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  1.  xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR
  2. pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1
  3. -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg
  4. TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg
  5. sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr
  6. 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add
  7. 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp
  8. {pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72
  9. div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray}
  10. N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict
  11. maxlength dict begin /magscale false def normalscale currentpoint TR
  12. /psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts
  13. /psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx
  14. psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy
  15. scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR
  16. /showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{
  17. psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2
  18. roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath
  19. moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{SDict
  20. begin /SpecialSave save N gsave normalscale currentpoint TR
  21. @SpecialDefaults count /ocount X /dcount countdictstack N}N /@setspecial
  22. {CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto
  23. closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx
  24. sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR
  25. }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse
  26. CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury
  27. lineto closepath clip}if /showpage{}N /erasepage{}N /copypage{}N newpath
  28. }N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{
  29. end}repeat grestore SpecialSave restore end}N /@defspecial{SDict begin}
  30. N /@fedspecial{end}B /li{lineto}B /rl{rlineto}B /rc{rcurveto}B /np{
  31. /SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX
  32. SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X
  33. /startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad
  34. yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end
  35. %%EndProcSet
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  1467. (:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)g(:)
  1468. h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)59 b Fr(34)172 1296
  1469. y(6.2.1)51 b(Examples)32 b Fn(:)23 b(:)f(:)g(:)h(:)f(:)h(:)f(:)g(:)h(:)
  1470. f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)g(:)h(:)f
  1471. (:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)59 b Fr(35)0
  1472. 1427 y Fo(7)42 b(Builtin)20 b(functions)1462 b(37)68
  1473. 1513 y Fr(7.1)45 b(F)l(unction)17 b(Beha)o(vior)38 b
  1474. Fn(:)22 b(:)g(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g
  1475. (:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)
  1476. h(:)f(:)g(:)59 b Fr(38)0 1644 y Fo(8)42 b(Input)18 b(and)g(Output)1434
  1477. b(39)0 1776 y(9)42 b(Plotting)1661 b(40)68 1862 y Fr(9.1)45
  1478. b(2-D)15 b(Plotting)e Fn(:)23 b(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)g
  1479. (:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)g(:)
  1480. h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)59 b
  1481. Fr(41)68 1948 y(9.2)45 b(Histograms)38 b Fn(:)23 b(:)fIONS)972 2788 y Fr(6)p eop
  1482. %%Page: 7 8
  1483. 7 7 bop 0 87 a Fk(>)23 b(help)h(WARRANTY)0 221 y Fr(The)13
  1484. b(subsequen)o(t)h(topics)f(refer)g(to)g(commands)g(that)f(ha)o(v)o(e)h
  1485. (b)q(een)h(written)f(in)h(R)1369 231 y(L)1386 215 y(a)1404
  1486. 221 y(B)21 b(script)14 b(\014les,)g(whic)o(h)g(w)o(e)f(refer)0
  1487. 277 y(to)g(as)h(\\R-\014les".)21 b(These)14 b(R-\014les)i(are)e(stored)
  1488. f(in)i(directories,)g(whic)o(h)h(the)e Fk(help)f Fr(command)h(searc)o
  1489. (hes.)20 b(The)14 b(help)0 334 y(\014les)20 b(in)h(the)e
  1490. Fn(:)8 b(:)g(:)e Fh(/rlib)19 b Fr(directory)h(come)f(as)g(a)g(standard)
  1491. h(part)e(of)i(R)1204 344 y(L)1221 328 y(a)1239 334 y(B)8
  1492. b(,)19 b(and)g(the)h(remainder)g(refer)g(to)e(lo)q(cal)0
  1493. 390 y(R-\014les)f(that)d(ha)o(v)o(e)h(b)q(een)h(setup)g(for)e(y)o(ou)h
  1494. (b)o(y)g(who)q(ev)o(er)g(installed)i(y)o(our)e(R)1280
  1495. 400 y(L)1297 384 y(a)1315 390 y(B)8 b(.)0 476 y(In)19
  1496. b(general,)g(the)f(functions)i(listed)f(in)g(the)g(\014rst)f(group)g
  1497. (are)g(the)g(most)g(e\016cien)o(t)h(as)f(they)g(are)g(compiled)j(in)o
  1498. (to)0 533 y(the)16 b(core)g(of)f(R)254 542 y(L)272 527
  1499. y(a)290 533 y(B)7 b(.)16 b(In)h(con)o(trast,)d(R)631
  1500. 542 y(L)648 527 y(a)667 533 y(B)7 b('s)16 b(R-\014les)h(ha)o(v)o(e)f
  1501. (the)g(extra)f(o)o(v)o(erhead)h(of)g(reading)g(and)g(in)o(terpretation)
  1502. 0 589 y(b)q(efore)d(they)h(are)f(executed.)20 b(This)14
  1503. b(lo)o(w)o(er)f(e\016ciency)h(asso)q(ciated)g(with)f(R-\014le)i(in)o
  1504. (terpretation)f(is)g(traded)f(for)f(the)0 646 y(b)q(ene\014t)j(of)e(b)q
  1505. (eing)i(able)g(to)e(write)h(y)o(our)f(o)o(wn)g(features)h(in)o(to)f(R)
  1506. 1065 655 y(L)1083 640 y(a)1101 646 y(B)7 b(.)14 b(If)g(an)g(R-\014le)h
  1507. (feature)f(is)g(really)h(useful,)f(it)g(can)0 702 y(b)q(e)i(added)f(to)
  1508. g(the)g(core)g(R)451 712 y(L)469 696 y(a)487 702 y(B)23
  1509. b(program)14 b(since)i(y)o(ou)f(ha)o(v)o(e)g(the)g(source)g(co)q(de)
  1510. 1332 685 y Fi(2)1353 702 y Fr(.)0 853 y Fm(2.3)55 b(Simple)17
  1511. b(calculations)0 968 y Fr(R)26 978 y(L)43 962 y(a)61
  1512. 968 y(B)28 b(is)22 b(designed)f(for)f(mathematical)h(calculations)h(so)
  1513. e(let's)h(do)f(some.)36 b(The)21 b(four)f(basic)h(arithmetic)g(op-)0
  1514. 1025 y(erators)c(ha)o(v)o(e)i(sym)o(b)q(ols)g Fk(+,)24
  1515. b(-,)f(*,)h(/)18 b Fr(represen)o(ting)i(addition,)g(subtraction,)g(m)o
  1516. (ultiplication,)i(and)d(division)0 1081 y(resp)q(ectiv)o(ely)l(.)i(No)o
  1517. (w)15 b(en)o(ter)g(some)g(one)g(line)i(expressions)f(as)f(sho)o(wn)g
  1518. (here:)0 1215 y Fk(>)23 b(2*4)191 1272 y(8)0 1328 y(>)g(1/2)143
  1519. 1384 y(0.5)0 1441 y(>)g(1+11)167 1497 y(12)0 1554 y(>)g(1-11)143
  1520. 1610 y(-10)0 1667 y(>)g(1*2/3+4-5)71 1723 y(-0.333)0
  1521. 1780 y(>)g(1/0)143 1836 y(inf)0 1893 y(>)g(0/\(1/0\))191
  1522. 1949 y(0)0 2005 y(>)g(0/0)143 2062 y(NaN)0 2196 y Fr(The)12
  1523. b(5)113 2179 y Fd(th)159 2196 y Fr(expression)g(illustrates)h
  1524. (compliance)g(with)f(the)g(usual)g(op)q(erator)f(hierarc)o(h)o(y)h(and)
  1525. g(then)g(w)o(e)f(observ)o(e)g(that)0 2252 y(R)26 2262
  1526. y(L)43 2246 y(a)61 2252 y(B)25 b(can)17 b(handle)i(exceptions)557
  1527. 2236 y Fi(3)595 2252 y Fr(suc)o(h)e(as)g(when)h Fq(1)f
  1528. Fr(\()p Fk(inf)p Fr(\))g(is)g(a)g(result)h(or)e(an)i(input)g(to)e
  1529. (further)h(calculation;)0 2309 y(and)e(also)g(\\not-a-n)o(um)o(b)q(er")
  1530. f(\()p Fk(NaN)p Fr(\).)g(R)669 2319 y(L)686 2303 y(a)704
  1531. 2309 y(B)23 b(can)15 b(use)h(complex)g(n)o(um)o(b)q(ers)f(as)g(w)o(ell)
  1532. h(as)e(real)i(n)o(um)o(b)q(ers)f(so)g(no)o(w)f(try)0
  1533. 2443 y Fk(>)23 b(1/1i)191 2499 y(0)g(-)h(1i)p 0 2529
  1534. 787 2 v 52 2556 a Fg(2)69 2572 y Ff(Dynamic)15 b(linking)g(is)f(part)f
  1535. (of)g(the)g(plan)i(for)d(a)h(future)h(release)52 2602
  1536. y Fg(3)69 2618 y Ff(The)g(abilit)o(y)j(to)d(prop)q(erly)i(handle)g
  1537. (\015oating)g(p)q(oin)o(t)g(exceptions)g(is)f(dep)q(enden)o(t)h(up)q
  1538. (on)g(the)e(capabiliti)q(es)j(of)d(the)h(hardw)o(are)g(and)0
  1539. 2663 y(op)q(erating)g(system,)e(as)g(w)o(ell)h(as)f(the)g(in)o(terests)
  1540. h(of)f(the)g(p)q(erson)h(installing)i(R)1122 2671 y(L)1137
  1541. 2658 y(a)1152 2663 y(B)k(.)972 2788 y Fr(7)p eop
  1542. %%Page: 8 9
  1543. 8 8 bop 0 87 a Fk(>)23 b(1/1i)h(+)g(1/1j)191 143 y(0)f(-)h(2i)0
  1544. 200 y(>)f(1/1i)h(*)g(1/1j)167 256 y(-1)0 313 y(>)f(1/1i/1j)167
  1545. 369 y(-1)0 501 y Fr(where)18 b(w)o(e)f(see)h(that)f Fk(i)h
  1546. Fr(or)f Fk(j)g Fr(can)h(represen)o(t)g(the)g(complex)g(n)o(um)o(b)q(er)
  1547. 1235 466 y Fq(p)p 1273 466 59 2 v 35 x(\000)p Fr(1.)27
  1548. b(No)18 b(four)f(function)i(calculator)f(is)0 558 y(complete)e(without)
  1549. f(a)g(memory)f(so)h(no)o(w)g(w)o(e)g(lo)q(ok)g(at)g(ho)o(w)g(to)f
  1550. (store)h(results)g(in)h(a)f(v)m(ariable.)0 708 y Fm(2.4)55
  1551. b(V)-5 b(ariable)19 b(assignmen)n(t)e(and)j(displa)n(y)0
  1552. 824 y Fr(In)h(R)88 833 y(L)105 818 y(a)123 824 y(B)8
  1553. b(,)20 b(v)m(ariables)h(can)f(ha)o(v)o(e)g(names)g(of)g(an)o(y)g
  1554. (length)h(con)o(taining)g(most)e(prin)o(table)i(c)o(haracters)f
  1555. (including)0 880 y Fq(f)p Fn(a)8 b(:)g(:)g(:)d(z)r(;)j(A)g(:)g(:)g(:)t
  1556. (Z)q(;)p 315 880 14 2 v 24 w Fq(g)p Fr(.)19 b(Y)l(ou)c(will)h(observ)o
  1557. (e)e(that)g(w)o(e)g(ha)o(v)o(e)g(to)g(exclude)i(sp)q(ecial)g(c)o
  1558. (haracters)e(suc)o(h)h(as)f Fk(+,)24 b(-,)f(*,)h(/)0
  1559. 937 y Fr(and)16 b(the)f Fk(SPACE)g Fr(c)o(haracter.)21
  1560. b(The)16 b(actual)g(assignmen)o(t)g(op)q(erator)e(sym)o(b)q(ol)i(is)h
  1561. (\\=")e(and)h(an)g(assignmen)o(t)f(state-)0 993 y(men)o(t)g(lo)q(oks)g
  1562. (lik)o(e)382 1125 y Fk(variable_name)22 b(=)h(expression_to_evaluate)0
  1563. 1257 y Fr(and)15 b(an)g(example)h(is)0 1389 y Fk(>)23
  1564. b(radius=2)24 1445 y(radius)g(=)191 1502 y(2)0 1558 y(>)g
  1565. (circumference=2)f(*)i(pi)g(*)f(radius)24 1615 y(circumference)f(=)119
  1566. 1671 y(12.6)0 1803 y Fr(where)i(a)g(v)m(ariable)h Fk(radius)f
  1567. Fr(is)g(created)g(and)h(initialised)i(with)d(the)g(real)h(v)m(alue)g
  1568. (2,)h(and)e(then)g(a)g(v)m(ariable)0 1860 y Fk(circumference)10
  1569. b Fr(is)j(created)f(and)g(\014lled)j(with)d(the)g(result)h(of)f(ev)m
  1570. (aluating)h(the)g(righ)o(t)f(hand)g(side)h(of)f(the)h(equation.)0
  1571. 1916 y(T)l(o)j(see)g(the)h(v)m(alue)g(of)f(either)h(of)f(these)g(v)m
  1572. (ariables,)i(just)e(en)o(ter)g(their)g(name)h(and)f(R)1450
  1573. 1926 y(L)1467 1910 y(a)1485 1916 y(B)24 b(will)18 b(prin)o(t)f(their)g
  1574. (v)m(alue.)0 1973 y(F)l(or)d(a)h(description)i(of)e(v)m(ariable)h
  1575. (names,)f(please)h(read)f(the)h(help)g(on)f Fk(VARIABLES)p
  1576. Fr(.)0 2059 y(As)g(y)o(ou)g(ha)o(v)o(e)g(probably)h(noticed)g(b)o(y)f
  1577. (no)o(w,)g(the)g(result)h(of)f(eac)o(h)g(expression)h(is)g
  1578. (automatically)g(prin)o(ted)g(to)e(the)0 2115 y(screen.)20
  1579. b(This)15 b(feature)f(can)h(b)q(e)g(con)o(trolled)h(b)o(y)e(using)h
  1580. (the)g(`)p Fk(;)p Fr(')f(c)o(haracter.)19 b(T)l(erminating)c(an)g
  1581. (expression)g(with)g(a)0 2171 y(`)p Fk(;)p Fr(')c(will)k(suppress)e
  1582. (prin)o(ting)g(of)g(the)f(result.)20 b(Lik)o(ewise,)14
  1583. b(terminating)f(an)g(expression)g(with)g(the)g(`)p Fk(?)p
  1584. Fr(')f(is)h(an)f(explicit)0 2228 y(w)o(a)o(y)i(to)g(force)h(prin)o
  1585. (ting.)0 2379 y Fm(2.5)55 b(User)19 b(In)n(terface:)24
  1586. b(command)16 b(recall)i(&)g(editing)0 2494 y Fr(Command)i(line)j
  1587. (recall)f(and)g(editing)g(is)g(v)o(ery)e(useful)j(for)d(correcting)h
  1588. (command)g(errors)g(or)f(to)h(allo)o(w)g(y)o(our)0 2550
  1589. y(commands)14 b(to)f(ev)o(olv)o(e.)20 b(R)458 2560 y(L)475
  1590. 2544 y(a)493 2550 y(B)i(pro)o(vides)15 b(a)e(command)h(recall)i(and)e
  1591. (edit)h(facilit)o(y)g(mo)q(deled)h(on)e(\(and)g(sometimes)0
  1592. 2607 y(actually)e(using\))f(the)g(GNU)g(readline)i(facilit)o(y)l(.)19
  1593. b(If)12 b(y)o(ou)e(are)h(familiar)h(with)f(GNU)g(emacs)g(or)f(the)h
  1594. (GNU)g(bash)g(shell,)0 2663 y(then)h(try)g(en)o(tering)h
  1595. Fk(C-p)f Fr(to)g(scroll)h(bac)o(k)f(through)g(previous)i(commands)e(\()
  1596. p Fk(C-p)f Fr(means)i(hold)g(do)o(wn)f(the)h Fk(control)972
  1597. 2788 y Fr(8)p eop
  1598. %%Page: 9 10
  1599. 9 9 bop 0 87 a Fr(k)o(ey)17 b(and)g(press)g Fk(p)p Fr(\).)26
  1600. b(If)17 b(this)h(is)f(successful,)i(test)e(the)g(standard)f(c)o
  1601. (haracter)h(and)g(w)o(ord)g(editing)h(commands)f(to)0
  1602. 143 y(mo)q(dify)f(previous)f(en)o(tries)h(-)f(if)h(it)f(w)o(orks,)f
  1603. (skip)i(to)f(section)h(3.)0 229 y(Ho)o(w)o(ev)o(er,)k(if)i(the)e(w)o
  1604. (ord)g(GNU)h(just)f(means)h(\\an)o(y)f(of)g(sev)o(eral)h(African)g(an)o
  1605. (telop)q(es)g(constituting)h(the)e(gen)o(us)0 286 y Fh(Conno)n(chaetes)
  1606. 14 b Fr(...")348 269 y Fi(4)387 286 y Fr(but)i(y)o(our)e(k)o(eyb)q
  1607. (oard)i(do)q(es)f(ha)o(v)o(e)h(the)f(arro)o(w)f(k)o(eys)h
  1608. Fq(f)g( )h(")f(#)g(!)h(g)p Fr(,)f(then)h(y)o(ou)f(migh)o(t)g(still)0
  1609. 342 y(b)q(e)j(able)g(to)f(tak)o(e)g(adv)m(an)o(tage)g(of)g(command)h
  1610. (line)h(recall)g(and)e(editing.)29 b(T)l(ry)17 b(t)o(yping)h(the)f
  1611. Fq(")h Fr(k)o(ey)f(to)g(see)h(if)g(an)o(y)0 399 y(previous)e(R)207
  1612. 409 y(L)224 393 y(a)242 399 y(B)24 b(commands)15 b(are)g(displaassigned)g(to)f(in)i(whole)f(or)f
  1613. (in)h(part.)30 b(W)l(e)18 b(ha)o(v)o(e)g(sho)o(wn)h(complete)g(matrix)f
  1614. (assignmen)o(t)h(in)0 2247 y(the)c(examples)g(of)g(the)g(last)f(few)h
  1615. (pages.)20 b(In)15 b(the)g(same)f(w)o(a)o(y)g(that)g(matrix)h(elemen)o
  1616. (ts)g(can)g(b)q(e)h(referenced)g(singly)l(,)0 2304 y(or)f(in)h(groups,)
  1617. e(matrices)h(can)h(ha)o(v)o(e)f(single)h(elemen)o(ts)g(re-assigned,)g
  1618. (or)f(groups)g(of)f(elemen)o(ts)i(re-assigned.)21 b(The)0
  1619. 2360 y(result)12 b(of)f(an)g(assignmen)o(t)h(expression)g(is)h(the)e
  1620. (left-hand-side)j(\(LHS\).)d(This)h(is)h(more)e(con)o(v)o(enien)o(t)h
  1621. (when)g(w)o(orking)0 2417 y(in)o(teractiv)o(ely)l(,)k(and)f(when)h
  1622. (creating)f(in)o(termediate)h(function)g(argumen)o(ts.)0
  1623. 2550 y Fk(>)23 b(a[2;2])h(=)f(200)24 2607 y(a)g(=)191
  1624. 2663 y(1)238 b(2)h(3)960 2788 y Fr(15)p eop
  1625. %%Page: 16 17
  1626. 16 16 bop 191 87 a Fk(4)190 b(200)239 b(6)191 143 y(7)f(8)h(9)0
  1627. 200 y(>)23 b(a[2,3;2,3])g(=)h([200,300;300,400])24 256
  1628. y(a)f(=)191 313 y(1)238 b(2)h(3)191 369 y(4)190 b(200)h(300)191
  1629. 426 y(7)f(300)h(400)0 559 y Fr(The)14 b(ro)o(w)f(and)h(column)h
  1630. (dimensions)g(of)f(the)g(matrices)g(on)g(the)g(RHS,)g(and)g(the)g
  1631. (matrix)g(description)h(within)g(the)0 616 y(`)p Fk([)23
  1632. b(])p Fr(')15 b(m)o(ust)f(ha)o(v)o(e)h(the)g(same)g(dimensions.)0
  1633. 765 y Fo(3.3.6)51 b(Matrix)18 b(Op)q(erations)0 881 y
  1634. Fr(The)d(usual)h(mathematical)f(op)q(erators)g Fk(+,-,*,/)f
  1635. Fr(op)q(erate)h(on)g(matrices)g(as)g(w)o(ell)h(as)f(scalars.)20
  1636. b(F)l(or)14 b Fk(A)24 b(binop)f(B)p Fr(:)0 1014 y Fk(+)f
  1637. Fr(Do)q(es)d(elemen)o(t-b)o(y-elemen)o(t)h(addition)f(of)f(t)o(w)o(o)f
  1638. (matrices.)30 b(The)19 b(ro)o(w)e(and)i(column)g(dimensions)h(of)e(b)q
  1639. (oth)h Fk(A)113 1071 y Fr(and)d Fk(B)g Fr(m)o(ust)g(b)q(e)g(the)g
  1640. (same.)22 b(An)16 b(exception)h(to)e(the)h(aforemen)o(tioned)h(rule)f
  1641. (o)q(ccurs)h(when)f(either)h Fk(A)e Fr(or)h Fk(B)113
  1642. 1127 y Fr(is)g(a)f(1-b)o(y-1)g(matrix;)f(in)i(this)g(case)f(a)g
  1643. (scalar-matrix)g(addition)h(op)q(eration)g(is)g(p)q(erformed.)0
  1644. 1221 y Fk(-)22 b Fr(Do)q(es)14 b(elemen)o(t-b)o(y-elemen)o(t)i
  1645. (subtraction)f(of)e(t)o(w)o(o)g(matrices.)20 b(The)14
  1646. b(ro)o(w)f(and)i(column)g(dimensions)h(of)d(b)q(oth)i
  1647. Fk(A)113 1277 y Fr(and)h Fk(B)g Fr(m)o(ust)g(b)q(e)g(the)g(same.)22
  1648. b(An)16 b(exception)h(to)e(the)h(aforemen)o(tioned)h(rule)f(o)q(ccurs)h
  1649. (when)f(either)h Fk(A)e Fr(or)h Fk(B)113 1333 y Fr(is)g(a)f(1-b)o(y-1)g
  1650. (matrix;)f(in)i(this)g(case)f(a)g(scalar-matrix)g(addition)h(op)q
  1651. (eration)g(is)g(p)q(erformed.)0 1427 y Fk(*)22 b Fr(P)o(erforms)13
  1652. b(matrix)g(m)o(ultiplication)j(on)d(the)h(t)o(w)o(o)e(op)q(erands.)20
  1653. b(The)14 b(column)g(dimension)h(of)e Fk(A)h Fr(m)o(ust)f(matc)o(h)f
  1654. (the)113 1483 y(ro)o(w)17 b(dimension)i(of)e Fk(B)p Fr(.)g(An)g
  1655. (exception)i(to)d(the)i(aforemen)o(tioned)f(rule)h(o)q(ccurs)g(when)g
  1656. (either)g Fk(A)f Fr(or)g Fk(B)g Fr(is)h(a)113 1540 y(1-b)o(y-1)d
  1657. (matrix;)g(in)h(this)f(case)h(a)f(scalar-matrix)g(m)o(ultiplication)i
  1658. (is)f(p)q(erformed.)0 1633 y Fk(/)22 b Fr(P)o(erforms)12
  1659. b(matrix)h(\\righ)o(t-division")h(on)f(its)h(op)q(erands.)19
  1660. b(The)14 b(matrix)e(righ)o(t-division)j(\()p Fk(B/A)p
  1661. Fr(\))d(can)i(b)q(e)f(though)o(t)113 1689 y(of)e(as)h
  1662. Fk(B*inv)23 b(\(A\))p Fr(.)11 b(The)g(column)i(dimensions)g(of)e
  1663. Fk(A)g Fr(and)h Fk(B)f Fr(m)o(ust)g(b)q(e)i(the)e(same.)18
  1664. b(In)o(ternally)13 b(righ)o(t)f(division)113 1746 y(is)k(the)f(same)g
  1665. (as)g(\\left-division")i(with)f(the)f(argumen)o(ts)f(transp)q(osed.)848
  1666. 1873 y Fn(B)r(=)m(A)g Fr(=)f(\()p Fn(A)1052 1855 y Fd(T)1089
  1667. 1873 y Fq(n)d Fn(B)1158 1855 y Fd(T)1186 1873 y Fr(\))1204
  1668. 1855 y Fd(T)113 1992 y Fr(The)15 b(exception)h(to)e(the)g(aforemen)o
  1669. (tioned)h(dimension)h(rule)g(o)q(ccurs)f(when)g Fk(A)f
  1670. Fr(is)h(a)f(1-b)o(y-1)h(matrix;)f(in)h(this)113 2049
  1671. y(case)h(a)e(matrix-scalar)h(divide)j(o)q(ccurs.)0 2183
  1672. y(Additionally)l(,)f(R)297 2192 y(L)314 2177 y(a)333
  1673. 2183 y(B)23 b(has)15 b(sev)o(eral)g(other)g(op)q(erators)f(that)h
  1674. (function)h(on)f(matrix)g(op)q(erand\(s\).)0 2316 y Fk(.+)22
  1675. b Fr(P)o(erforms)16 b(elemen)o(t-b)o(y-elemen)o(t)i(addition)g(on)e
  1676. (its)h(op)q(erands.)24 b(The)17 b(op)q(erands)g(m)o(ust)f(ha)o(v)o(e)g
  1677. (the)g(same)g(ro)o(w)113 2373 y(and)g(column)g(dimensionsn)o(y)130 b(all)154 b(i\013t)113 2001
  1678. y(When)16 b(using)g(a)e(v)o(ector)h(orien)o(ted)g(function,)h(lik)o(e)g
  1679. Fk(max\(\))f Fr(it)g(is)h(p)q(ossible)g(to)f(op)q(erate)g(on)g(matrix)g
  1680. (ob)s(jects.)113 2057 y(F)l(or)i(example)g(the)g(maxim)o(um)g(v)m(alue)
  1681. h(in)f(a)g(matrix)f(can)h(b)q(e)h(obtained)f(via)g Fk(max)24
  1682. b(\(max)f(\(a\)\))p Fr(.)h(The)17 b(\014rst)113 2114
  1683. y(call)g(to)e Fk(max\(\))g Fr(returns)h(a)f(v)o(ector)g(of)g(the)h
  1684. (maxim)o(um)g(v)m(alues)h(from)d(eac)o(h)i(column,)h(and)e(the)h
  1685. (second)g(call)113 2170 y(to)f Fk(max\(\))f Fr(returns)h(the)h(maxim)o
  1686. (um)f(v)m(alue)h(in)g(the)g(matrix.)0 2263 y Fo(Matrix)h(F)l(unctions:)
  1687. 23 b Fr(These)15 b(functions)h(op)q(erate)f(on)h(matrices)f(as)g(a)f
  1688. (single)j(en)o(tit)o(y)l(.)j(Some)15 b(examples)h(are:)113
  1689. 2381 y(balance)53 b(c)o(hol)122 b(det)138 b(eig)113 2437
  1690. y(hess)120 b(in)o(v)141 b(lu)164 b(norm)113 2494 y(pin)o(v)116
  1691. b(qr)159 b(rank)111 b(rcond)113 2550 y(reshap)q(e)51
  1692. b(solv)o(e)105 b(svd)134 b(symm)113 2607 y(factor)85
  1693. b(bac)o(ksub)42 b(issymm)960 2788 y(39)p eop
  1694. %%Page: 40 41
  1695. 40 40 bop 0 87 a Fo(Misc.)22 b(F)l(unctions:)h Fr(These)d(functions)g
  1696. (are)g(in)g(this)g(particular)g(category)f(simply)i(b)q(ecause)f(they)g
  1697. (don't)f(\014t)113 143 y(an)o(ywhere)d(else.)k(Some)c(examples)f(are:)
  1698. 113 266 y(system)65 b(getline)71 b(sho)o(w)103 b(who)113
  1699. 322 y(what)f(tic)151 b(to)q(c)139 b(prin)o(tf)113 379
  1700. y(format)67 b(write)100 b(read)115 b(readm)0 608 y Fp(8)69
  1701. b(Input)23 b(and)h(Output)0 739 y Fr(There)15 b(are)g(t)o(w)o(o)f(t)o
  1702. (yp)q(es)h(if)h(I/O)f(in)h(R)623 748 y(L)641 733 y(a)659
  1703. 739 y(B)23 b(.)55 872 y(1.)f(Ra)o(w)15 b(data,)f(suc)o(h)i(as)f
  1704. (matrices,)g(lists,)g(and)h(strings.)j(In)d(this)g(case)f(the)g
  1705. (formatting)f(is)i(irrelev)m(an)o(t.)55 965 y(2.)22 b(F)l(ormatted)13
  1706. b(I/O,)h(suc)o(h)g(as)g(data)f(from)g(other)g(programs,)g(and)h
  1707. (formatted)f(output)g(in)o(tended)j(for)d(rep)q(orts)113
  1708. 1022 y(and)j(suc)o(h.)0 1155 y(In)k(either)f(case)h(\014le)g(names,)f
  1709. (or)g(\014le-handles,)j(are)d(the)g(same.)32 b(A)19 b(\014le-handle)j
  1710. (is)d Fh(always)g Fr(a)g(string,)h(either)g(a)0 1212
  1711. y(string)15 b(constan)o(t,)f(a)h(string)g(v)m(ariable,)h(or)f(a)g
  1712. (string)g(expression.)21 b(F)l(or)14 b(example:)0 1345
  1713. y Fk(>)23 b(write)h(\("file.rd",)e(A\);)0 1458 y(>)h(f)h(=)g
  1714. ("file.rd";)e(write)i(\(f,)f(A\);)0 1571 y(>)g(write)h(\("file")f(+)g
  1715. (".rd",)g(A\);)0 1705 y Fr(are)15 b(all)h(equiv)m(alen)o(t.)0
  1716. 1791 y(There)f(are)g(three)g(sp)q(ecial)i(\014le-handles)h(in)e(R)788
  1717. 1800 y(L)805 1785 y(a)823 1791 y(B)23 b(;)15 b(they)g(are:)20
  1718. b Fk("stdin")p Fr(,)14 b Fk("stdout")p Fr(,)f(and)j Fk("stderr")p
  1719. Fr(.)0 1877 y Fk("stdin")h Fr(is)i(connected)g(to)f(R)534
  1720. 1886 y(L)551 1871 y(a)569 1877 y(B)8 b('s)18 b(standard)g(input,)i
  1721. (usually)f(the)g(k)o(eyb)q(oard.)29 b Fk("stdout")17
  1722. b Fr(is)i(connected)g(to)0 1933 y(R)26 1943 y(L)43 1927
  1723. y(a)61 1933 y(B)8 b('s)20 b(standard)g(output,)i(usually)g(the)f
  1724. (screen.)37 b(And)21 b Fk("stderr")f Fr(is)h(connected)g(to)g(the)f
  1725. (standard)h(error,)0 1990 y(again,)15 b(usually)h(the)f(screen.)0
  1726. 2076 y(Files)k(are)e(automatically)h(op)q(ened)h(b)o(y)f(the)g
  1727. (functions)g(that)f(p)q(erform)h(input)h(or)e(output.)27
  1728. b(In)19 b(most)e(cases)g(the)0 2132 y(\014les)f(will)h(automatically)f
  1729. (b)q(e)f(closed)i(after)d(the)h(function)h(has)g(completed)g(its)f
  1730. (task.)k(The)d(follo)o(wing)g(will)h(force)0 2188 y(a)e(\014le)h
  1731. (closure)g(after)e(their)i(task)e(is)i(complete:)21 b
  1732. Fk(rfile)p Fr(,)14 b Fk(load)p Fr(,)g Fk(read)p Fr(,)g(and)i
  1733. Fk(readm)p Fr(.)0 2274 y(Ho)o(w)o(ev)o(er,)d Fk(write)p
  1734. Fr(,)g Fk(writem)p Fr(,)g Fk(fprintf)p Fr(,)h(and)g Fk(getline)f
  1735. Fr(will)j(lea)o(v)o(e)f(their)f(\014les)i(op)q(en)f(after)e
  1736. (completion,)i(so)f(that)0 2331 y(they)h(ma)o(y)g(b)q(e)g(used)h
  1737. (subsequen)o(tly)h(without)e(complicated)h(\014le)h(p)q(ositioning)f
  1738. (op)q(erations.)0 2417 y(R)26 2427 y(L)43 2411 y(a)61
  1739. 2417 y(B)26 b(has)18 b(another)g(sp)q(ecial)i(t)o(yp)q(e)e(of)g
  1740. (\014le-handle.)31 b(When)18 b(a)g(string,)g(starting)g(with)g(a)g(`)p
  1741. Fk(|)p Fr(')f(is)i(used)g(as)f(a)f(\014le-)0 2473 y(handle,)f(a)f(pro)q
  1742. (cess)h(is)g(created.)k(Either)c(the)g(sub-pro)q(cess)g(inp72 1263 D 1196 1214 D 1171 1165 D 1189 1116 D
  1743. 1167 1067 D 1184 1018 D Z
  1744. 1166 2393 M 1145 2345 D 1145 2345 D Z
  1745. 1059 2105 M 1055 2099 D 1033 2049 D 993 2001 D 983 1951 D 947 1902 D
  1746. 957 1853 D 944 1804 D 962 1768 D Z
  1747. 1167 1067 M 1184 1018 D Z
  1748. 1187 2443 M 1166 2393 D 1171 2345 D 1147 2295 D 1147 2295 D 1147 2295 D
  1749. 1139 2246 D 1110 2197 D 1086 2148 D 1081 2140 D Z
  1750. 1037 1660 M 1040 1657 D 1061 1607 D 1129 1558 D 1132 1509 D 1196 1460 D
  1751. 1179 1411 D 1225 1362 D 1196 1313 D 1227 1263 D 1196 1214 D 1217 1165 D
  1752. 1189 1116 D 1206 1067 D 1184 1018 D 1200 968 D Z
  1753. 1187 2443 M 1166 2393 D 1166 2393 D Z
  1754. 1055 2099 M 1017 2049 D 993 2001 D 955 1951 D 947 1902 D 930 1853 D
  1755. 944 1804 D 944 1804 D 944 1804 D 960 1761 D Z
  1756. 1184 1018 M 1200 968 D Z
  1757. 1207 2492 M 1187 2443 D 1196 2393 D 1171 2345 D 1171 2345 D 1171 2345 D
  1758. 1170 2295 D 1139 2246 D 1122 2197 D 1086 2148 D Z
  1759. 1036 1668 M 1040 1657 D 1125 1607 D 1129 1558 D 1212 1509 D 1196 1460 D
  1760. 1259 1411 D 1225 1362 D 1265 1313 D 1227 1263 D 1251 1214 D 1217 1165 D
  1761. 1234 1116 D 1206 1067 D 1222 1018 D 1200 968 D 1216 919 D Z
  1762. 1207 2492 M 1187 2443 D 1187 2443 D Z
  1763. 1060 2107 M 1054 2099 D 1017 2049 D 981 2001 D 955 1951 D 937 1902 D
  1764. 930 1853 D 930 1853 D Z
  1765. 1200 968 M 1216 919 D Z
  1766. 1226 2541 M 1207 2492 D 1218 2443 D 1196 2393 D 1200 2345 D 1170 2295 D
  1767. 1161 2246 D 1122 2197 D 1100 2148 D 1073 2119 D Z
  1768. 1033 1700 M 1122 1657 D 1125 1607 D 1229 1558 D 1212 1509 D 1295 1460 D
  1769. 1259 1411 D 1311 1362 D 1265 1313 D 1294 1263 D 1251 1214 D 1268 1165 D
  1770. 1234 1116 D 1248 1067 D 1222 1018 D 1236 968 D 1216 919 D 1232 870 D Z
  1771. 1226 2541 M 1207 2492 D 1207 2492 D Z
  1772. 1054 2099 M 1054 2099 D Z
  1773. 981 2001 M 981 2001 D Z
  1774. 937 1902 M 937 1902 D Z
  1775. 1216 919 M 1232 870 D Z
  1776. 1244 2590 M 1226 2541 D 1240 2492 D 1218 2443 D 1227 2393 D 1200 2345 D
  1777. 1200 2345 D 1200 2345 D 1199 2295 D 1161 2246 D 1148 2197 D 1100 2148 D
  1778. 1078 2099 D 1063 2085 D Z
  1779. 1030 1748 M 1125 1706 D 1122 1657 D 1246 1607 D 1229 1558 D 1334 1509 D
  1780. 1295 1460 D 1364 1411 D 1311 1362 D 1347 1313 D 1294 1263 D 1312 1214 D
  1781. 1268 1165 D 1280 1116 D 1248 1067 D 1261 1018 D 1236 968 D 1251 919 D
  1782. 1232 870 D 1248 821 D Z
  1783. 1244 2590 M 1226 2541 D 1226 2541 D Z
  1784. 1232 870 M 1248 821 D Z
  1785. 1262 2639 M 1244 2590 D 1260 2541 D 1240 2492 D 1252 2443 D 1227 2393 D
  1786. 1233 2345 D 1199 2295 D 1195 2246 D 1148 2197 D 1136 2148 D 1078 2099 D
  1787. 1071 2049 D 1052 2034 D Z
  1788. 1032 1866 M 1049 1853 D 1030 1816 D Z
  1789. 1030 1801 M 1138 1755 D 1125 1706 D 1263 1657 D 1246 1607 D 1370 1558 D
  1790. 1334 1509 D 1419 1460 D 1364 1411 D 1407 1362 D 1347 1313 D 1365 1263 D
  1791. 1312 1214 D 1320 1165 D 1280 1116 D 1289 1067 D 1261 1018 D 1273 968 D
  1792. 1251 919 D 1266 870 D 1248 821 D 1264 772 D Z
  1793. 1262 2639 M 1244 2590 D 1244 2590 D Z
  1794. 1248 821 M 1264 772 D Z
  1795. 1280 2688 M 1262 2639 D 1278 2590 D 1260 2541 D 1274 2492 D 1252 2443 D
  1796. 1262 2393 D 1233 2345 D 1236 2295 D 1195 2246 D 1192 2197 D 1136 2148 D
  1797. 1135 2099 D 1071 2049 D 1071 2049 D 1089 2001 D 1039 1959 D Z
  1798. 1037 1945 M 1090 1902 D 1049 1853 D 1159 1804 D 1138 1755 D 1280 1706 D
  1799. 1263 1657 D 1401 1607 D 1370 1558 D 1470 1509 D 1419 1460 D 1471 1411 D
  1800. 1407 1362 D 1426 1313 D 1365 1263 D 1369 1214 D 1320 1165 D 1324 1116 D
  1801. 1289 1067 D 1298 1018 D 1273 968 D 1286 919 D 1266 870 D 1282 821 D
  1802. 1264 772 D 1280 723 D Z
  1803. 1280 2688 M 1262 2639 D 1262 2639 D Z
  1804. 1264 772 M 1280 723 D Z
  1805. 1280 2688 M 1296 2639 D 1278 2590 D 1294 2541 D 1274 2492 D 1287 2443 D
  1806. 1262 2393 D 1271 2345 D 1236 2295 D 1240 2246 D 1192 2197 D 1192 2197 D
  1807. 1195 2148 D 1135 2099 D 1135 2099 D 1152 2049 D 1089 2001 D 1141 1951 D
  1808. 1090 1902 D 1190 1853 D 1159 1804 D 1297 1755 D 1280 1706 D 1423 1657 D
  1809. 1401 1607 D 1511 1558 D 1470 1509 D 1530 1460 D 1471 1411 D 1489 1362 D
  1810. 1426 1313 D 1426 1313 D 1426 1313 D 1424 1263 D 1369 1214 D 1369 1214 D
  1811. 1369 1214 D 1365 1165 D 1324 1116 D 1327 1067 D 1298 1018 D Z
  1812. 1298 1018 M 1308 968 D 1286 919 D 1300 870 D 1282 821 D 1298 772 D
  1813. 1280 723 D 1280 723 D Z
  1814. 1280 2688 M 1280 2688 D Z
  1815. 1296 2639 M 1312 2590 D 1294 2541 D 1309 2492 D 1287 2443 D 1299 2393 D
  1816. 1271 2345 D 1280 2295 D 1240 2246 D 1248 2197 D 1195 2148 D 1213 2099 D
  1817. 1152 2049 D 1196 2001 D 1141 1951 D 1226 1902 D 1190 1853 D 1314 1804 D
  1818. 1297 1 @endspecial 703 2123 a Fr(Figure)16 b(4:)j(Example)d(3D)f(Plot)960
  1819. 2788 y(46)p eop
  1820. %%Page: 47 48
  1821. 47 47 bop 0 87 a Fk(//)23 b(sum)h(of)f(odd)h(harmonics)e(-)i(we)g(will)
  1822. f(demonstrate.)0 143 y(//)g(Start)h(up)f(a)h(plot)f(window...)0
  1823. 256 y(pstart\(2,2,)f("xwin"\);)0 369 y(//)h(Compute)g(the)h(1st)f(term)
  1824. g(in)h(the)g(Fourier)e(series)h(and)h(plot.)0 482 y(t)f(=)h
  1825. (\(0:10:.1\)';)0 539 y(y)f(=)h(sin)g(\(t\);)0 651 y(ptitle)f
  1826. (\("Fundamental)f(Frequency"\);)0 708 y(plwid\(10\);)0
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  2119. 717 2672 D 723 2672 D 728 2675 D
  2120. 730 2677 D 732 2682 D 732 2686 D
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  2122. 708 2697 D 703 2695 D Z 701 2686 M 703 2682 D
  2123. 710 2677 D 717 2675 D 726 2675 D
  2124. 730 2677 D Z 723 2664 M 728 2661 D 732 2657 D
  2125. 732 2650 D 730 2648 D 726 2648 D
  2126. 717 2650 D 701 2655 D Z 732 2653 M 730 2650 D
  2127. 726 2650 D 717 2653 D 701 2657 D
  2128. Z 717 2650 M 726 2646 D 730 2642 D 732 2637 D
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  2131. 701 2628 D Z 732 2632 M 728 2628 D 723 2628 D
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  2137. 703 2603 D 701 2601 D Z 732 2608 M 732 2588 D
  2138. Z 728 2539 M 728 2499 D Z 715 2539 M 715 2499 D Z 739 2439 M 737 2436 D
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  2144. 737 2417 D 732 2419 D 728 2423 D
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  2146. 717 2419 D 710 2419 D 706 2421 D
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  2158. Z 748 2319 M 701 2332 D Z 748 2316 M 701 2330 D Z 748 2325 M 748 2309 D
  2159. Z 701 2338 M 701 2323 D Z 748 2290 M 717 2298 D 708 2301 D
  2160. 703 2301 D 701 2298 D 701 2292 D
  2161. 706 2287 D 710 2285 D Z 748 2287 M 717 2296 D
  2162. 708 2298 D 703 2298 D 701 2296 D
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  2172. Z 732 2258 M 730 2263 D 723 2267 D 717 2269 D
  2173. 708 2269 D 703 2267 D Z 748 2214 M 717 2223 D
  2174. 708 2225 D 703 2225 D 701 2223 D
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  2177. 701 2221 D Z 748 2221 M 748 2211 D Z 748 2185 M 746 2187 D
  2178. 744 2185 D 746 2183 D 748 2185 D
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  2181. 703 2192 D 701 2190 D Z 732 2192 M 730 2190 D
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  2194. 686 2136 D Z 757 2116 M 750 2114 D 739 2111 D
  2195. 728 2111 D 717 2114 D 710 2116 D
  2196. 701 2121 D 692 2127 D S
  2197. /lw 1 def
  2198. @lwidth
  2199.  Z 272 769 M 225 769 D
  2200. Z 272 767 M 240 742 D Z 268 767 M 236 742 D Z 283 742 M 236 742 D
  2201. Z 269 775 M 272 767 D Z 280 748 M 285 736 D Z 222 775 M 228 762 D
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  2206. 278 699 D 281 703 D 281 709 D
  2207. 279 713 D 275 717 D 269 722 D
  2208. 261 723 D 257 723 D 251 722 D
  2209. 248 717 D 248 713 D Z 249 709 M 253 705 D
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  2213. 265 680 D Z 333 618 M 286 618 D Z 334 616 M 287 616 D
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  2263. 513 463 D 529 463 D 513 463 D
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  2276. Z 655 297 M 655 293 D 653 290 D 649 288 D
  2277. 645 288 D 640 290 D 633 297 D
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  2281. 614 288 D 619 286 D 624 286 D
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  2295. Z 704 294 M 658 294 D Z 704 294 M 661 317 D 675 284 D
  2296. Z 654 303 M 660 288 D Z 724 365 M 719 371 D 711 375 D
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  2300. 711 348 D 721 350 D 726 354 D
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  2314. 704 299 D 709 293 D 715 288 D
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  2317. 727 307 D 721 311 D 714 313 D
  2318. Z 750 301 M 746 305 D 740 309 D 735 311 D
  2319. 725 313 D 711 313 D 706 311 D
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  2373. 443 1238 D 445 1244 D Z 463 1238 M 460 1234 D
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  2381. 419 1232 D 418 1234 D 417 1238 D
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  2399. 1176 848 D 1177 848 D 1180 846 D
  2400. 1182 841 D 1182 833 D 1180 828 D
  2401. 1177 826 D 1173 823 D 1157 823 D
  2402. 1153 821 D 1151 819 D Z 1177 826 M 1157 826 D
  2403. 1153 823 D 1151 819 D 1151 817 D
  2404. Z 1173 826 M 1171 828 D 1169 841 D 1166 848 D
  2405. 1162 850 D 1157 850 D 1153 848 D
  2406. 1151 841 D 1151 835 D 1153 830 D
  2407. 1157 826 D Z 1169 841 M 1166 846 D 1162 848 D
  2408. 1157 848 D 1153 846 D 1151 841 D
  2409. Z 1198 766 M 1151 766 D Z 1198 763 M 1151 763 D Z 1184 750 M 1166 750 D
  2410. Z 1198 772 M 1198 737 D 1184 737 D 1198 739 D
  2411. Z 1176 763 M 1176 750 D Z 1151 772 M 1151 757 D Z 1182 712 M 1180 719 D
  2412. 1176 723 D 1169 725 D 1164 725 D
  2413. 1157 723 D 1153 719 D 1151 712 D
  2414. 1151 708 D 1153 701 D 1157 696 D
  2415. 1164 694 D 1169 694 D 1176 696 D
  2416. 1180 701 D 1182 708 D 1182 712 D
  2417. 1180 717 D 1176 721 D 1169 723 D
  2418. 1164 723 D 1157 721 D 1153 717 D
  2419. 1151 712 D Z 1151 708 M 1153 704 D 1157 699 D
  2420. 1164 696 D 1169 696 D 1176 699 D
  2421. 1180 704 D 1182 708 D Z 1182 677 M 1157 677 D
  2422. 1153 675 D 1151 668 D 1151 663 D
  2423. 1153 657 D 1157 652 D Z 1182 675 M 1157 675 D
  2424. 1153 672 D 1151 668 D Z 1182 652 M 1151 652 D
  2425. Z 1182 650 M 1151 650 D Z 1182 683 M 1182 675 D Z 1182 659 M 1182 650 D
  2426. Z 1151 652 M 1151 643 D Z 1182 628 M 1151 628 D Z 1182 625 M 1151 625 D
  2427. Z 1169 625 M 1176 623 D 1180 619 D 1182 614 D
  2428. 1182 608 D 1180 606 D 1177 606 D
  2429. 1176 608 D 1177 610 D 1180 608 D
  2430. Z 1182 635 M 1182 625 D Z 1151 635 M 1151 619 D Z 1198 590 M 1195 592 D
  2431. 1193 590 D 1195 588 D 1198 590 D
  2432. Z 1182 590 M 1151 590 D Z 1182 588 M 1151 588 D Z 1182 596 M 1182 588 D
  2433. Z 1151 596 M 1151 581 D Z 1169 568 M 1169 541 D 1173 541 D
  2434. 1177 543 D 1180 545 D 1182 550 D
  2435. 1182 556 D 1180 563 D 1176 568 D
  2436. 1169 570 D 1164 570 D 1157 568 D
  2437. 1153 563 D 1151 556 D 1151 552 D
  2438. 1153 545 D 1157 541 D Z 1169 543 M 1176 543 D
  2439. 1180 545 D Z 1182 556 M 1180 561 D 1176 565 D
  2440. 1169 568 D 1164 568 D 1157 565 D
  2441. 1153 561 D 1151 556 D Z 1182 523 M 1151 523 D
  2442. Z 1182 521 M 1151 521 D Z 1169 521 M 1176 519 D 1180 514 D
  2443. 1182 510 D 1182 503 D 1180 501 D
  2444. 1177 501 D 1176 503 D 1177 505 D
  2445. 1180 503 D Z 1182 530 M 1182 521 D Z 1151 530 M 1151 514 D
  2446. Z 1191 425 M 1198 423 D 1184 423 D 1191 425 D
  2447. 1195 429 D 1198 436 D 1198 443 D
  2448. 1195 450 D 1191 454 D 1186 454 D
  2449. 1182 452 D 1180 450 D 1177 445 D
  2450. 1173 432 D 1171 427 D 1166 423 D
  2451. Z 1186 454 M 1182 450 D 1180 445 D 1176 432 D
  2452. 1173 427 D 1171 425 D 1166 423 D
  2453. 1157 423 D 1153 427 D 1151 434 D
  2454. 1151 441 D 1153 447 D 1157 452 D
  2455. 1164 454 D 1151 454 D 1157 452 D
  2456. Z 1169 407 M 1169 381 D 1173 381 D 1177 383 D
  2457. 1180 385 D 1182 389 D 1182 396 D
  2458. 1180 403 D 1176 407 D 1169 410 D
  2459. 1164 410 D 1157 407 D 1153 403 D
  2460. 1151 396 D 1151 392 D 1153 385 D
  2461. 1157 381 D Z 1169 383 M 1176 383 D 1180 385 D
  2462. Z 1182 396 M 1180 400 D 1176 405 D 1169 407 D
  2463. 1164 407 D 1157 405 D 1153 400 D
  2464. 1151 396 D Z 1182 363 M 1151 363 D Z 1182 360 M 1151 360 D
  2465. Z 1169 360 M 1176 358 D 1180 354 D 1182 349 D
  2466. 1182 343 D 1180 341 D 1177 341 D
  2467. 1176 343 D 1177 345 D 1180 343 D
  2468. Z 1182 369 M 1182 360 D Z 1151 369 M 1151 354 D Z 1198 325 M 1195 327 D
  2469. 1193 325 D 1195 323 D 1198 325 D
  2470. Z 1182 325 M 1151 325 D Z 1182 323 M 1151 323 D Z 1182 331 M 1182 323 D
  2471. Z 1151 331 M 1151 316 D Z 1169 302 M 1169 276 D 1173 276 D
  2472. 1177 278 D 1180 280 D 1182 285 D
  2473. 1182 291 D 1180 298 D 1176 302 D
  2474. 1169 305 D 1164 305 D 1157 302 D
  2475. 1153 298 D 1151 291 D 1151 287 D
  2476. 1153 280 D 1157 276 D Z 1169 278 M 1176 278 D
  2477. 1180 280 D Z 1182 291 M 1180 296 D 1176 300 D
  2478. 1169 302 D 1164 302 D 1157 300 D
  2479. 1153 296 D 1151 291 D Z 1177 240 M 1182 238 D
  2480. 1173 238 D 1177 240 D 1