787 V 490 1789 153 2 v 517 1788 100 2 v 26 w(\017)p 516 1787 2 5 v 33 w(\014)p 615 1787 V 550 1751 34 2 v 566 1750 2 13 v 684 1775 a Fl(3)43 b(1)f Ff(f)p Fj(n)p Ff(g)199 b Fl(\(gw)o(cmc)84 b(=)i(graphic)g Fk(w)p Fl(ide)1095 1833 y Fk(c)p Fl(o)p Fk(m)p Fl(ultiplication)59 b Fk(c)p Fl(losed\))h(wide)1095 1891 y(closed)14 b(com)o(ultiplication) e(sym)o(b)q(ol)h(*\))71 1963 y Ff(n)p Fl(gev)p 349 1938 V 349 1964 a Fi(\012)p 399 1938 V(\011)p 515 1925 103 2 v 515 1975 2 50 v 616 1975 V 515 1977 103 2 v 540 1938 2 13 v 91 w(\012)p 590 1938 V(\011)684 1963 y Fl(2)43 b(1)f(none)178 b(\(gev)15 b(=)f(graphic)h Fk(ev)p Fl(aluation\))i(ev)m (alu-)1095 2021 y(ation)71 2080 y Ff(n)p Fl(gdb)349 2056 y Fi(\013)p 349 2092 V(\010)p 399 2092 V 515 2042 103 2 v 515 2092 2 50 v 616 2092 V 515 2094 103 2 v 91 w(\013)p 540 2092 2 13 v(\010)p 590 2092 V 684 2080 a Fl(2)43 b(1)f(none)178 b(\(gdb)24 b(=)f(graphic)g Fk(d)p Fl(ual)g Fk(b)p Fl(asis\))h(dual)1095 2138 y(basis)71 2197 y Ff(n)p Fl(gw)o(ev)p 325 2164 2 5 v 325 2198 a Fi(\016)p 424 2164 V 33 w(\015)p 359 2198 34 2 v 490 2160 153 2 v 490 2209 2 50 v 641 2209 V 490 2211 153 2 v 516 2164 2 5 v 26 w(\016)p 615 2164 V 33 w(\015)p 550 2198 34 2 v 684 2197 a Fl(3)43 b(1)f Ff(f)p Fj(n)p Ff(g)199 b Fl(\(gw)o(ev)14 b(=)g(graphic)g Fk(w)p Fl(ide)g Fk(ev)p Fl(aluation\))1095 2255 y(wide)i(ev)m(aluation)71 2314 y Ff(n)p Fl(gwdb)325 2290 y Fi(\017)p 325 2326 2 5 v 33 w(\014)p 424 2326 V 359 2290 34 2 v 490 2277 153 2 v 490 2326 2 50 v 641 2326 V 490 2328 153 2 v 26 w(\017)p 516 2326 2 5 v 33 w(\014)p 615 2326 V 550 2290 34 2 v 684 2314 a Fl(3)43 b(1)f Ff(f)p Fj(n)p Ff(g)199 b Fl(\(gwdb)16 b(=)g(graphic)g Fk(w)p Fl(ide)f Fk(d)p Fl(ual)h Fk(b)p Fl(asis\))1095 2372 y(wide)g(dual)g(basis)71 2431 y Ff(n)p Fl(gbr)p 351 2395 2 2 v 351 2395 V 351 2396 V 351 2396 V 351 2397 V 351 2397 V 351 2398 V 351 2398 V 351 2399 V 351 2399 V 351 2400 V 352 2400 V 352 2401 V 352 2401 V 352 2402 V 352 2402 V 353 2403 V 353 2403 V 353 2404 V 353 2404 V 354 2405 V 354 2405 V 354 2406 V 354 2406 V 355 2407 V 355 2407 V 355 2408 V 356 2408 V 356 2408 V 357 2409 V 357 2409 V 357 2410 V 358 2410 V 358 2410 V 359 2411 V 359 2411 V 360 2412 V 360 2412 V 361 2412 V 361 2413 V 362 2413 V 362 2413 V 363 2414 V 364 2414 V 364 2415 V 365 2415 V 365 2415 V 366 2416 V 367 2416 V 367 2416 V 368 2417 V 369 2417 V 369 2417 V 370 2418 V 371 2418 V 372 2418 V 372 2418 V 373 2419 V 374 2419 V 375 2419 V 376 2420 V 376 2420 V 376 2420 V 377 2420 V 378 2420 V 379 2421 V 380 2421 V 380 2421 V 381 2422 V 382 2422 V 383 2422 V 383 2423 V 384 2423 V 385 2423 V 385 2424 V 386 2424 V 387 2424 V 387 2425 V 388 2425 V 388 2425 V 389 2426 V 389 2426 V 390 2426 V 391 2427 V 391 2427 V 392 2428 V 392 2428 V 393 2428 V 393 2429 V 393 2429 V 394 2430 V 394 2430 V 395 2430 V 395 2431 V 396 2431 V 396 2432 V 396 2432 V 397 2433 V 397 2433 V 397 2433 V 397 2434 V 398 2434 V 398 2435 V 398 2435 V 399 2436 V 399 2437 V 399 2437 V 399 2438 V 399 2438 V 400 2439 V 400 2439 V 400 2440 V 400 2440 V 400 2441 V 400 2441 V 400 2442 V 400 2442 V 400 2443 V 400 2443 V 401 2444 V 401 2444 V 401 2445 V 351 2445 V 351 2444 V 351 2443 V 351 2442 V 351 2442 V 351 2441 V 351 2440 V 351 2439 V 351 2439 V 352 2438 V 352 2437 V 352 2437 V 352 2436 V 352 2435 V 353 2434 V 353 2434 V 353 2433 V 354 2433 V 354 2432 V 354 2432 V 355 2431 V 355 2430 V 356 2430 V 356 2430 V 357 2429 V 357 2429 V 358 2428 V 358 2428 V 359 2427 V 359 2427 V 360 2427 V 361 2426 V 361 2426 V 362 2426 V 363 2425 V 363 2425 V 364 2425 V 365 2424 V 366 2424 V 367 2424 V 367 2424 V 401 2395 V 401 2395 V 401 2396 V 400 2397 V 400 2398 V 400 2399 V 400 2399 V 400 2400 V 400 2401 V 400 2402 V 400 2402 V 399 2403 V 399 2404 V 399 2404 V 399 2405 V 398 2405 V 398 2406 V 398 2407 V 397 2407 V 397 2408 V 396 2408 V 396 2409 V 396 2409 V 395 2410 V 395 2410 V 394 2411 V 394 2411 V 393 2411 V 392 2412 V 392 2412 V 391 2413 V 391 2413 V 390 2413 V 389 2414 V 389 2414 V 388 2414 V 387 2414 V 386 2415 V 386 2415 V 385 2415 V 384 2415 V 515 2394 103 2 v 515 2444 2 50 v 616 2444 V 515 2446 103 2 v 542 2395 2 2 v 542 2395 V 542 2396 V 542 2396 V 542 2397 V 542 2397 V 542 2398 V 542 2398 V 542 2399 V 542 2399 V 542 2400 V 543 2400 V 543 2401 V 543 2401 V 543 2402 V 543 2402 V 543 2403 V 544 2403 V 544 2404 V 544 2404 V 544 2405 V 545 2405 V 545 2406 V 545 2406 V 546 2407 V 546 2407 V 546 2408 V 547 2408 V 547 2408 V 548 2409 V 548 2409 V 548 2410 V 549 2410 V 549 2410 V 550 2411 V 550 2411 V 551 2412 V 551 2412 V 552 2412 V 552 2413 V 553 2413 V 553 2413 V 554 2414 V 554 2414 V 555 2415 V 556 2415 V 556 2415 V 557 2416 V 558 2416 V 558 2416 V 559 2417 V 560 2417 V 560 2417 V 561 2418 V 562 2418 V 563 2418 V 563 2418 V 564 2419 V 565 2419 V 566 2419 V 567 2420 V 567 2420 V 567 2420 V 568 2420 V 569 2420 V 570 2421 V 571 2421 V 571 2421 V 572 2422 V 573 2422 V 574 2422 V 574 2423 V 575 2423 V 576 2423 V 576 2424 V 577 2424 V 577 2424 V 578 2425 V 579 2425 V 579 2425 V 580 2426 V 580 2426 V 581 2426 V 582 2427 V 582 2427 V 583 2428 V 583 2428 V 584 2428 V 584 2429 V 584 2429 V 585 2430 V 585 2430 V 586 2430 V 586 2431 V 586 2431 V 587 2432 V 587 2432 V 588 2433 V 588 2433 V 588 2433 V 588 2434 V 589 2434 V 589 2435 V 589 2435 V 590 2436 V 590 2437 V 590 2437 V 590 2438 V 590 2438 V 591 2439 V 591 2439 V 591 2440 V 591 2440 V 591 2441 V 591 2441 V 591 2442 V 591 2442 V 591 2443 V 591 2443 V 591 2444 V 591 2444 V 592 2445 V 542 2445 V 542 2444 V 542 2443 V 542 2442 V 542 2442 V 542 2441 V 542 2440 V 542 2439 V 542 2439 V 543 2438 V 543 2437 V 543 2437 V 543 2436 V 543 2435 V 544 2434 V 544 2434 V 544 2433 V 545 2433 V 545 2432 V 545 2432 V 546 2431 V 546 2430 V 547 2430 V 547 2430 V 548 2429 V 548 2429 V 549 2428 V 549 2428 V 550 2427 V 550 2427 V 551 2427 V 552 2426 V 552 2426 V 553 2426 V 554 2425 V 554 2425 V 555 2425 V 556 2424 V 557 2424 V 557 2424 V 558 2424 V 592 2395 V 591 2395 V 591 2396 V 591 2397 V 591 2398 V 591 2399 V 591 2399 V 591 2400 V 591 2401 V 591 2402 V 590 2402 V 590 2403 V 590 2404 V 590 2404 V 589 2405 V 589 2405 V 589 2406 V 589 2407 V 588 2407 V 588 2408 V 587 2408 V 587 2409 V 586 2409 V 586 2410 V 586 2410 V 585 2411 V 584 2411 V 584 2411 V 583 2412 V 583 2412 V 582 2413 V 582 2413 V 581 2413 V 580 2414 V 580 2414 V 579 2414 V 578 2414 V 577 2415 V 577 2415 V 576 2415 V 575 2415 V 518 w(2)43 b(1)f(none)178 b(\(gbr)17 b(=)f(graphic)g Fk(br)p Fl(aid\))g(braid)71 2526 y Ff(n)p Fl(gibr)p 401 2489 V 401 2490 V 401 2490 V 400 2491 V 400 2491 V 400 2492 V 400 2492 V 400 2493 V 400 2493 V 400 2494 V 400 2494 V 400 2495 V 400 2495 V 399 2496 V 399 2496 V 399 2497 V 399 2497 V 399 2498 V 398 2498 V 398 2499 V 398 2499 V 398 2500 V 397 2500 V 397 2501 V 397 2501 V 396 2502 V 396 2502 V 396 2502 V 395 2503 V 395 2503 V 394 2504 V 394 2504 V 393 2505 V 393 2505 V 393 2505 V 392 2506 V 392 2506 V 391 2506 V 391 2507 V 390 2507 V 389 2508 V 389 2508 V 388 2508 V 388 2509 V 387 2509 V 387 2509 V 386 2510 V 385 2510 V 385 2510 V 384 2511 V 383 2511 V 383 2511 V 382 2512 V 381 2512 V 380 2512 V 380 2513 V 379 2513 V 378 2513 V 377 2514 V 376 2514 V 376 2514 V 376 2514 V 375 2514 V 374 2515 V 373 2515 V 372 2515 V 372 2516 V 371 2516 V 370 2516 V 369 2516 V 369 2517 V 368 2517 V 367 2517 V 367 2518 V 366 2518 V 365 2518 V 365 2519 V 364 2519 V 364 2519 V 363 2520 V 362 2520 V 362 2521 V 361 2521 V 361 2521 V 360 2522 V 360 2522 V 359 2522 V 359 2523 V 358 2523 V 358 2524 V 357 2524 V 357 2524 V 357 2525 V 356 2525 V 356 2526 V 355 2526 V 355 2527 V 355 2527 V 354 2527 V 354 2528 V 354 2528 V 354 2529 V 353 2529 V 353 2530 V 353 2530 V 353 2531 V 352 2531 V 352 2532 V 352 2532 V 352 2533 V 352 2533 V 351 2534 V 351 2534 V 351 2535 V 351 2535 V 351 2536 V 351 2536 V 351 2537 V 351 2537 V 351 2538 V 351 2538 V 351 2539 V 401 2539 V 401 2538 V 401 2537 V 400 2536 V 400 2536 V 400 2535 V 400 2534 V 400 2533 V 400 2533 V 400 2532 V 400 2531 V 399 2531 V 399 2530 V 399 2529 V 399 2529 V 398 2528 V 398 2528 V 398 2527 V 397 2527 V 397 2526 V 396 2525 V 396 2525 V 396 2524 V 395 2524 V 395 2524 V 394 2523 V 394 2523 V 393 2522 V 392 2522 V 392 2521 V 391 2521 V 391 2521 V 390 2520 V 389 2520 V 389 2520 V 388 2519 V 387 2519 V 386 2519 V 386 2519 V 385 2518 V 384 2518 V 351 2489 V 351 2490 V 351 2491 V 351 2492 V 351 2492 V 351 2493 V 351 2494 V 351 2495 V 351 2495 V 352 2496 V 352 2497 V 352 2497 V 352 2498 V 352 2499 V 353 2499 V 353 2500 V 353 2500 V 354 2501 V 354 2502 V 354 2502 V 355 2503 V 355 2503 V 356 2504 V 356 2504 V 357 2505 V 357 2505 V 358 2505 V 358 2506 V 359 2506 V 359 2507 V 360 2507 V 361 2507 V 361 2508 V 362 2508 V 363 2508 V 363 2509 V 364 2509 V 365 2509 V 366 2509 V 367 2510 V 367 2510 V 515 2488 103 2 v 515 2538 2 50 v 616 2538 V 515 2540 103 2 v 592 2489 2 2 v 591 2490 V 591 2490 V 591 2491 V 591 2491 V 591 2492 V 591 2492 V 591 2493 V 591 2493 V 591 2494 V 591 2494 V 591 2495 V 591 2495 V 590 2496 V 590 2496 V 590 2497 V 590 2497 V 590 2498 V 589 2498 V 589 2499 V 589 2499 V 588 2500 V 588 2500 V 588 2501 V 588 2501 V 587 2502 V 587 2502 V 586 2502 V 586 2503 V 586 2503 V 585 2504 V 585 2504 V 584 2505 V 584 2505 V 584 2505 V 583 2506 V 583 2506 V 582 2506 V 582 2507 V 581 2507 V 580 2508 V 580 2508 V 579 2508 V 579 2509 V 578 2509 V 577 2509 V 577 2510 V 576 2510 V 576 2510 V 575 2511 V 574 2511 V 574 2511 V 573 2512 V 572 2512 V 571 2512 V 571 2513 V 570 2513 V 569 2513 V 568 2514 V 567 2514 V 567 2514 V 567 2514 V 566 2514 V 565 2515 V 564 2515 V 563 2515 V 563 2516 V 562 2516 V 561 2516 V 560 2516 V 560 2517 V 559 2517 V 558 2517 V 558 2518 V 557 2518 V 556 2518 V 556 2519 V 555 2519 V 554 2519 V 554 2520 V 553 2520 V 553 2521 V 552 2521 V 552 2521 V 551 2522 V 551 2522 V 550 2522 V 550 2523 V 549 2523 V 549 2524 V 548 2524 V 548 2524 V 548 2525 V 547 2525 V 547 2526 V 546 2526 V 546 2527 V 546 2527 V 545 2527 V 545 2528 V 545 2528 V 544 2529 V 544 2529 V 544 2530 V 544 2530 V 543 2531 V 543 2531 V 543 2532 V 543 2532 V 543 2533 V 543 2533 V 542 2534 V 542 2534 V 542 2535 V 542 2535 V 542 2536 V 542 2536 V 542 2537 V 542 2537 V 542 2538 V 542 2538 V 542 2539 V 592 2539 V 591 2538 V 591 2537 V 591 2536 V 591 2536 V 591 2535 V 591 2534 V 591 2533 V 591 2533 V 591 2532 V 590 2531 V 590 2531 V 590 2530 V 590 2529 V 589 2529 V 589 2528 V 589 2528 V 589 2527 V 588 2527 V 588 2526 V 587 2525 V 587 2525 V 586 2524 V 586 2524 V 586 2524 V 585 2523 V 584 2523 V 584 2522 V 583 2522 V 583 2521 V 582 2521 V 582 2521 V 581 2520 V 580 2520 V 580 2520 V 579 2519 V 578 2519 V 577 2519 V 577 2519 V 576 2518 V 575 2518 V 542 2489 V 542 2490 V 542 2491 V 542 2492 V 542 2492 V 542 2493 V 542 2494 V 542 2495 V 542 2495 V 543 2496 V 543 2497 V 543 2497 V 543 2498 V 543 2499 V 544 2499 V 544 2500 V 544 2500 V 545 2501 V 545 2502 V 545 2502 V 546 2503 V 546 2503 V 547 2504 V 547 2504 V 548 2505 V 548 2505 V 549 2505 V 549 2506 V 550 2506 V 550 2507 V 551 2507 V 552 2507 V 552 2508 V 553 2508 V 554 2508 V 554 2509 V 555 2509 V 556 2509 V 557 2509 V 557 2510 V 558 2510 V 504 w(2)43 b(1)f(none)178 b(\(gibr)16 b(=)g(graphic)g Fk(i)p Fl(n)o(v)o(erse)f Fk(br)p Fl(aid\))h(in-)1095 2584 y(v)o(erse)f(braid)71 2643 y Ff(n)p Fl(gbrc)376 2630 y Fi(e)p 351 2606 V 351 2607 V 351 2607 V 351 2608 V 351 2609 V 351 2609 V 351 2610 V 351 2610 V 351 2611 V 351 2611 V 351 2612 V 352 2612 V 352 2613 V 352 2613 V 352 2614 V 352 2614 V 353 2615 V 353 2615 V 353 2616 V 353 2616 V 354 2616 V 354 2617 V 354 2617 V 354 2618 V 355 2618 V 355 2619 V 355 2619 V 356 2620 V 356 2620 V 357 2620 V 357 2621 V 357 2621 V 358 2622 V 358 2622 V 359 2622 V 359 2623 V 360 2623 V 360 2624 V 361 2624 V 361 2624 V 362 2625 V 362 2625 V 363 2626 V 364 2626 V 364 2626 V 365 2627 V 365 2627 V 366 2627 V 367 2628 V 367 2628 V 368 2628 V 369 2629 V 369 2629 V 370 2629 V 371 2629 V 372 2630 V 372 2630 V 373 2630 V 374 2631 V 375 2631 V 376 2631 V 376 2631 V 376 2632 V 377 2632 V 378 2632 V 379 2632 V 380 2633 V 380 2633 V 381 2633 V 382 2634 V 383 2634 V 383 2634 V 384 2635 V 385 2635 V 385 2635 V 386 2636 V 387 2636 V 387 2636 V 388 2637 V 388 2637 V 389 2637 V 389 2638 V 390 2638 V 391 2638 V 391 2639 V 392 2639 V 392 2640 V 393 2640 V 393 2640 V 393 2641 V 394 2641 V 394 2642 V 395 2642 V 395 2642 V 396 2643 V 396 2643 V 396 2644 V 397 2644 V 397 2645 V 397 2645 V 397 2646 V 398 2646 V 398 2646 V 398 2647 V 399 2647 V 399 2648 V 399 2648 V 399 2649 V 399 2649 V 400 2650 V 400 2650 V 400 2651 V 400 2651 V 400 2652 V 400 2652 V 400 2653 V 400 2653 V 400 2654 V 400 2654 V 401 2655 V 401 2655 V 401 2656 V 351 2656 V 351 2655 V 351 2654 V 351 2653 V 351 2653 V 351 2652 V 351 2651 V 351 2650 V 351 2650 V 352 2649 V 352 2648 V 352 2648 V 352 2647 V 352 2647 V 353 2646 V 353 2645 V 353 2645 V 354 2644 V 354 2644 V 354 2643 V 355 2643 V 355 2642 V 356 2642 V 356 2641 V 357 2641 V 357 2640 V 358 2640 V 358 2639 V 359 2639 V 359 2639 V 360 2638 V 361 2638 V 361 2638 V 362 2637 V 363 2637 V 363 2637 V 364 2636 V 365 2636 V 366 2636 V 367 2636 V 367 2635 V 401 2606 V 401 2607 V 401 2608 V 400 2609 V 400 2610 V 400 2610 V 400 2611 V 400 2612 V 400 2612 V 400 2613 V 400 2614 V 399 2615 V 399 2615 V 399 2616 V 399 2616 V 398 2617 V 398 2618 V 398 2618 V 397 2619 V 397 2619 V 396 2620 V 396 2620 V 396 2621 V 395 2621 V 395 2622 V 394 2622 V 394 2623 V 393 2623 V 392 2623 V 392 2624 V 391 2624 V 391 2625 V 390 2625 V 389 2625 V 389 2626 V 388 2626 V 387 2626 V 386 2626 V 386 2627 V 385 2627 V 384 2627 V 515 2606 103 2 v 515 2655 2 50 v 616 2655 V 515 2657 103 2 v 166 w(e)p 542 2606 2 2 v 542 2607 V 542 2607 V 542 2608 V 542 2609 V 542 2609 V 542 2610 V 542 2610 V 542 2611 V 542 2611 V 542 2612 V 543 2612 V 543 2613 V 543 2613 V 543 2614 V 543 2614 V 543 2615 V 544 2615 V 544 2616 V 544 2616 V 544 2616 V 545 2617 V 545 2617 V 545 2618 V 546 2618 V 546 2619 V 546 2619 V 547 2620 V 547 2620 V 548 2620 V 548 2621 V 548 2621 V 549 2622 V 549 2622 V 550 2622 V 550 2623 V 551 2623 V 551 2624 V 552 2624 V 552 2624 V 553 2625 V 553 2625 V 554 2626 V 554 2626 V 555 2626 V 556 2627 V 556 2627 V 557 2627 V 558 2628 V 558 2628 V 559 2628 V 560 2629 V 560 2629 V 561 2629 V 562 2629 V 563 2630 V 563 2630 V 564 2630 V 565 2631 V 566 2631 V 567 2631 V 567 2631 V 567 2632 V 568 2632 V 569 2632 V 570 2632 V 571 2633 V 571 2633 V 572 2633 V 573 2634 V 574 2634 V 574 2634 V 575 2635 V 576 2635 V 576 2635 V 577 2636 V 577 2636 V 578 2636 V 579 2637 V 579 2637 V 580 2637 V 580 2638 V 581 2638 V 582 2638 V 582 2639 V 583 2639 V 583 2640 V 584 2640 V 584 2640 V 584 2641 V 585 2641 V 585 2642 V 586 2642 V 586 2642 V 586 2643 V 587 2643 V 587 2644 V 588 2644 V 588 2645 V 588 2645 V 588 2646 V 589 2646 V 589 2646 V 589 2647 V 590 2647 V 590 2648 V 590 2648 V 590 2649 V 590 2649 V 591 2650 V 591 2650 V 591 2651 V 591 2651 V 591 2652 V 591 2652 V 591 2653 V 591 2653 V 591 2654 V 591 2654 V 591 2655 V 591 2655 V 592 2656 V 542 2656 V 542 2655 V 542 2654 V 542 2653 V 542 2653 V 542 2652 V 542 2651 V 542 2650 V 542 2650 V 543 2649 V 543 2648 V 543 2648 V 543 2647 V 543 2647 V 544 2646 V 544 2645 V 544 2645 V 545 2644 V 545 2644 V 545 2643 V 546 2643 V 546 2642 V 547 2642 V 547 2641 V 548 2641 V 548 2640 V 549 2640 V 549 2639 V 550 2639 V 550 2639 V 551 2638 V 552 2638 V 552 2638 V 553 2637 V 554 2637 V 554 2637 V 555 2636 V 556 2636 V 557 2636 V 557 2636 V 558 2635 V 592 2606 V 591 2607 V 591 2608 V 591 2609 V 591 2610 V 591 2610 V 591 2611 V 591 2612 V 591 2612 V 591 2613 V 590 2614 V 590 2615 V 590 2615 V 590 2616 V 589 2616 V 589 2617 V 589 2618 V 589 2618 V 588 2619 V 588 2619 V 587 2620 V 587 2620 V 586 2621 V 586 2621 V 586 2622 V 585 2622 V 584 2623 V 584 2623 V 583 2623 V 583 2624 V 582 2624 V 582 2625 V 581 2625 V 580 2625 V 580 2626 V 579 2626 V 578 2626 V 577 2626 V 577 2627 V 576 2627 V 575 2627 V 684 2643 a Fl(2)43 b(1)f(none)178 b(\(gbrc)13 b(=)g(graphic)h Fk(br)p Fl(aid)f Fk(c)p Fl(ircled\))f(cir-)1095 2701 y(cled)j(braid)p eop %%Page: 4 4 4 3 bop 0 118 a Fb(4)761 b(B.)17 b(P)m(AREIGIS)71 212 y Fl(name)127 b(sym)o(b.)40 b(b)q(o)o(xed)h(x)g(y)h(parameters)e (description)480 270 y(sym)o(b.)46 b(dim)p 50 289 1739 2 v 71 348 a Ff(n)p Fl(gibrc)376 336 y Fi(e)p 400 312 2 2 v 400 312 V 400 313 V 400 313 V 400 314 V 400 314 V 400 315 V 400 315 V 400 316 V 400 316 V 400 317 V 400 317 V 399 318 V 399 318 V 399 319 V 399 319 V 399 320 V 398 320 V 398 321 V 398 321 V 398 322 V 397 322 V 397 323 V 397 323 V 396 323 V 396 324 V 396 324 V 395 325 V 395 325 V 395 326 V 394 326 V 394 326 V 393 327 V 393 327 V 392 328 V 392 328 V 392 328 V 391 329 V 390 329 V 390 330 V 389 330 V 389 330 V 388 331 V 388 331 V 387 331 V 386 332 V 386 332 V 385 332 V 385 333 V 384 333 V 383 333 V 382 334 V 382 334 V 381 334 V 380 335 V 380 335 V 379 335 V 378 336 V 377 336 V 376 336 V 376 336 V 376 336 V 375 337 V 374 337 V 373 337 V 372 338 V 372 338 V 371 338 V 370 338 V 369 339 V 369 339 V 368 339 V 367 340 V 367 340 V 366 340 V 365 341 V 365 341 V 364 341 V 363 342 V 363 342 V 362 343 V 362 343 V 361 343 V 361 344 V 360 344 V 360 344 V 359 345 V 359 345 V 358 346 V 358 346 V 357 346 V 357 347 V 356 347 V 356 348 V 356 348 V 355 348 V 355 349 V 355 349 V 354 350 V 354 350 V 354 351 V 353 351 V 353 352 V 353 352 V 353 353 V 352 353 V 352 353 V 352 354 V 352 354 V 352 355 V 352 355 V 351 356 V 351 356 V 351 357 V 351 357 V 351 358 V 351 358 V 351 359 V 351 359 V 351 360 V 351 360 V 351 361 V 400 361 V 400 360 V 400 359 V 400 358 V 400 358 V 400 357 V 400 356 V 400 355 V 400 355 V 400 354 V 399 353 V 399 353 V 399 352 V 399 352 V 398 351 V 398 351 V 398 350 V 397 349 V 397 349 V 397 348 V 396 348 V 396 347 V 395 347 V 395 346 V 395 346 V 394 345 V 393 345 V 393 345 V 392 344 V 392 344 V 391 343 V 391 343 V 390 343 V 389 342 V 388 342 V 388 342 V 387 342 V 386 341 V 386 341 V 385 341 V 384 341 V 351 312 V 351 312 V 351 313 V 351 314 V 351 315 V 351 315 V 351 316 V 351 317 V 351 318 V 352 318 V 352 319 V 352 320 V 352 320 V 352 321 V 353 322 V 353 322 V 353 323 V 354 323 V 354 324 V 354 324 V 355 325 V 355 326 V 356 326 V 356 326 V 357 327 V 357 327 V 358 328 V 358 328 V 359 329 V 359 329 V 360 329 V 361 330 V 361 330 V 362 330 V 363 331 V 363 331 V 364 331 V 365 332 V 366 332 V 366 332 V 367 332 V 491 311 103 2 v 491 360 2 50 v 592 360 V 491 362 103 2 v 142 w(e)p 567 312 2 2 v 567 312 V 567 313 V 567 313 V 567 314 V 567 314 V 567 315 V 567 315 V 567 316 V 567 316 V 567 317 V 567 317 V 566 318 V 566 318 V 566 319 V 566 319 V 566 320 V 565 320 V 565 321 V 565 321 V 565 322 V 564 322 V 564 323 V 564 323 V 563 323 V 563 324 V 563 324 V 562 325 V 562 325 V 562 326 V 561 326 V 561 326 V 560 327 V 560 327 V 559 328 V 559 328 V 558 328 V 558 329 V 557 329 V 557 330 V 556 330 V 556 330 V 555 331 V 555 331 V 554 331 V 553 332 V 553 332 V 552 332 V 552 333 V 551 333 V 550 333 V 549 334 V 549 334 V 548 334 V 547 335 V 547 335 V 546 335 V 545 336 V 544 336 V 543 336 V 543 336 V 543 336 V 542 337 V 541 337 V 540 337 V 539 338 V 539 338 V 538 338 V 537 338 V 536 339 V 536 339 V 535 339 V 534 340 V 534 340 V 533 340 V 532 341 V 532 341 V 531 341 V 530 342 V 530 342 V 529 343 V 529 343 V 528 343 V 528 344 V 527 344 V 527 344 V 526 345 V 526 345 V 525 346 V 525 346 V 524 346 V 524 347 V 523 347 V 523 348 V 523 348 V 522 348 V 522 349 V 522 349 V 521 350 V 521 350 V 521 351 V 520 351 V 520 352 V 520 352 V 520 353 V 519 353 V 519 353 V 519 354 V 519 354 V 519 355 V 518 355 V 518 356 V 518 356 V 518 357 V 518 357 V 518 358 V 518 358 V 518 359 V 518 359 V 518 360 V 518 360 V 518 361 V 567 361 V 567 360 V 567 359 V 567 358 V 567 358 V 567 357 V 567 356 V 567 355 V 567 355 V 567 354 V 566 353 V 566 353 V 566 352 V 566 352 V 565 351 V 565 351 V 565 350 V 564 349 V 564 349 V 564 348 V 563 348 V 563 347 V 562 347 V 562 346 V 561 346 V 561 345 V 560 345 V 560 345 V 559 344 V 559 344 V 558 343 V 557 343 V 557 343 V 556 342 V 555 342 V 555 342 V 554 342 V 553 341 V 552 341 V 552 341 V 551 341 V 518 312 V 518 312 V 518 313 V 518 314 V 518 315 V 518 315 V 518 316 V 518 317 V 518 318 V 518 318 V 519 319 V 519 320 V 519 320 V 519 321 V 520 322 V 520 322 V 520 323 V 521 323 V 521 324 V 521 324 V 522 325 V 522 326 V 523 326 V 523 326 V 524 327 V 524 327 V 525 328 V 525 328 V 526 329 V 526 329 V 527 329 V 528 330 V 528 330 V 529 330 V 530 331 V 530 331 V 531 331 V 532 332 V 533 332 V 533 332 V 534 332 V 648 348 a Fl(2)e(1)e(none)177 b(\(gibrc)33 b(=)h(graphic)g Fk(i)p Fl(n)o(v)o(erse)e Fk(br)p Fl(aid)1059 406 y Fk(c)p Fl(ircled\))15 b(in)o(v)o(erse)g(circled)f(braid)71 478 y Ff(n)p Fl(gu)p 375 490 2 25 v 376 465 a Fi(r)p 516 440 54 2 v 516 490 2 50 v 567 490 V 516 492 54 2 v 542 490 2 25 v 155 w(r)648 478 y Fl(1)44 b(1)e Ff(f)p Fj(n)p Ff(g)198 b Fl(\(gu)17 b(=)f(graphic)g Fk(u)p Fl(nit\))g(unit)g (*\))71 572 y Ff(n)p Fl(gcu)p 375 560 V 376 560 a Fi(r)p 516 535 54 2 v 516 585 2 50 v 567 585 V 516 587 54 2 v 542 560 2 25 v 155 w(r)648 572 y Fl(1)44 b(1)e Ff(f)p Fj(n)p Ff(g)198 b Fl(\(gcu)16 b(=)f(graphic)h Fk(c)p Fl(o-)p Fk(u)p Fl(nit\))g(counit)f(*\))71 667 y Ff(n)p Fl(gmp)p 375 633 2 5 v 375 679 V 376 654 a Fi(h)364 666 y Fg(S)p 516 629 54 2 v 516 679 2 50 v 567 679 V 516 681 54 2 v 542 633 2 5 v 542 679 V 543 654 a Fi(h)531 666 y Fg(S)648 667 y Fl(1)44 b(1)e Ff(f)p Fj(S)s Ff(g)194 b Fl(\(gmp)18 b(=)g(graphic)h Fk(m)p Fl(or)p Fk(p)p Fl(hism\))e(mor-) 1059 725 y(phism)j(-)i(sp)q(eci\014cation)f Fj(S)k Fl(giv)o(en)20 b(b)o(y)1059 783 y(the)c(parameter)71 852 y Ff(n)p Fl(gbmp)p 375 818 V 375 864 V 353 818 45 2 v 353 860 2 42 v 364 850 a Fg(S)p 396 860 V 353 862 45 2 v 516 814 54 2 v 516 864 2 50 v 567 864 V 516 866 54 2 v 542 818 2 5 v 542 864 V 520 818 45 2 v 520 860 2 42 v 146 w(S)p 563 860 V 520 862 45 2 v 648 852 a Fl(1)44 b(1)e Ff(f)p Fj(S)s Ff(g)194 b Fl(\(gbmp)84 b(=)h(graphic)h Fk(b)p Fl(o)o(xed)1059 910 y Fk(m)p Fl(or)p Fk(p)p Fl(hism\))70 b(b)q(o)o(xed)i(morphism)1059 968 y(-)34 b(sp)q(eci\014cation)f Fj(S)j Fl(giv)o(en)d(b)o(y)g(the)1059 1026 y(parameter)71 1095 y Ff(n)p Fl(glmptb)p 375 1061 2 5 v 375 1107 V 355 1104 50 2 v 355 1062 V 354 1103 2 42 v 516 1057 54 2 v 516 1107 2 50 v 567 1107 V 516 1109 54 2 v 542 1061 2 5 v 542 1107 V 522 1104 50 2 v 522 1062 V 521 1103 2 42 v 399 w(1)44 b(1)e(none)177 b(\(glmptb)22 b(=)h(graphic)g Fk(l)p Fl(eft)g([part)g(of)s(])1059 1153 y Fk(m)p Fl(or)p Fk(p)p Fl(hism)13 b([with])h Fk(t)p Fl(op)h Fk(b)p Fl(ottom)f([con-)1059 1211 y(nectors]\))22 b(left)f(part)i(of)f(long)h(b)q(o)o(xed)1059 1269 y(morphism)10 b(-)j(sp)q(eci\014cation)f Fj(S)k Fl(can)d(b)q(e)1059 1327 y(inserted)h(with)h Ff(n)p Fl(gnot)h(-)f(has)h(top)f(and)1059 1385 y(b)q(ottom)h(connectors)71 1444 y Ff(n)p Fl(glmpt)p 375 1411 2 5 v 355 1412 50 2 v 355 1454 V 354 1453 2 42 v 516 1407 54 2 v 516 1457 2 50 v 567 1457 V 516 1459 54 2 v 542 1411 2 5 v 522 1412 50 2 v 522 1454 V 521 1453 2 42 v 426 w(1)44 b(1)e(none)177 b(\(glmpt)27 b(=)i(graphic)f Fk(l)p Fl(eft)h([part)f(of)s(])1059 1502 y Fk(m)p Fl(or)p Fk(p)p Fl(hism)18 b([with])h Fk(t)p Fl(op)h([connector]\))1059 1561 y(left)c(part)h(of)g(long)g(b)q(o)o(xed)g(morphism)1059 1619 y(-)g(has)g(only)f(top)g(connector)71 1687 y Ff(n)p Fl(glmpb)p 375 1700 2 5 v 355 1697 50 2 v 355 1655 V 354 1696 2 42 v 516 1650 54 2 v 516 1700 2 50 v 567 1700 V 516 1702 54 2 v 542 1700 2 5 v 522 1697 50 2 v 522 1655 V 521 1696 2 42 v 418 w(1)44 b(1)e(none)177 b(\(glmpb)26 b(=)h(graphic)g Fk(l)p Fl(eft)g([part)f(of)s(])1059 1746 y Fk(m)p Fl(or)p Fk(p)p Fl(hism)17 b([with])g Fk(b)p Fl(ottom)h([connec-)1059 1804 y(tor]\))f(left)e(part)j(of)f(long)g(b)q (o)o(xed)f(mor-)1059 1862 y(phism)g(-)i(has)g(only)g(b)q(ottom)f (connec-)1059 1920 y(tor)71 1979 y Ff(n)p Fl(glmp)p 355 1947 50 2 v 355 1988 V 354 1987 2 42 v 516 1942 54 2 v 516 1991 2 50 v 567 1991 V 516 1993 54 2 v 522 1947 50 2 v 522 1988 V 521 1987 2 42 v 445 w(1)44 b(1)e(none)177 b(\(glmp)31 b(=)h(graphic)h Fk(l)p Fl(eft)f([part)g(of)s(])1059 2037 y Fk(m)p Fl(or)p Fk(p)p Fl(hism\))12 b(left)h(part)h(of)g(long)g (b)q(o)o(xed)1059 2095 y(morphism)g(-)i(has)h(no)g(connectors)71 2164 y Ff(n)p Fl(gcmptb)p 375 2131 2 5 v 375 2176 V 351 2173 50 2 v 351 2132 V 516 2127 54 2 v 516 2176 2 50 v 567 2176 V 516 2178 54 2 v 542 2131 2 5 v 542 2176 V 518 2173 50 2 v 518 2132 V 391 w(1)44 b(1)e(none)177 b(\(gcmptb)25 b(=)g(graphic)h Fk(c)p Fl(en)o(ter)f([part)1059 2222 y(of)s(])h Fk(m)p Fl(or)p Fk(p)p Fl(hism)f([with])g Fk(t)p Fl(op)i Fk(b)p Fl(ottom)1059 2280 y([connectors]\))13 b(cen)o(ter)f(of)i(long)g(b)q(o)o(xed)1059 2338 y(morphism)c(-)j(sp)q (eci\014cation)f Fj(S)k Fl(can)d(b)q(e)1059 2396 y(inserted)h(with)h Ff(n)p Fl(gnot)h(-)f(has)h(top)f(and)1059 2454 y(b)q(ottom)h (connectors)71 2514 y Ff(n)p Fl(gcmpt)p 375 2480 2 5 v 351 2523 50 2 v 351 2481 V 516 2476 54 2 v 516 2526 2 50 v 567 2526 V 516 2528 54 2 v 542 2480 2 5 v 518 2523 50 2 v 518 2481 V 418 w(1)44 b(1)e(none)177 b(\(gcmpt)13 b(=)i(graphic)g Fk(c)p Fl(en)o(ter)f([part)g(of)s(])1059 2572 y Fk(m)p Fl(or)p Fk(p)p Fl(hism)k([with])h Fk(t)p Fl(op)h([connector]\))1059 2630 y(cen)o(ter)e(of)i(long)g(b)q(o)o(xed)f (morphism)e(-)1059 2688 y(has)g(only)f(top)h(connector)p eop %%Page: 5 5 5 4 bop 557 118 a Fb(GRAPHICAL)16 b(CALCULUS)g(PR)o(OGRAM)538 b(5)71 212 y Fl(name)137 b(sym)o(b.)63 b(b)q(o)o(xed)53 b(x)42 b(y)f(parameters)f(description)514 270 y(sym)o(b.)57 b(dim)p 50 289 1784 2 v 71 348 a Ff(n)p Fl(gcmpb)p 384 360 2 5 v 360 357 50 2 v 360 316 V 550 311 54 2 v 550 360 2 50 v 601 360 V 550 362 54 2 v 575 360 2 5 v 551 357 50 2 v 551 316 V 456 w(1)43 b(1)f(none)177 b(\(gcmpb)12 b(=)h(graphic)g Fk(c)p Fl(en)o(ter)g([part)g(of)s(])1104 406 y Fk(m)p Fl(or)p Fk(p)p Fl(hism)k([with])h Fk(b)p Fl(ottom)g([connec-)1104 464 y(tor]\))26 b(cen)o(ter)f(of)h(long)h(b)q (o)o(xed)f(mor-)1104 522 y(phism)16 b(-)i(has)h(only)e(b)q(ottom)g (connec-)1104 580 y(tor)71 640 y Ff(n)p Fl(gcmp)p 360 649 V 360 607 V 550 602 54 2 v 550 652 2 50 v 601 652 V 550 654 54 2 v 551 649 50 2 v 551 607 V 483 w(1)43 b(1)f(none)177 b(\(gcmp)18 b(=)g(graphic)g Fk(c)p Fl(en)o(ter)g([part)h (of)s(])1104 698 y Fk(m)p Fl(or)p Fk(p)p Fl(hism\))k(cen)o(ter)g(of)i (long)g(b)q(o)o(xed)1104 756 y(morphism)14 b(-)j(has)g(no)f(connectors) 71 825 y Ff(n)p Fl(grmptb)p 384 791 2 5 v 384 837 V 356 834 50 2 v 356 792 V 405 833 2 42 v 550 787 54 2 v 550 837 2 50 v 601 837 V 550 839 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V 875 1617 V 949 1662 2 5 v 925 1658 50 2 v 925 1617 V 999 1616 2 5 v 999 1662 V 971 1658 50 2 v 971 1617 V 1020 1657 2 42 v 838 1711 a(3)76 b(7)25 b(9)0 1786 y(at)19 b(o)q(dd)h(p)q(ositions.)30 b(There)18 b(are)h(some)f(morphisms)e(\(denoted)j(b)o(y)f(*\)\))i(that)f(ha)o(v)o (e)f(connectors)0 1844 y(at)f(ev)o(en)e(p)q(ositions)i(for)f(example) 863 1904 y(1)26 b(3)p 849 1921 103 2 v 849 1970 2 50 v 950 1970 V 849 1972 103 2 v 874 1933 2 13 v 874 1959 a Fi(\012)p 924 1933 V(\011)p 899 1970 V 888 2020 a Fl(2)0 2085 y(W)l(e)14 b(coun)o(t)g(the)g(p)q(ositions)h(of)g(the)f(p)q (ossible)g(connectors)g(along)i(the)d(\(imaginary\))g(b)q(o)o(x)i(in)f (whic)o(h)0 2143 y(the)j(morphism)e(is)i(p)q(ositioned)h(from)e(0)i(to) f(2)p Ff(\002)p Fl(length)h(of)f(the)g(b)q(o)o(x,)h(so)g(for)f(the)g(m) o(ultiplication)0 2201 y(b)q(o)o(x)d(\(2)5 b Ff(\002)g Fl(1\))14 b(from)e(0)i(to)g(4.)20 b(These)13 b(connectors)h(m)o(ust)e (b)q(e)i(connected)e(to)i(other)f(connectors.)21 b(F)l(or)0 2259 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