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b(tag)e(placemen)n(t)39 b(.)i(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h (.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)132 b(7)863 2787 y(2.9)84 b(V)-7 b(ertical)28 b(spacing)e(and)i(page)e(breaks)h(in) h(m)n(ultiline)g(displa)n(ys)75 b(.)42 b(.)f(.)h(.)g(.)f(.)132 b(7)863 2889 y(2.10)42 b(T)-7 b(extual)28 b(in)n(terjections)f(within)h (a)f(displa)n(y)g(.)41 b(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.) h(.)g(.)f(.)132 b(8)863 2991 y(2.11)42 b(Equation)27 b(n)n(um)n(b)r(ering)58 b(.)42 b(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.) h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)132 b(8)739 3178 y Fm(3)76 b(Miscellaneous)30 b(mathematics)f(features)j (\()p Fh(amsmath)e Fm(pac)m(k)-5 b(age\))428 b(9)863 3280 y Fp(3.1)84 b(Matrices)38 b(.)k(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h (.)f(.)h(.)g(.)f(.)132 b(9)863 3382 y(3.2)84 b(Math)28 b(spacing)f(commands)i(.)41 b(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h (.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(10)863 3484 y(3.3)84 b(Ov)n(er)27 b(and)g(under)g(arro)n(ws)g(.)42 b(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f (.)h(.)f(.)h(.)g(.)f(.)90 b(11)863 3586 y(3.4)84 b(Dots)52 b(.)42 b(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.) h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(11)863 3689 y(3.5)84 b(Non)n(breaking)26 b(dashes)79 b(.)42 b(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(11)863 3791 y(3.6)84 b(Accen)n(ts)28 b(in)g(math)78 b(.)42 b(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f (.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.) 90 b(12)863 3893 y(3.7)84 b(Ro)r(ots)75 b(.)41 b(.)h(.)g(.)f(.)h(.)f(.) h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(12)863 3995 y(3.8)84 b(Bo)n(xed)27 b(form)n(ulas)46 b(.)41 b(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h (.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) f(.)90 b(13)863 4097 y(3.9)84 b(Extensible)28 b(arro)n(ws)f(.)42 b(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(13)863 4199 y(3.10)42 b(A\016xing)28 b(sym)n(b)r(ols)f(to)g(other)g(sym)n(b)r(ols)81 b(.)42 b(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.) 90 b(13)863 4301 y(3.11)42 b(F)-7 b(ractions)27 b(and)g(related)g (constructions)38 b(.)k(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f (.)h(.)g(.)f(.)90 b(13)863 4403 y(3.12)42 b(Con)n(tin)n(ued)28 b(fractions)c(.)41 b(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.) h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(14)863 4505 y(3.13)42 b(Smash)28 b(options)82 b(.)41 b(.)h(.)f(.)h(.)g(.)f(.)h (.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.) h(.)g(.)f(.)90 b(15)863 4607 y(3.14)42 b(Delimiters)h(.)f(.)f(.)h(.)f (.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.) g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(15)739 4794 y Fm(4)76 b(Op)s(erator)32 b(names)f(\()p Fh(amsopn)p Fm(,)e Fh(amsmath)g Fm(pac)m(k)-5 b(ages\))849 b(17)863 4896 y Fp(4.1)84 b(De\014ning)28 b(new)g(op)r(erator)e(names)62 b(.)42 b(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.) h(.)g(.)f(.)90 b(17)863 4998 y(4.2)84 b Fh(\\mod)26 b Fp(and)i(its)g(relativ)n(es)21 b(.)42 b(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(18)p eop %DVIPSSectionPage: 3 3 2 bop 291 282 a Fo(CONTENTS)2394 b Fp(iii)291 515 y Fm(5)76 b(The)32 b Fh(\\text)e Fm(command)g(\()p Fh(amstext)p Fm(,)e Fh(amsmath)h Fm(pac)m(k)-5 b(ages\))632 b(18)291 717 y(6)76 b(The)32 b Fh(\\boldsymbol)27 b Fm(command)j(\()p Fh(amsbsy)p Fm(,)f Fh(amsmath)g Fm(pac)m(k)-5 b(ages\))414 b(18)291 918 y(7)76 b(In)m(tegrals)32 b(and)g(sums)e(\()p Fh(amsmath)p Fm(,)f Fh(amsintx)g Fm(pac)m(k)-5 b(ages\))689 b(19)415 1029 y Fp(7.1)84 b(Multiple)28 b(in)n(tegral)f(signs)54 b(.)41 b(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.) f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(19)415 1140 y(7.2)84 b(Multiline)29 b(subscripts)e(and)g(sup)r(erscripts)42 b(.)g(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(19)415 1251 y(7.3)84 b(The)28 b Fh(\\sideset)c Fp(command)34 b(.)42 b(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.) h(.)f(.)h(.)g(.)f(.)h(.)90 b(20)415 1362 y(7.4)84 b(The)28 b Fh(amsintx)c Fp(pac)n(k)-5 b(age)82 b(.)41 b(.)h(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(20)291 1563 y Fm(8)76 b(Comm)m(utativ)m(e)30 b(diagrams)g(\()p Fh(amscd)g Fm(pac)m(k)-5 b(age\))994 b(20)291 1765 y(9)76 b(Using)31 b(math)g(fon)m(ts)1924 b(21)415 1875 y Fp(9.1)84 b(In)n(tro)r(duction)25 b(.)42 b(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.) f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f (.)h(.)90 b(21)415 1986 y(9.2)84 b(Recommended)28 b(use)f(of)h(math)f (fon)n(t)h(commands)78 b(.)42 b(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h (.)90 b(21)291 2188 y Fm(10)28 b(Theorems)i(and)j(related)e(structures) i(\()p Fh(amsthm)c Fm(pac)m(k)-5 b(age\))554 b(22)415 2299 y Fp(10.1)42 b(In)n(tro)r(duction)25 b(.)42 b(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.) h(.)f(.)h(.)g(.)f(.)h(.)90 b(22)415 2409 y(10.2)42 b(The)28 b Fh(\\newtheorem)23 b Fp(command)32 b(.)42 b(.)f(.)h(.)g(.)f(.)h(.)f (.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(23)415 2520 y(10.3)42 b(Num)n(b)r(ering)28 b(mo)r(di\014cations)82 b(.)41 b(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.) f(.)h(.)g(.)f(.)h(.)90 b(23)415 2631 y(10.4)42 b(Changing)27 b(st)n(yles)g(for)g(theorem-lik)n(e)f(en)n(vironmen)n(ts)20 b(.)42 b(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(24)415 2742 y(10.5)42 b(Pro)r(ofs)52 b(.)42 b(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.) h(.)f(.)h(.)g(.)f(.)h(.)90 b(25)291 2944 y Fm(A)52 b(Installation)31 b(instructions)1646 b(27)415 3054 y Fp(A.1)64 b(In)n(tro)r(duction)25 b(.)42 b(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.) h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(27)415 3165 y(A.2)64 b(Putting)28 b(\014les)f(in)h(a)f(suitable)h (place)f(on)g(y)n(our)f(system)60 b(.)41 b(.)h(.)f(.)h(.)f(.)h(.)g(.)f (.)h(.)90 b(27)415 3276 y(A.3)64 b(T)-7 b(esting)85 b(.)42 b(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f (.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(27)415 3387 y(A.4)64 b(Extra)26 b(math)i(fon)n(ts)47 b(.)41 b(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.) g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(27)415 3498 y(A.5)64 b(Memory)27 b(requiremen)n(ts)72 b(.)41 b(.)h(.)f(.)h(.)f(.)h (.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.) 90 b(27)415 3609 y(A.6)64 b(Files)28 b(included)g(in)g(this)g (distribution)41 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f (.)h(.)g(.)f(.)h(.)90 b(28)291 3810 y Fm(B)56 b(Error)32 b(messages)d(and)k(output)f(problems)1097 b(29)415 3921 y Fp(B.1)67 b(General)27 b(remarks)73 b(.)41 b(.)h(.)g(.)f(.)h(.)f(.)h (.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) f(.)h(.)90 b(29)415 4032 y(B.2)67 b(Error)25 b(messages)60 b(.)42 b(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.) h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(30)415 4143 y(B.3)67 b(W)-7 b(rong)27 b(output)33 b(.)41 b(.)h(.)f(.)h(.)g(.)f (.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.) f(.)h(.)g(.)f(.)h(.)90 b(34)291 4344 y Fm(C)55 b(Other)32 b(useful)f(items)e(for)j(mathematical)e(do)s(cumen)m(ts)642 b(35)415 4455 y Fp(C.1)66 b(AMS)28 b(do)r(cumen)n(tclasses)f(\()p Fh(amsart)p Fp(,)e Fh(amsbook)p Fp(,)g Fh(amsproc)p Fp(\))k(.)41 b(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(35)415 4566 y(C.2)66 b(Extra)26 b(math)i(fon)n(ts)g(\(the)g(AMSF)-7 b(on)n(ts)28 b(collection\))g(.)42 b(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(36)415 4677 y(C.3)66 b(Syn)n(tax)27 b(c)n(hec)n(king)g(\(the)h Fh(syntonly)c Fp(pac)n(k)-5 b(age\))33 b(.)42 b(.)f(.)h(.)g(.)f(.)h(.)f (.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(36)415 4788 y(C.4)66 b(V)-7 b(erbatim)28 b(and)f(commen)n(ts)g(\(the)i Fh(verbatim)24 b Fp(pac)n(k)-5 b(age\))53 b(.)42 b(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(36)415 4899 y(C.5)66 b(Comm)n(utativ)n(e)31 b(diagrams)f(and)i(other) f(diagrams)g(\(pac)n(k)-5 b(ages)30 b Fh(diagram)p Fp(,)606 4998 y Fh(xypic)p Fp(,)c Fh(pstricks)p Fp(\))21 b(.)41 b(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f (.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)90 b(36)p eop %DVIPSSectionPage: 4 4 3 bop 739 282 a Fp(iv)2396 b Fo(CONTENTS)739 515 y Fm(D)51 b(Where)32 b(to)g(\014nd)f(other)h(information)1286 b(36)863 615 y Fp(D.1)63 b(T)-7 b(ec)n(hnical)27 b(notes)51 b(.)41 b(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.) f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(37)863 715 y(D.2)63 b(Di\013erences)22 b(b)r(et)n(w)n(een)g Fj(A)1837 732 y(M)1926 715 y(S)p Fp(-L)2026 698 y Fi(A)2063 715 y Fp(T)2109 732 y(E)2155 715 y(X)g(v)n(ersion)e(1.1)h(and)g Fj(A)2850 732 y(M)2940 715 y(S)p Fp(-L)3040 698 y Fi(A)3077 715 y Fp(T)3123 732 y(E)3169 715 y(X)h(v)n(er-)1054 814 y(sion)27 b(1.2)73 b(.)42 b(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f (.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.) g(.)f(.)90 b(37)739 997 y Fm(E)61 b(Getting)32 b(help)2115 b(37)863 1096 y Fp(E.1)69 b(F)-7 b(urther)28 b(information)78 b(.)42 b(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)90 b(37)739 1279 y Fm(Bibliograph)m(y) 2233 b(38)739 1462 y(Index)2533 b(39)p eop %DVIPSSectionPage: 5 5 4 bop 291 282 a Fo(WHA)-6 b(T)23 b(IS)i(`)p Fg(A)690 296 y(M)765 282 y(S)p Fo(-L)851 271 y Ff(A)884 282 y Fo(T)923 296 y(E)962 282 y(X')8 b(?)2035 b Fp(v)291 786 y Fn(What)37 b(is)g(`)p Fe(A)821 809 y(M)943 786 y(S)p Fn(-L)1076 764 y Fd(A)1120 786 y Fn(T)1179 809 y(E)1240 786 y(X',)h(and)g(wh)m(y)g(w)m(ould)f(an)m(y)m(one)h(w)m(an)m(t)f(to)g (use)291 903 y(it?)291 1124 y Fm(What)32 b(is)f(`)p Fl(A)741 1142 y(M)843 1124 y(S)p Fm(-L)956 1107 y Fk(A)998 1124 y Fm(T)1048 1142 y(E)1099 1124 y(X')11 b(?)366 1269 y Fp(The)38 b(name)f Fj(A)830 1287 y(M)920 1269 y(S)p Fp(-L)1020 1252 y Fi(A)1057 1269 y Fp(T)1103 1287 y(E)1149 1269 y(X)h(is)f(used)h(for)f(con)n(v)n(enience)g(to)g(describ)r(e)g(a)h(set) f(of)h(lo)r(osely)291 1368 y(related)18 b(\014les)g(that)h(are)f (distributed)h(together)e(b)n(y)i(the)g(American)f(Mathematical)g(So)r (ciet)n(y)-7 b(.)291 1468 y(Basically)33 b(they)i(ma)n(y)f(b)r(e)h (describ)r(ed)f(as)g(miscellaneous)g(enhancemen)n(ts)g(to)h(L)2830 1451 y Fi(A)2867 1468 y Fp(T)2913 1486 y(E)2958 1468 y(X)g(for)291 1568 y Fc(sup)l(erior)27 b(information)i(structur)l(e)c (of)j(mathematic)l(al)h(do)l(cuments)i Fp(and)24 b Fc(sup)l(erior)k (printe)l(d)291 1667 y(output)p Fp(.)34 b(Because)20 b Fj(A)941 1685 y(M)1031 1667 y(S)p Fp(-L)1131 1650 y Fi(A)1168 1667 y Fp(T)1214 1685 y(E)1259 1667 y(X)i(is)f(an)g (extension)g(for)g(L)2033 1650 y Fi(A)2070 1667 y Fp(T)2116 1685 y(E)2162 1667 y(X,)i(whic)n(h)e(in)h(turn)f(is)g(a)g(`macro)291 1767 y(pac)n(k)-5 b(age')24 b(for)h(the)h(T)933 1785 y(E)979 1767 y(X)g(t)n(yp)r(esetting)g(program,)e(it)j(follo)n(ws)d (that)i(in)g(order)f(to)g(use)h(an)n(y)f(of)291 1867 y(the)j(pieces)f(of)g Fj(A)820 1884 y(M)910 1867 y(S)p Fp(-L)1010 1850 y Fi(A)1047 1867 y Fp(T)1093 1884 y(E)1139 1867 y(X)h(y)n(ou)f(need)g(to)h(ha)n(v)n(e)e(T)1918 1884 y(E)1965 1867 y(X)h(and)h(L)2238 1850 y Fi(A)2275 1867 y Fp(T)2321 1884 y(E)2367 1867 y(X)g(installed)f(\014rst.)415 1972 y(L)437 1955 y Fi(A)474 1972 y Fp(T)520 1990 y(E)566 1972 y(X)c(b)n(y)f(itself)h(do)r(es)f(a)g(rather)f(go)r(o)r(d)h(job)g (of)g(t)n(yp)r(esetting)h(mathematics,)g(compared)291 2071 y(to)33 b(non-T)606 2089 y(E)651 2071 y(X-based)g(soft)n(w)n(are;) h(it)f(do)r(esn't)g(add)g(m)n(uc)n(h,)i(ho)n(w)n(ev)n(er,)d(to)h(the)g (basic)g(set)g(of)291 2171 y(mathematical)27 b(capabilities)g(that)h (it)g(adopted)f(from)g(the)h(Plain)f(T)2430 2189 y(E)2476 2171 y(X)h(macro)f(pac)n(k)-5 b(age.)415 2276 y(A)n(t)19 b(the)g(same)f(time)h(that)g(L)1232 2259 y Fi(A)1269 2276 y Fp(T)1315 2294 y(E)1360 2276 y(X)g(w)n(as)f(b)r(eing)g(dev)n (elop)r(ed)h(b)n(y)f(Leslie)g(Lamp)r(ort)g(\(roughly)291 2376 y(1982{1986\),)h(the)j(American)g(Mathematical)f(So)r(ciet)n(y)h (w)n(as)f(thro)n(wing)g(its)h(resources)e(in)n(to)291 2475 y(the)29 b(dev)n(elopmen)n(t)g(of)h(a)f(di\013eren)n(t)g(macro)g (pac)n(k)-5 b(age)28 b(kno)n(wn)g(as)h Fj(A)2399 2493 y(M)2489 2475 y(S)p Fp(-T)2613 2493 y(E)2659 2475 y(X,)i(written)e(b)n (y)291 2575 y(Mic)n(hael)22 b(Spiv)-5 b(ak.)35 b(By)22 b(1987)f(or)h(so)g(it)h(b)r(ecame)f(eviden)n(t)h(that)g Fj(A)2284 2593 y(M)2374 2575 y(S)p Fp(-T)2498 2593 y(E)2544 2575 y(X)g(and)f(L)2807 2558 y Fi(A)2844 2575 y Fp(T)2890 2593 y(E)2936 2575 y(X)h(had)291 2674 y(complemen)n(tary)h(feature)i (sets:)35 b Fj(A)1393 2692 y(M)1483 2674 y(S)p Fp(-T)1607 2692 y(E)1653 2674 y(X)27 b(fo)r(cused)e(on)h(the)g(t)n(yp)r(esetting)g (of)g(math)g(for-)291 2774 y(m)n(ulas)g(and)i(on)f(\014ne-tuning)g(t)n (ypically)g(done)g(b)n(y)g(publishers,)g(and)g(w)n(as)g(relativ)n(ely)f (w)n(eak)291 2874 y(in)35 b(other)g(areas)f(\(for)h(example)g(no)g (automatic)f(n)n(um)n(b)r(ering)h(or)g(cross-reference)d(facili-)291 2973 y(ties\);)25 b(L)518 2956 y Fi(A)555 2973 y Fp(T)601 2991 y(E)647 2973 y(X)f(fo)r(cused)f(on)g(do)r(cumen)n(t)h(structure)f (and)g(logical)g(markup)f(of)i(text,)h(and)e(had)291 3073 y(a)j(comparativ)n(ely)f(limited)j(set)f(of)g(features)f(for)h (dealing)f(with)h(math)g(form)n(ula)g(con)n(ten)n(ts.)291 3173 y(This)21 b(situation)g(led)g(to)g(dissatisfaction)g(among)f(b)r (oth)i Fj(A)2072 3190 y(M)2162 3173 y(S)p Fp(-T)2286 3190 y(E)2332 3173 y(X)f(and)g(L)2592 3156 y Fi(A)2629 3173 y Fp(T)2675 3190 y(E)2721 3173 y(X)h(users)e(who)291 3272 y(sa)n(w)j(desirable)h(features)h(tan)n(talizingly)f(out)h(of)g (reac)n(h)e(in)i(the)h(other)e(macro)g(pac)n(k)-5 b(age.)34 b(So)291 3372 y(the)24 b(American)f(Mathematical)g(So)r(ciet)n(y)h(lo)r (ok)n(ed)f(in)n(to)g(the)h(question)g(of)f(pro)r(ducing)g(some)291 3471 y(sort)k(of)i(com)n(bination)f(of)h(the)g(t)n(w)n(o)f(macro)f(pac) n(k)-5 b(ages)27 b(that)i(w)n(ould)g(b)r(etter)g(serv)n(e)e(mathe-)291 3571 y(maticians)e(in)i(their)f(writing)g(tasks.)36 b(The)26 b(decision)g(that)g(w)n(as)g(ev)n(en)n(tually)f(tak)n(en)h(w)n(as)f(to) 291 3671 y(graft)k(the)i(mathematical)f(capabilities)g(of)g Fj(A)1750 3689 y(M)1840 3671 y(S)p Fp(-T)1964 3689 y(E)2010 3671 y(X)h(on)n(to)f(the)h(base)f(sto)r(c)n(k)f(of)i(L)2964 3654 y Fi(A)3001 3671 y Fp(T)3047 3689 y(E)3093 3671 y(X)291 3770 y(through)k(an)g(extension)g(pac)n(k)-5 b(age:)52 b Fj(A)1521 3788 y(M)1611 3770 y(S)p Fp(-L)1711 3753 y Fi(A)1748 3770 y Fp(T)1794 3788 y(E)1840 3770 y(X.)61 b(Most)36 b(of)g(the)g(programming)d(w)n(ork)291 3870 y(w)n(as)25 b(done)h(b)n(y)h(F)-7 b(rank)25 b(Mittelbac)n(h)i(and) f(Rainer)g(Sc)n(h\177)-42 b(opf)27 b(in)f(1989{1990)c(and)27 b(v)n(ersion)e(1.0)291 3970 y(of)i Fj(A)437 3987 y(M)527 3970 y(S)p Fp(-L)627 3953 y Fi(A)664 3970 y Fp(T)710 3987 y(E)756 3970 y(X)h(w)n(as)e(released)h(in)g(mid-1990.)291 4151 y Fm(Wh)m(y)32 b(w)m(ould)f(a)i(L)902 4134 y Fk(A)944 4151 y Fm(T)994 4169 y(E)1045 4151 y(X)f(user)f(w)m(an)m(t)j(to)d(b)s (other)h(with)f Fl(A)2289 4169 y(M)2392 4151 y(S)p Fm(-L)2505 4134 y Fk(A)2547 4151 y Fm(T)2597 4169 y(E)2648 4151 y(X?)322 4296 y Fp(If)g(y)n(ou)g(are)f(just)i(starting)e(out)h(as)g(a)g (L)1544 4279 y Fi(A)1581 4296 y Fp(T)1627 4314 y(E)1672 4296 y(X)h(user,)f(y)n(ou'll)g(probably)f(ha)n(v)n(e)g(to)h(tak)n(e)g (our)291 4395 y(w)n(ord)26 b(for)h(this)h(\(or)f(the)h(w)n(ord)e(of)i (friends)g(and)f(colleagues\),)f(but:)415 4500 y(If)36 b(y)n(our)e(writing)h(con)n(tains)g(a)g(signi\014can)n(t)g(prop)r (ortion)f(of)h(mathematics,)i(and)f(y)n(ou)291 4600 y(care)e(ab)r(out)i (the)g(qualit)n(y)f(of)g(the)h(prin)n(ted)f(results,)j(then)e(so)r (oner)e(or)h(later)f(y)n(ou'll)h(\014nd)291 4700 y(shortcomings)30 b(in)i(standard)e(L)1272 4683 y Fi(A)1309 4700 y Fp(T)1355 4717 y(E)1401 4700 y(X)i(and)g(w)n(an)n(t)f(to)h(remedy)f(them.)50 b(Chances)31 b(are)g(that)291 4799 y(at)i(least)g(the)g(\014rst)g(few)h (of)f(the)h(shortcomings)d(y)n(ou)i(encoun)n(ter)f(will)i(b)r(e)g(ones) e(that)i(are)291 4899 y(already)d(addressed)g(b)n(y)h(an)g Fj(A)1265 4917 y(M)1355 4899 y(S)p Fp(-L)1455 4882 y Fi(A)1492 4899 y Fp(T)1538 4917 y(E)1584 4899 y(X)h(pac)n(k)-5 b(age.)50 b(If)33 b(y)n(ou)e(w)n(an)n(t)h(to)h(ha)n(v)n(e)e(maxim)n(um) 291 4998 y(mathematical)c(t)n(yp)r(esetting)h(p)r(o)n(w)n(er)e(ready)h (at)h(hand,)g(rather)f(than)g(stop)h(to)g(cast)f(ab)r(out)p eop %DVIPSSectionPage: 6 6 5 bop 739 282 a Fp(vi)2012 b Fo(WHA)-6 b(T)24 b(IS)g(`)p Fg(A)3217 296 y(M)3292 282 y(S)p Fo(-L)3378 271 y Ff(A)3411 282 y Fo(T)3450 296 y(E)3490 282 y(X')8 b(?)739 515 y Fp(for)21 b(a)h(solution)f(whenev)n(er)g(y)n(ou)g(run)g(in)n(to)h(some) f(un)n(usual)h(demand)f(in)i(y)n(our)d(writing,)j(then)739 615 y Fj(A)791 633 y(M)881 615 y(S)p Fp(-L)981 598 y Fi(A)1018 615 y Fp(T)1064 633 y(E)1109 615 y(X)28 b(will)g(go)f(a)g (long)g(w)n(a)n(y)f(to)n(w)n(ard)g(meeting)i(y)n(our)e(needs.)863 715 y(If)h(y)n(ou)e(are)g(a)h(long-time)f(L)1694 698 y Fi(A)1731 715 y Fp(T)1777 732 y(E)1823 715 y(X)i(user)e(and)h(ha)n(v) n(e)f(lots)h(of)g(mathematics)g(in)g(what)g(y)n(ou)739 814 y(write,)k(then)h(y)n(ou)e(ma)n(y)g(recognize)f(solutions)h(for)h (some)f(familiar)g(problems)h(in)g(this)g(list)739 914 y(of)d Fj(A)885 932 y(M)975 914 y(S)p Fp(-L)1075 897 y Fi(A)1112 914 y Fp(T)1158 932 y(E)1204 914 y(X)h(features:)863 1080 y Fj(\017)41 b Fp(A)29 b(con)n(v)n(enien)n(t)e(w)n(a)n(y)g(to)h (de\014ne)g(new)h(`op)r(erator)d(name')i(commands)g(analogous)d(to)946 1179 y Fh(\\sin)k Fp(and)g Fh(\\lim)p Fp(,)g(including)h(prop)r(er)f (side)h(spacing)f(and)h(automatic)f(selection)g(of)946 1279 y(the)f(correct)f(fon)n(t)g(st)n(yle)g(and)h(size)f(\(ev)n(en)h (when)f(used)h(in)g(sub-)f(or)g(sup)r(erscripts\).)863 1445 y Fj(\017)41 b Fp(Multiple)27 b(substitutes)f(for)f(the)h Fh(eqnarray)d Fp(en)n(vironmen)n(t)h(to)i(mak)n(e)f(v)-5 b(arious)24 b(kinds)946 1545 y(of)k(equation)f(arrangemen)n(ts)e (easier)i(to)g(write.)863 1711 y Fj(\017)41 b Fp(Equation)26 b(n)n(um)n(b)r(ers)f(automatically)h(adjust)g(up)h(or)e(do)n(wn)h(to)g (a)n(v)n(oid)f(o)n(v)n(erprin)n(ting)946 1810 y(on)j(the)g(equation)f (con)n(ten)n(ts)g(\(unlik)n(e)g Fh(eqnarray)p Fp(\).)863 1976 y Fj(\017)41 b Fp(Spacing)26 b(around)e(equals)h(signs)g(matc)n (hes)g(the)h(normal)f(spacing)f(in)i(the)g Fh(equation)946 2076 y Fp(en)n(vironmen)n(t)h(\(unlik)n(e)h Fh(eqnarray)p Fp(\).)863 2242 y Fj(\017)41 b Fp(A)30 b(w)n(a)n(y)d(to)i(pro)r(duce)f (m)n(ultiline)h(subscripts)g(as)f(are)f(often)i(used)g(with)g (summation)946 2342 y(or)e(pro)r(duct)h(sym)n(b)r(ols.)863 2508 y Fj(\017)41 b Fp(An)25 b(easy)f(w)n(a)n(y)f(to)i(substitute)g(a)f (v)-5 b(arian)n(t)24 b(equation)g(n)n(um)n(b)r(er)g(for)g(a)g(giv)n(en) g(equation)946 2607 y(instead)k(of)f(the)h(automatically)f(supplied)h (n)n(um)n(b)r(er.)863 2773 y Fj(\017)41 b Fp(An)26 b(easy)f(w)n(a)n(y)f (to)i(pro)r(duce)f(sub)r(ordinate)g(equation)f(n)n(um)n(b)r(ers)h(of)h (the)g(form)f(\(1.3a\))946 2873 y(\(1.3b\))j(\(1.3c\))f(for)g(selected) h(groups)e(of)h(equations.)863 3039 y Fj(\017)41 b Fp(A)22 b Fh(\\boldsymbol)16 b Fp(command)21 b(for)f(prin)n(ting)h(b)r(old)g(v) n(ersions)e(of)i(individual)g(sym)n(b)r(ols,)946 3139 y(including)28 b(things)g(lik)n(e)f Fj(1)h Fp(and)f(lo)n(w)n(ercase)e (Greek)i(letters.)863 3305 y Fj(\017)41 b Fp(An)33 b Fh(amsthm)c Fp(pac)n(k)-5 b(age)30 b(that)i(pro)n(vides)f(a)g(useful)i Fh(proof)c 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b(equations)h(with)f(alignmen)m(t)291 914 y Fq(Lik)n(e)25 b Fk(multline)p Fq(,)e(the)k Fk(split)d Fq(en)n(vironmen)n(t)h(is)h(for)f Fi(single)33 b Fq(equations)26 b(that)g(are)f(to)r(o)h(long)291 1013 y(to)36 b(\014t)h(on)f(one)g (line)h(and)f(hence)h(m)n(ust)g(b)r(e)g(split)f(in)n(to)h(m)n(ultiple)g (lines.)63 b(Unlik)n(e)37 b Fk(mult-)291 1113 y(line)p Fq(,)28 b(ho)n(w)n(ev)n(er,)h(the)h Fk(split)e Fq(en)n(vironmen)n(t)h (pro)n(vides)f(for)h(alignmen)n(t)h(among)e(the)j(split)291 1213 y(lines,)d(using)f Fk(&)h Fq(to)g(mark)f(alignmen)n(t)h(p)r(oin)n (ts,)g(as)f(usual.)38 b(In)28 b(addition,)g(unlik)n(e)g(the)g(other)291 1312 y Fk(amsmath)k Fq(equation)j(structures,)h(the)f Fk(split)f Fq(en)n(vironmen)n(t)g(pro)n(vides)g(no)g(n)n(um)n(b)r (ering,)291 1412 y(b)r(ecause)k(it)h(is)f(in)n(tended)h(to)f(b)r(e)h (used)g(only)f(inside)g(some)g(other)g(displa)n(y)n(ed)g(equation)291 1512 y(structure,)26 b(usually)f(an)h Fk(equation)p Fq(,)d Fk(align)p Fq(,)i(or)g Fk(gather)f 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Fg(h)1958 2127 y Fq(\()p Fe(n)h Fm(\000)f Fe(l)r Fq(\))2201 2093 y Fl(2)2256 2127 y Fm(\000)2382 2019 y Fd(p)2339 2048 y Fg(X)2342 2225 y Fd(j)s Fl(=1)2459 2127 y Fq(\()p Fe(n)2541 2139 y Fd(i)2587 2127 y Fm(\000)g Fe(l)2695 2139 y Fd(i)2723 2127 y Fq(\))2755 2093 y Fl(2)2792 2035 y Fg(i)2832 2127 y Fe(:)291 1987 y Fq(\(2.11\))291 2362 y Fk(\\begin{equation)o(}\\l)o (ab)o(el)o({e:)o(ba)o(rwq)o(}\\)o(beg)o(in)o({s)o(pli)o(t})291 2462 y(H_c&=\\frac{1}{2)o(n})37 b(\\sum^n_{l=0}\(-1\)^)o({l)o(}\()o (n-{)o(l})o(\)^{)o(p-)o(2})291 2562 y(\\sum_{l)j(_1+\\dots+)g(l)j (_p=l}\\prod^p_{i=1)o(})37 b(\\binom{n_i}{l)i(_i}\\\\)291 2661 y(&\\quad\\cdot[\(n-)o(l)f(\)-\(n_i-l)i(_i\)]^{n_i-l)f(_i}\\cdot) 291 2761 y(\\Bigl[\(n-l)g(\)^2-\\sum^p_{j=1})o(\(n_)o(i-)o(l)f (_i\)^2\\Bigr].)291 2861 y(\\end{split}\\end)o({eq)o(ua)o(ti)o(on})291 3012 y Fn(2.5)94 b(Equation)32 b(groups)f(without)h(alignmen)m(t)291 3151 y Fq(The)20 b Fk(gather)e Fq(en)n(vironmen)n(t)i(is)g(used)h(for)f (a)g(group)g(of)g(consecutiv)n(e)g(equations)f(when)i(there)291 3251 y(is)k(no)g(alignmen)n(t)g(desired)g(among)f(them;)j(eac)n(h)d (one)h(is)h(cen)n(tered)f(separately)e(within)k(the)291 3351 y(text)h(width)g(\(see)f(T)-7 b(able)28 b(2.1\).)291 3510 y Fn(2.6)94 b(Equation)32 b(groups)f(with)h(m)m(utual)f(alignmen)m (t)291 3650 y Fq(The)e Fk(align)e Fq(en)n(vironmen)n(t)h(is)h(used)g (for)f(t)n(w)n(o)g(or)g(more)h(equations)f(when)h(v)n(ertical)f(align-) 291 3749 y(men)n(t)36 b(is)g(desired;)k(usually)c(binary)f(relations)g (suc)n(h)h(as)g(equal)g(signs)f(are)g(aligned)h(\(see)291 3849 y(T)-7 b(able)27 b(2.1\).)415 3948 y(T)-7 b(o)23 b(ha)n(v)n(e)g(sev)n(eral)f(equation)h(columns)g(side-b)n(y-side,)g (use)h(extra)e(amp)r(ersands)h(to)g(sep-)291 4048 y(arate)j(the)i (columns:)945 4200 y Fe(x)23 b Fq(=)g Fe(y)641 b(X)29 b Fq(=)23 b Fe(Y)538 b(a)23 b Fq(=)g Fe(b)18 b Fq(+)g Fe(c)-2594 b Fq(\(2.12\))921 4324 y Fe(x)968 4290 y Fc(0)1015 4324 y Fq(=)23 b Fe(y)1147 4290 y Fc(0)1761 4324 y Fe(X)1837 4290 y Fc(0)1883 4324 y Fq(=)g Fe(Y)2037 4290 y Fc(0)2534 4324 y Fe(a)2578 4290 y Fc(0)2624 4324 y Fq(=)g Fe(b)-2457 b Fq(\(2.13\))772 4449 y Fe(x)19 b Fq(+)f Fe(x)968 4414 y Fc(0)1015 4449 y Fq(=)23 b Fe(y)e Fq(+)d Fe(y)1292 4414 y Fc(0)1585 4449 y Fe(X)24 b Fq(+)18 b Fe(X)1837 4414 y Fc(0)1883 4449 y Fq(=)23 b Fe(Y)37 b Fq(+)18 b Fe(Y)2206 4414 y Fc(0)2499 4449 y Fe(a)2543 4414 y Fc(0)2566 4449 y Fe(b)k Fq(=)h Fe(c)2748 4414 y Fc(0)2771 4449 y Fe(b)-2516 b Fq(\(2.14\))291 4600 y Fk(\\begin{align})291 4700 y(x&=y)303 b(&)43 b(X&=Y)304 b(&)43 b(a&=b+c\\\\)291 4799 y(x'&=y')215 b(&)43 b(X'&=Y')216 b(&)43 b(a'&=b\\\\)291 4899 y(x+x'&=y+y')c(&)k(X+X'&=Y+Y')d(&)j(a'b&=c'b)291 4998 y(\\end{align})p eop %DVIPSSectionPage: 6 6 11 bop 739 282 a Fq(6)1172 b Fp(2.)31 b(DISPLA)-6 b(YED)24 b(EQUA)-6 b(TIONS)24 b(\()p Fh(AMSMATH)i Fp(P)-6 b(A)n(CKA)n(GE\))739 515 y Fq(Line-b)n(y-line)23 b(annotations)g(on)h(an)g(equation)f(can)h (b)r(e)g(done)g(b)n(y)g(judicious)g(application)f(of)739 615 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Fq(\(0\))p Fe(y)1682 2625 y Fc(0)2565 2659 y Fq(b)n(y)k(Axiom)h(1.)-2274 b(\(2.20\))739 2852 y Fk(\\begin{alignat}{)o(2})739 2952 y(x&)43 b(=)g (y_1-y_2+y_3-y_5+)o(y_)o(8-\\)o(do)o(ts)1523 3051 y(&\\quad&)e (\\text{by)f(\\eqref{eq:C}}\\\\)782 3151 y(&)k(=)f(y'\\circ)e(y^*)85 b(&&)43 b(\\text{by)d(\\eqref{eq:D}}\\\\)782 3250 y(&)k(=)f(y\(0\))f (y')260 b(&&)43 b(\\text)f({by)g(Axiom)g(1.})739 3350 y(\\end{alignat})739 3526 y Fn(2.7)94 b(Alignmen)m(t)30 b(building)g(blo)s(c)m(ks)739 3669 y Fq(Some)f(other)f(equation)h (alignmen)n(t)f(en)n(vironmen)n(ts,)g(suc)n(h)h(as)f Fk(aligned)f Fq(and)h Fk(gathered)p Fq(,)739 3769 y(construct)k (self-con)n(tained)g(units)h(that)g(can)f(b)r(e)h(used)g(inside)g(of)g (other)f(expressions,)g(or)739 3869 y(set)24 b(side-b)n(y-side.)34 b(These)24 b(en)n(vironmen)n(ts)f(tak)n(e)g(an)h(optional)f(argumen)n (t)g(to)h(sp)r(ecify)g(their)739 3968 y(v)n(ertical)29 b(p)r(ositioning)h(with)h(resp)r(ect)g(to)f(the)h(material)f(on)g (either)g(side.)46 b(The)30 b(default)h(is)739 4068 y(`middle')j (placemen)n(t)g(with)h(the)f(v)n(ertical)f(midp)r(oin)n(t)h(of)g(the)g (total)g(unit)h(falling)e(on)h(the)739 4168 y(math)28 b(axis)1098 4137 y Fl(2)1134 4168 y Fq(.)37 b(F)-7 b(or)27 b(example:)1468 4352 y Fe(\013)d Fq(=)e Fe(\013\013)1470 4476 y(\014)28 b Fq(=)22 b Fe(\014)t(\014)t(\014)t(\014)t(\014)1474 4601 y(\015)28 b Fq(=)22 b Fe(\015)2055 4477 y Fq(v)n(ersus)193 b Fe(\016)26 b Fq(=)c Fe(\016)s(\016)2468 4602 y(\021)k Fq(=)c Fe(\021)s(\021)s(\021)s(\021)s(\021)s(\021)2457 4726 y(')i Fq(=)e Fe(')p 739 4921 1146 4 v 831 4975 a Fj(2)866 4998 y Fp(The)i(heigh)n(t)h(of)e(the)i(cross-bar)d(in)i(the)g (+)g(sym)n(b)r(ol.)p eop %DVIPSSectionPage: 7 7 12 bop 291 282 a Fp(2.)31 b(DISPLA)-6 b(YED)24 b(EQUA)-6 b(TIONS)23 b(\()p Fh(AMSMATH)j Fp(P)-6 b(A)n(CKA)n(GE\))1173 b Fq(7)291 515 y Fk(\\begin{equation)o(*})291 615 y(\\begin{aligned}) 291 715 y(\\alpha&=\\alpha\\)o(alp)o(ha)o(\\\\)291 814 y(\\beta&=\\beta\\be)o(ta\\)o(be)o(ta)o(\\be)o(ta)o(\\be)o(ta)o(\\\\) 291 914 y(\\gamma&=\\gamma)291 1013 y(\\end{aligned})291 1113 y(\\qquad\\text{ver)o(sus)o(}\\)o(qq)o(uad)291 1213 y(\\begin{aligned})o([t])291 1312 y(\\delta&=\\delta\\)o(del)o(ta)o (\\\\)291 1412 y(\\eta&=\\eta\\eta\\)o(eta)o(\\e)o(ta)o(\\et)o(a\\)o (eta)o(\\\\)291 1512 y(\\varphi&=\\varph)o(i)291 1611 y(\\end{aligned})291 1711 y(\\end{equation*})415 1888 y Fq(\\Cases")26 b(constructions)g(lik)n(e)h(the)h(follo)n(wing)f(are)g (common)g(in)g(mathematics:)975 2136 y Fe(P)1028 2148 y Fd(r)r Fc(\000)p Fd(j)1171 2136 y Fq(=)1259 1994 y Fg(\()1326 2079 y Fq(0)526 b(if)29 b Fe(r)21 b Fm(\000)d Fe(j)32 b Fq(is)c(o)r(dd)p Fe(;)1326 2199 y(r)r Fq(!)14 b(\()p Fm(\000)p Fq(1\))1573 2169 y Fl(\()p Fd(r)r Fc(\000)p Fd(j)s Fl(\))p Fd(=)p Fl(2)1894 2199 y Fq(if)29 b Fe(r)21 b Fm(\000)d Fe(j)32 b Fq(is)c(ev)n(en)o Fe(:)291 2136 y Fq(\(2.21\))291 2383 y(and)j(in)g(the)h Fk(amsmath)c Fq(pac)n(k)-5 b(age)30 b(there)h(is)g(a)g 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(rules)g(out)h(the)g(use)g(of)f Fn(|)h Fu(and)f Fn(\\|)g Fu(for)g(delimiters,)p eop %DVIPSSectionPage: 17 17 22 bop 291 282 a Ft(4.)31 b(OPERA)-6 b(TOR)23 b(NAMES)g(\()p Fk(AMSOPN)p Ft(,)i Fk(AMSMATH)h Ft(P)-6 b(A)n(CKA)n(GES\))1011 b Fu(17)291 515 y(as)25 b(in)h(the)g(notations)f(for)g(absolute)g(v)-5 b(alue)25 b(or)g(norm,)h(b)r(ecause)f(left)h(and)g(righ)n(t)f (delimiters)291 615 y(are)f(distinct)i(usages)e(that)h(do)g(not)h (relate)e(in)i(the)g(same)e(w)n(a)n(y)g(to)i(adjacen)n(t)e(sym)n(b)r (ols;)i(rec-)291 715 y(ommended)31 b(practice)h(is)f(therefore)g(to)h (de\014ne)g(suitable)f(commands)g(in)i(the)f(do)r(cumen)n(t)291 814 y(pream)n(ble)26 b(for)h(an)n(y)g(paired-delimiter)g(use)g(of)h(v)n (ert)f(bar)g(sym)n(b)r(ols:)291 952 y Fn(\\newcommand{\\ab)o(s}[)o(1])o ({\\)o(lve)o(rt)o(#1\\)o(rv)o(ert)o(})291 1051 y(\\newcommand{\\no)o (rm})o([1)o(]{)o(\\lV)o(er)o(t#1)o(\\r)o(Ver)o(t})291 1189 y Fu(whereup)r(on)g(the)i(do)r(cumen)n(t)f(w)n(ould)g(con)n(tain)f Fn(\\abs{z})e 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y(names'.)53 b(As)34 b(the)g Fn(amsopn)d Fu(pac)n(k)-5 b(age)31 b(is)j(loaded)e(in)n(ternally)h(b)n(y)g(the)h Fn(amsmath)c Fu(pac)n(k)-5 b(age,)291 2682 y(the)29 b(follo)n(wing)f (features)g(are)g(a)n(v)-5 b(ailable)28 b(there)h(also.)40 b(T)-7 b(o)29 b(de\014ne)g(a)g(math)g(function)g Fn(\\xxx)291 2782 y Fu(to)e(w)n(ork)f(lik)n(e)h Fn(\\sin)p Fu(,)g(y)n(ou)f(write)291 2919 y Fn(\\DeclareMathOpe)o(rat)o(or)o({\\)o(xxx)o(}{)o(xxx)o(})291 3057 y Fu(whereup)r(on)33 b(ensuing)h(uses)g(of)g Fn(\\xxx)e Fu(will)i(pro)r(duce)g(xxx)g(in)g(the)g(prop)r(er)g(fon)n(t)g(and)g (au-)291 3157 y(tomatically)c(add)g(prop)r(er)g(spacing)g(on)g(either)h (side)f(when)h(necessary)-7 b(,)30 b(so)g(that)h(y)n(ou)f(get)291 3256 y Fh(A)14 b Fu(xxx)f Fh(B)31 b Fu(instead)c(of)f Fh(A)p Fu(xxx)p Fh(B)t Fu(.)37 b(In)27 b(the)g(second)g(argumen)n(t)e (of)i Fn(\\DeclareMathOper)o(ato)o(r)291 3356 y Fu(\(the)d(name)g (text\),)h(a)f(pseudo-text)g(mo)r(de)g(prev)-5 b(ails:)34 b(the)24 b(h)n(yphen)g(c)n(haracter)e Fn(-)i Fu(will)g(prin)n(t)291 3455 y(as)d(a)h(text)g(h)n(yphen)g(rather)f(than)h(a)g(min)n(us)g(sign) g(and)f(an)h(asterisk)f Fn(*)h Fu(will)g(prin)n(t)g(as)f(a)h(raised)291 3555 y(text)31 b(asterisk)g(instead)g(of)g(a)g(cen)n(tered)g(math)h (star.)47 b(\(Compare)31 b Fl(a)6 b Fu(-)p Fl(b)f Fu(*)p Fl(c)37 b Fu(and)31 b Fh(a)21 b Fp(\000)f Fh(b)h Fp(\003)g Fh(c)p Fu(.\))291 3655 y(But)j(otherwise)g(the)h(name)f(text)h(is)f (prin)n(ted)h(in)g(math)f(mo)r(de,)i(so)e(that)g(y)n(ou)g(can)g(use,)h (e.g.,)291 3754 y(subscripts)i(and)g(sup)r(erscripts)g(there.)415 3854 y(If)22 b(the)h(new)f(op)r(erator)e(should)i(ha)n(v)n(e)e (subscripts)i(and)f(sup)r(erscripts)h(placed)f(in)h(`limits')291 3954 y(p)r(osition)40 b(ab)r(o)n(v)n(e)g(and)h(b)r(elo)n(w)g(as)f(with) i(lim,)j(sup,)f(or)d(max)o(,)k(use)c(the)g Fn(*)g Fu(form)f(of)i(the) 291 4053 y Fn(\\DeclareMathOpe)o(rat)o(or)21 b Fu(command:)291 4191 y Fn(\\DeclareMathOpe)o(rat)o(or)o(*{)o(\\Li)o(m})o({Li)o(m})415 4329 y Fu(A)27 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y Fg(;x)1704 3278 y Fd(i)1730 3270 y Fo(])1780 3255 y Fu(is)i(monotonic,)82 b Fh(i)23 b Fu(=)g(1)p Fh(;)14 b(:)g(:)g(:)f(;)h(c)k Fu(+)g(1)-2154 b(\(5.1\))739 3445 y Fn(f_{[x_{i-1},x_i])o(})37 b(\\text{)42 b(is)g(monotonic,})739 3545 y(\\quad)f(i)j(=)f(1,\\dots,c+1)739 3885 y Fs(|6|)739 4062 y(The)38 b Fi(\\boldsymbol)i Fs(command)d(\()p Fi(amsbsy)p Fs(,)i Fi(amsmath)g Fs(pac)m(k)-6 b(ages\))739 4281 y Fu(The)24 b Fn(\\boldsymbol)19 b Fu(and)24 b Fn(\\pmb)f Fu(commands)g(are)g(de\014ned)h(b)n(y)g(the)g Fn(amsbsy)e Fu(pac)n(k)-5 b(age)22 b(\(also)739 4380 y(loaded)c(b)n(y)g Fn(amsmath)p Fu(\).)31 b(The)19 b Fn(\\boldsymbol)14 b Fu(command)k(is)g(used)h(to)f(obtain)g(b)r(old)h(n)n(um)n(b)r(ers)739 4480 y(and)31 b(other)h(nonalphab)r(etic)f(sym)n(b)r(ols,)h(as)f(w)n (ell)h(as)f(b)r(old)g(Greek)h(letters,)g(whic)n(h)g(cannot)739 4579 y(b)r(e)f(made)g(b)r(old)g(via)g(the)g Fn(\\mathbf)d Fu(command.)2266 4549 y Fo(1)2350 4579 y Fu(It)j(can)g(also)e(b)r(e)j (used)f(to)f(obtain)h(b)r(old)739 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y(FTP)-7 b(,)28 b(36)2316 3014 y Fd(ftp.cdrom.com)p Fl(,)23 b(27)2316 3114 y Fd(ftp.dante.de)p Fl(,)g(27)2316 3214 y Fd(ftp.tex.ac.uk)p Fl(,)g(27)2316 3314 y(function)h(names,)g Fc(se)l(e)29 b Fl(op)r(erator)22 b(names)2316 3508 y Fd(gather)k Fl(en)n(vironmen)n (t,)g(5,)h(30,)g(34)2316 3608 y Fd(gathered)e Fl(en)n(vironmen)n(t,)h (6)2316 3709 y Fd(\\genfrac)p Fl(,)f(13,)h(14,)h(31)2316 3902 y Fd(\\Hat)p Fl(,)f(12)2316 4003 y Fd(\\hat)p Fl(,)g(12)2316 4103 y Fd(\\hdotsfor)p Fl(,)e(10)2316 4203 y(horizon)n(tal)i(space)2482 4303 y(around)h(op)r(erator)f(names,)h(17)2482 4404 y(in)h(math)g(mo)r (de,)g(10)2316 4597 y Fd(\\idotsint)p Fl(,)c(19)2316 4698 y Fd(\\iiiint)p Fl(,)h(19)2316 4798 y Fd(\\iiint)p Fl(,)h(19)2316 4898 y Fd(\\iint)p Fl(,)g(19)2316 4998 y Fd(inputs)p Fl(,)g(27)p eop %DVIPSSectionPage: 41 41 46 bop 291 282 a Fk(INDEX)2548 b Fl(41)291 515 y(installation,)27 b(27)291 615 y Fd(instr-l.tex)p Fl(,)c(29)291 715 y Fd(\\int)p Fl(,)j(20)291 814 y(in)n(tegrals,)g(20)457 914 y(m)n(ultiple,)i(19)457 1013 y(placemen)n(t)f(of)h(limits,)g(2)291 1113 y Fd(\\intertext)p Fl(,)23 b(8)291 1213 y Fd(intlimits)h Fl(option,)j(2)291 1379 y Fd(\\label)p Fl(,)e(9)291 1478 y(Lamp)r(ort,)i(Leslie,)g(v)291 1578 y Fd(\\langle)p Fl(,)d(16)291 1678 y Fd(\\left)p Fl(,)h(15,)i(16,)g(33)291 1777 y Fd(\\leftroot)p Fl(,)d(12)291 1877 y Fd(leqno)h Fl(option,)j(2)291 1976 y Fd(\\lim)p Fl(,)e(vi,)h(1,)h(17)291 2076 y(limits,)20 b Fc(se)l(e)25 b Fl(subscripts)18 b(and)g(sup)r(erscripts)291 2176 y Fd(\\log)p Fl(,)26 b(17)291 2275 y Fd(\\lVert)p Fl(,)f(16)291 2375 y Fd(\\lvert)p Fl(,)g(16)291 2541 y Fd(math)p Fl(,)h(27)291 2641 y(math)h(fon)n(ts,)h(21)457 2740 y(b)r(old)f(sym)n(b)r(ols,)g(18) 291 2840 y(math)g(sym)n(b)r(ols,)g Fc(se)l(e)34 b Fl(math)28 b(fon)n(ts)291 2940 y Fd(\\mathbf)p Fl(,)c(18,)j(21,)g(22)291 3039 y Fd(\\mathcal)p Fl(,)d(21)291 3139 y Fd(\\mathit)p Fl(,)g(21)291 3238 y Fd(\\mathrm)p Fl(,)g(21)291 3338 y Fd(\\mathsf)p Fl(,)g(21)291 3438 y Fd(\\mathtt)p Fl(,)g(21)291 3537 y(matrices,)i(9)457 3637 y(ellipsis)h(dots,)g(10)291 3737 y Fd(matrix)e Fl(en)n(vironmen)n(t,)h(9)291 3836 y Fd(\\mbox)p Fl(,)f(18)291 3936 y Fd(\\medspace)p Fl(,)f(10)291 4035 y(Metafon)n(t)j(source)f(\014les,)i(31)291 4135 y(Mittelbac)n(h,)f(F)-7 b(rank,)27 b(v)291 4235 y Fd(\\mod)p Fl(,)f(18)291 4334 y Fd(mrabbrev.bib)p Fl(,)c(29)291 4434 y Fd(msam)p Fl(,)k(35)291 4534 y Fd(msbm)p Fl(,)g(35)291 4633 y Fd(\\mspace)p Fl(,)e(11)291 4733 y Fd(multline)g Fl(en)n(vironmen)n(t,)j(3,)g(5,)g(33)291 4832 y Fd(\\multlinegap)p Fl(,)22 b(3)291 4998 y Fd(namelimits)h Fl(option,)k(2)1868 515 y Fd(\\negmedspace)p Fl(,)c(10)1868 616 y Fd(\\negthickspace)p Fl(,)f(10)1868 716 y Fd(\\negthinspace)p Fl(,)g(10)1868 816 y Fd(\\newcommand)p Fl(,)h(12,)k(21)1868 916 y Fd(\\newenvironment) p Fl(,)22 b(23)1868 1017 y Fd(\\newtheorem)p Fl(,)h(vi,)28 b(1,)f(22{25)1868 1117 y Fd(\\newtheorem*)p Fl(,)c(23,)k(29)1868 1217 y Fd(\\newtheoremstyle)o Fl(,)22 b(25)1868 1317 y Fd(\\nobreakdash)p Fl(,)h(11,)k(12)1868 1417 y Fd(nointlimits)c Fl(option,)k(2)1868 1518 y Fd(\\nolimits)p Fl(,)d(20)1868 1618 y Fd(nonamelimits)f Fl(option,)k(2)1868 1718 y Fd(nosumlimits)c Fl(option,)k(2)1868 1818 y Fd(\\notag)p Fl(,)e(3)1868 1919 y Fd(\\numberwithin)p Fl(,)d(9,)28 b(34,)e(35)1868 2112 y(op)r(erator)g(names,)h(17)1868 2212 y Fd(\\over)p Fl(,)f(13)1868 2313 y Fd(\\overleftarrow)p Fl(,)c(11)1868 2413 y Fd(\\overleftrightar)o(row)o Fl(,)g(11)1868 2513 y Fd(\\overrightarrow)p Fl(,)g(11)1868 2613 y Fd(\\overset)p Fl(,)i(13)1868 2714 y Fd(\\overwithdelims)p Fl(,)e(13)1868 2907 y(page)27 b(breaks,)f(7)1868 3008 y Fd(\\pagebreak)p Fl(,)e(8)1868 3108 y Fd(plain)i Fl(theorem)h(st)n(yle,)g(24)1868 3208 y Fd(pmatrix)e Fl(en)n(vironmen)n(t,)h(9)1868 3308 y Fd(\\pmb)p Fl(,)g(1,)h(18,)g(19,)g(29)1868 3408 y Fd(\\pmod)p Fl(,)f(18)1868 3509 y Fd(\\pod)p Fl(,)g(18)1868 3609 y(P)n(ostScript)g(fon)n(ts,)i(31)1868 3709 y Fd(proof)e Fl(en)n(vironmen)n(t,)g(vi,)i(1,)f(22,)g(25)1868 3809 y(pro)r(ofs,)g(23)1868 3910 y Fd(pstricks)d Fl(pac)n(k)-5 b(age,)26 b(36)1868 4103 y Fd(\\qed)p Fl(,)g(25)1868 4203 y Fd(\\qedsymbol)p Fl(,)e(25)1868 4304 y Fd(\\qquad)p Fl(,)h(10)1868 4404 y Fd(\\quad)p Fl(,)h(10,)g(11)1868 4598 y Fd(\\R)p Fl(,)h(22)1868 4698 y Fd(\\raisetag)p Fl(,)d(7)1868 4798 y Fd(\\rangle)p Fl(,)h(16)1868 4898 y Fd(READ.ME)p Fl(,)g(27,)i(28)1868 4998 y Fd(\\ref)p Fl(,)f(1,)h(9,)h(29)p eop %DVIPSSectionPage: 42 42 47 bop 739 282 a Fl(42)2547 b Fk(INDEX)739 515 y Fd(remark)25 b Fl(theorem)i(st)n(yle,)g(24)739 615 y Fd(\\renewcommand)p Fl(,)22 b(22,)27 b(25)739 715 y Fd(reqno)f Fl(option,)h(2)739 815 y Fd(\\right)p Fl(,)e(15,)i(16,)g(33)739 916 y Fd(\\rVert)p Fl(,)e(16)739 1016 y Fd(\\rvert)p Fl(,)g(16)739 1206 y Fd(\\savebox)p Fl(,)f(12)739 1306 y(Sc)n(h\177)-42 b(opf,)27 b(Rainer,)g(v)739 1406 y Fd(\\scriptscriptsty)o(le)o Fl(,)22 b(14)739 1506 y Fd(\\scriptstyle)p Fl(,)h(14)739 1606 y Fd(\\section)p Fl(,)h(25)739 1706 y Fd(\\setcounter)p Fl(,)f(9,)k(10)739 1806 y Fd(\\setlength)p Fl(,)c(3)739 1907 y Fd(\\shoveleft)p Fl(,)g(3)739 2007 y Fd(\\shoveright)p Fl(,)g(3)739 2107 y Fd(\\sideset)p Fl(,)h(13,)j(20)739 2207 y Fd(\\sin)p Fl(,)f(vi,)i(1,)f(17)739 2307 y Fd(smallmatrix)c Fl(en)n(vironmen)n(t,)k(10)739 2407 y Fd(\\smash)p Fl(,)e(15,)i(33)739 2507 y(Spiv)-5 b(ak,)27 b(Mic)n(hael,)h(v)739 2607 y Fd(split)e Fl(en)n(vironmen)n(t,)g(3,)h(5,)h(30,)e(33,)h(34)739 2707 y Fd(\\square)p Fl(,)e(35)739 2807 y Fd(\\stackrel)p Fl(,)f(13)739 2907 y Fd(subarray)g Fl(en)n(vironmen)n(t,)j(19)739 3007 y Fd(subeqn.tex)p Fl(,)c(3,)28 b(27,)e(29)739 3107 y Fd(subequations)d Fl(en)n(vironmen)n(t,)j(9)739 3207 y(subscripts)h(and)g(sup)r(erscripts,)g(13)905 3307 y(m)n(ulti-line,)h (19)905 3408 y(on)f(sums,)h(20)905 3508 y(placemen)n(t,)f(2)739 3608 y Fd(\\subsection)p Fl(,)c(25)739 3708 y Fd(\\substack)p Fl(,)h(19)739 3808 y Fd(\\sum)p Fl(,)i(20)739 3908 y Fd(sumlimits)e Fl(option,)j(2)739 4008 y(sums,)g(20)739 4108 y(sup)r(erscripts,)h Fc(se)l(e)36 b Fl(subscripts)28 b(and)h(su-)1071 4208 y(p)r(erscripts)739 4308 y Fd(\\swapnumbers)p Fl(,)23 b(25)739 4408 y Fd(syntonly)h Fl(pac)n(k)-5 b(age,)26 b(36)739 4598 y Fd(tabular)f Fl(en)n(vironmen)n(t,)h(32)739 4698 y Fd(\\tag)p Fl(,)g(3)739 4798 y Fd(\\tag*)p Fl(,)g(3)739 4898 y Fd(\\tbinom)p Fl(,)f(14)739 4998 y Fd(tbtags)g Fl(option,)i(1)2316 515 y Fd(technote.tex)p Fl(,)c(13,)k(29,)g(34,)f (37)2316 615 y Fd(testmath.tex)p Fl(,)d(3,)k(27,)g(29)2316 715 y(T)2362 732 y(E)2409 715 y(X)g(Users)g(Group,)h(38)2316 814 y Fd(\\text)p Fl(,)e(1,)h(6,)g(7,)h(18,)e(29)2316 914 y(text)i(fragmen)n(ts)f(inside)g(math,)h(8,)g(18)2316 1013 y Fd(\\textstyle)p Fl(,)c(14)2316 1113 y Fd(\\tfrac)p Fl(,)i(13,)g(14)2316 1213 y Fd(\\theequation)p Fl(,)d(8,)k(9)2316 1312 y Fd(theorem)e Fl(pac)n(k)-5 b(age,)26 b(22)2316 1412 y(theorems,)h(23)2482 1512 y(n)n(um)n(b)r(ering,)g(23)2316 1611 y Fd(\\theoremstyle)p Fl(,)c(22,)j(24,)h(25,)g(29)2316 1711 y Fd(\\thickspace)p Fl(,)c(10)2316 1810 y Fd(\\thinspace)p Fl(,)h(10)2316 1910 y Fd(thmtest.tex)p Fl(,)f(22,)k(25,)g(29)2316 2010 y Fc(TUGb)l(o)l(at)p Fl(,)i(38)2316 2192 y Fd(\\underleftarrow)p Fl(,)22 b(11)2316 2292 y Fd(\\underleftrightar)o(ro)o(w)p Fl(,)g(11)2316 2392 y Fd(\\underrightarrow)p Fl(,)f(11)2316 2491 y Fd(\\underset)p Fl(,)j(13)2316 2591 y Fd(upref)i Fl(pac)n(k)-5 b(age,)26 b(1)2316 2690 y Fd(upref.dtx)p Fl(,)e(29)2316 2790 y Fd(\\uproot)p Fl(,)h(12)2316 2890 y Fd(\\usepackage)p Fl(,)e(1,)28 b(2,)f(31)2316 3072 y Fd(\\value)p Fl(,)f(9)2316 3172 y Fd(\\varinjlim)p Fl(,)e(17)2316 3272 y Fd(\\varliminf)p Fl(,)g(17)2316 3371 y Fd(\\varlimsup)p Fl(,)g(17)2316 3471 y Fd(\\varprojlim)p Fl(,)f(17)2316 3571 y Fd(\\vec)p Fl(,)j(22)2316 3670 y Fd(\\vector)p Fl(,)f(36)2316 3770 y Fd(verbatim)g Fl(en)n(vironmen)n (t,)h(36)2316 3869 y Fd(verbatim)f Fl(pac)n(k)-5 b(age,)26 b(36)2316 3969 y Fd(\\verbatiminput)p Fl(,)c(36)2316 4069 y Fd(Vmatrix)j Fl(en)n(vironmen)n(t,)i(9)2316 4168 y Fd(vmatrix)e Fl(en)n(vironmen)n(t,)i(9)2316 4268 y Fd(\\vphantom)p Fl(,)d(33)2316 4451 y Fd(\\xleftarrow)p Fl(,)f(13)2316 4550 y Fd(\\xrightarrow)p Fl(,)g(13)2316 4650 y Fd(\\xxx)p Fl(,)j(34)2316 4749 y Fd(xypic)g Fl(pac)n(k)-5 b(age,)26 b(36)p eop %DVIPSSectionTrailer eos end %DVIPSEndSection userdict /end-hook known{end-hook}if %%EOF