# # things supported by real insets in mathed # # decorations acute decoration none bar decoration none breve decoration none check decoration none dddot decoration none ddot decoration none dot decoration none grave decoration none hat decoration none mathring decoration none overbrace decoration none overleftarrow decoration none overleftrightarrow decoration none overline decoration none overrightarrow decoration none tilde decoration none underbar decoration none underbrace decoration none underleftarrow decoration none underleftrightarrow decoration none underline decoration none underrightarrow decoration none vec decoration none widehat decoration none widetilde decoration none # dots cdots dots none ddots dots none dotsb dots none dotsc dots none dotsi dots none dotsm dots none dotso dots none ldots dots none vdots dots none # font changes # name "font" math/text family series shape color # mathnormal should stay the first mathnormal font mathmode inherit medium up math frak font mathmode mathbb font mathmode mathbf font mathmode mathcal font mathmode mathfrak font mathmode mathit font mathmode mathrm font mathmode mathsf font mathmode mathtt font mathmode textnormal font textmode inherit medium up math text font textmode textbf font textmode textipa font textmode textit font textmode textmd font textmode textrm font textmode textsc font textmode textsl font textmode textsf font textmode texttt font textmode textup font textmode emph font textmode noun font textmode # old-style font commands bf oldfont none cal oldfont none it oldfont none rm oldfont none tt oldfont none # matrix environments Bmatrix matrix none Vmatrix matrix none bmatrix matrix none matrix matrix none pmatrix matrix none psmatrix matrix none vmatrix matrix none CD matrix none # references pageref ref none prettyref ref none ref ref none vpageref ref none vref ref none # spaces lyxnegspace space none lyxposspace space none ! space none negmedspace space none negthickspace space none , space none : space none ; space none quad space none qquad space none # styles displaystyle style 0 textstyle style 1 scriptstyle style 2 scriptscriptstyle style 3 # misc begin begin none right right none underset underset none parbox parbox none protect protect none mbox mbox forcetext newcommand newcommand none label label none left left none end end none fbox fbox none boxed fbox none # # symbols generated from fontmath.ltx # #symbol font charid charid-in-fallback-Xsymbol-font alpha cmm 174 97 mathord x beta cmm 175 98 mathord x gamma cmm 176 103 mathord x delta cmm 177 100 mathord x epsilon cmm 178 0 mathord x zeta cmm 179 122 mathord x eta cmm 180 104 mathord x theta cmm 181 113 mathord x iota cmm 182 105 mathord x kappa cmm 183 107 mathord x lambda cmm 184 108 mathord x mu cmm 185 109 mathord x nu cmm 186 110 mathord x xi cmm 187 120 mathord x pi cmm 188 112 mathord x rho cmm 189 114 mathord x sigma cmm 190 115 mathord x tau cmm 191 116 mathord x upsilon cmm 192 117 mathord x phi cmm 193 102 mathord x chi cmm 194 99 mathord x psi cmm 32 121 mathord x omega cmm 33 119 mathord x varepsilon cmm 34 101 mathord x vartheta cmm 35 74 mathord x varpi cmm 36 118 mathord x varrho cmm 37 0 mathord x varsigma cmm 38 86 mathord x varphi cmm 39 106 mathord x Gamma cmr 161 71 mathalpha x Delta cmr 162 68 mathalpha x Theta cmr 163 81 mathalpha x Lambda cmr 164 76 mathalpha x Xi cmr 165 88 mathalpha x Pi cmr 166 80 mathalpha x Sigma cmr 167 83 mathalpha x Upsilon cmr 168 161 mathalpha x Phi cmr 169 70 mathalpha x Psi cmr 170 89 mathalpha x Omega cmr 173 87 mathalpha x aleph cmsy 64 192 mathord x imath cmm 123 0 mathord x jmath cmm 124 0 mathord x ell cmm 96 0 mathord x wp cmm 125 195 mathord x Re cmsy 60 194 mathord x Im cmsy 61 193 mathord x partial cmm 64 182 mathord x infty cmsy 49 165 mathord x prime cmsy 48 162 mathord x emptyset cmsy 59 0 mathord x nabla cmsy 114 209 mathord x top cmsy 62 0 mathord x bot cmsy 63 94 mathord x triangle cmsy 52 0 mathord x forall cmsy 56 34 mathord x exists cmsy 57 36 mathord x neg cmsy 58 216 mathord x lnot cmsy 58 216 mathord x flat cmm 91 0 mathord x natural cmm 92 0 mathord x sharp cmm 93 35 mathord x clubsuit cmsy 124 167 mathord x diamondsuit cmsy 125 168 mathord x heartsuit cmsy 126 169 mathord x spadesuit cmsy 127 170 mathord x # We define lyxnot as mathrel in order to have proper alignment lyxnot cmsy 54 47 mathrel x iffont cmsy \def\not{\lyxnot\kern-12mu} else \def\not{\lyxnot\kern-20mu} endif coprod cmex 96 0 mathop x bigvee cmex 87 0 mathop x bigwedge cmex 86 0 mathop x biguplus cmex 85 0 mathop x bigcap cmex 84 0 mathop x bigcup cmex 83 0 mathop x int cmex 82 242 mathop ∫ prod cmex 81 213 mathop x sum cmex 80 229 mathop x bigotimes cmex 78 0 mathop x bigoplus cmex 76 0 mathop x bigodot cmex 74 0 mathop x oint cmex 72 0 mathop x bigsqcup cmex 70 0 mathop x smallint cmsy 115 0 mathop x triangleleft cmm 47 0 mathbin x triangleright cmm 46 0 mathbin x bigtriangleup cmsy 52 0 mathbin x bigtriangledown cmsy 53 0 mathbin x wedge cmsy 94 217 mathbin x land cmsy 94 217 mathbin x vee cmsy 95 218 mathbin x lor cmsy 95 218 mathbin x cap cmsy 92 199 mathbin x cup cmsy 91 200 mathbin x ddagger cmsy 122 0 mathbin x dagger cmsy 121 0 mathbin x sqcap cmsy 117 0 mathbin x sqcup cmsy 116 0 mathbin x uplus cmsy 93 0 mathbin x amalg cmsy 113 0 mathbin x diamond cmsy 166 224 mathbin x bullet cmsy 178 183 mathbin x wr cmsy 111 0 mathbin x div cmsy 165 184 mathbin x odot cmsy 175 0 mathbin x oslash cmsy 174 198 mathbin x otimes cmsy 173 196 mathbin x ominus cmsy 170 0 mathbin x oplus cmsy 169 197 mathbin x mp cmsy 168 0 mathbin x pm cmsy 167 177 mathbin x circ cmsy 177 0 mathbin x bigcirc cmsy 176 0 mathbin x setminus cmsy 110 0 mathbin x cdot cmsy 162 215 mathbin x ast cmsy 164 0 mathbin x times cmsy 163 180 mathbin x star cmm 63 0 mathbin x propto cmsy 47 181 mathrel x sqsubseteq cmsy 118 0 mathrel x sqsupseteq cmsy 119 0 mathrel x parallel cmsy 107 0 mathrel x mid cmsy 106 124 mathrel x dashv cmsy 97 0 mathrel x vdash cmsy 96 0 mathrel x nearrow cmsy 37 0 mathrel x searrow cmsy 38 0 mathrel x nwarrow cmsy 45 0 mathrel x swarrow cmsy 46 0 mathrel x Leftrightarrow cmsy 44 219 mathrel x Leftarrow cmsy 40 220 mathrel x Rightarrow cmsy 41 222 mathrel x leq cmsy 183 163 mathrel x le cmsy 183 163 mathrel x geq cmsy 184 179 mathrel x ge cmsy 184 179 mathrel x succ cmsy 194 0 mathrel x prec cmsy 193 0 mathrel x approx cmsy 188 187 mathrel x succeq cmsy 186 0 mathrel x preceq cmsy 185 0 mathrel x supset cmsy 190 201 mathrel x subset cmsy 189 204 mathrel x supseteq cmsy 182 202 mathrel x subseteq cmsy 181 205 mathrel x in cmsy 50 206 mathrel x ni cmsy 51 39 mathrel x owns cmsy 51 39 mathrel x gg cmsy 192 0 mathrel x ll cmsy 191 0 mathrel x leftrightarrow cmsy 36 171 mathrel x leftarrow cmsy 32 172 mathrel x gets cmsy 32 172 mathrel x rightarrow cmsy 33 174 mathrel x to cmsy 33 174 mathrel x mapstochar cmsy 55 0 mathrel x sim cmsy 187 126 mathrel x simeq cmsy 39 0 mathrel x perp cmsy 63 0 mathrel x equiv cmsy 180 186 mathrel x asymp cmsy 179 0 mathrel x smile cmm 94 0 mathrel x frown cmm 95 0 mathrel x leftharpoonup cmm 40 0 mathrel x leftharpoondown cmm 41 0 mathrel x rightharpoonup cmm 42 0 mathrel x rightharpoondown cmm 43 0 mathrel x lhook cmm 44 0 mathrel x rhook cmm 45 0 mathrel x ldotp cmm 58 0 mathpunct x cdotp cmsy 162 0 mathpunct x colon cmr 58 58 mathpunct x arrowvert cmsy 106 0 mathord x Arrowvert cmsy 107 0 mathord x Vert cmsy 107 0 mathord x | cmsy 107 0 mathord x vert cmsy 106 0 mathord x uparrow cmsy 34 173 mathrel x downarrow cmsy 35 175 mathrel x updownarrow cmsy 108 0 mathrel x Uparrow cmsy 42 221 mathrel x Downarrow cmsy 43 223 mathrel x Updownarrow cmsy 109 0 mathrel x backslash cmsy 110 0 mathord x rangle cmsy 105 241 mathclose x langle cmsy 104 225 mathopen x rbrace cmsy 103 0 mathclose x lbrace cmsy 102 0 mathopen x rceil cmsy 101 249 mathclose x lceil cmsy 100 233 mathopen x rfloor cmsy 99 251 mathclose x lfloor cmsy 98 235 mathopen x mathparagraph cmsy 123 0 mathord x mathsection cmsy 120 0 mathord x mathdollar cmr 36 0 mathord x # Generated from amsfonts.sty yen msa 85 0 mathord x checkmark msa 88 0 mathord x circledR msa 114 0 mathord x maltese msa 122 0 mathord x ulcorner msa 112 0 mathopen x urcorner msa 113 0 mathclose x llcorner msa 120 0 mathopen x lrcorner msa 121 0 mathclose x rightleftharpoons msa 173 0 mathrel x angle msa 92 208 mathord x hbar msb 126 0 mathord x sqsubset msa 64 0 mathrel x sqsupset msa 65 0 mathrel x mho msb 102 0 mathord x square msa 164 0 mathord x lozenge msa 167 0 mathord x vartriangleright msa 66 0 mathrel x vartriangleleft msa 67 0 mathrel x trianglerighteq msa 68 0 mathrel x trianglelefteq msa 69 0 mathrel x rightsquigarrow msa 32 0 mathrel x leadsto msa 32 0 mathrel x lhd msa 67 0 mathbin x unlhd msa 69 0 mathbin x rhd msa 66 0 mathbin x unrhd msa 68 0 mathbin x # Generated from amssymb.sty boxdot msa 161 0 mathbin x boxplus msa 162 0 mathbin x boxtimes msa 163 0 mathbin x blacksquare msa 165 0 mathord x centerdot msa 166 0 mathbin x blacklozenge msa 168 0 mathord x circlearrowright msa 169 0 mathrel x circlearrowleft msa 170 0 mathrel x leftrightharpoons msa 174 0 mathrel x boxminus msa 175 0 mathbin x Vdash msa 176 0 mathrel x Vvdash msa 177 0 mathrel x vDash msa 178 0 mathrel x twoheadrightarrow msa 179 0 mathrel x twoheadleftarrow msa 180 0 mathrel x leftleftarrows msa 181 0 mathrel x rightrightarrows msa 182 0 mathrel x upuparrows msa 183 0 mathrel x downdownarrows msa 184 0 mathrel x upharpoonright msa 185 0 mathrel x restriction msa 185 0 mathrel x downharpoonright msa 186 0 mathrel x upharpoonleft msa 187 0 mathrel x downharpoonleft msa 188 0 mathrel x rightarrowtail msa 189 0 mathrel x leftarrowtail msa 190 0 mathrel x leftrightarrows msa 191 0 mathrel x rightleftarrows msa 192 0 mathrel x Lsh msa 193 0 mathrel x Rsh msa 194 0 mathrel x leftrightsquigarrow msa 33 0 mathrel x looparrowleft msa 34 0 mathrel x looparrowright msa 35 0 mathrel x circeq msa 36 0 mathrel x succsim msa 37 0 mathrel x gtrsim msa 38 0 mathrel x gtrapprox msa 39 0 mathrel x multimap msa 40 0 mathrel x therefore msa 41 92 mathrel x because msa 42 0 mathrel x doteqdot msa 43 0 mathrel x Doteq msa 43 0 mathrel x triangleq msa 44 0 mathrel x precsim msa 45 0 mathrel x lesssim msa 46 0 mathrel x lessapprox msa 47 0 mathrel x eqslantless msa 48 0 mathrel x eqslantgtr msa 49 0 mathrel x curlyeqprec msa 50 0 mathrel x curlyeqsucc msa 51 0 mathrel x preccurlyeq msa 52 0 mathrel x leqq msa 53 0 mathrel x leqslant msa 54 0 mathrel x lessgtr msa 55 0 mathrel x backprime msa 56 0 mathord x risingdotseq msa 58 0 mathrel x fallingdotseq msa 59 0 mathrel x succcurlyeq msa 60 0 mathrel x geqq msa 61 0 mathrel x geqslant msa 62 0 mathrel x gtrless msa 63 0 mathrel x bigstar msa 70 0 mathord x between msa 71 0 mathrel x blacktriangledown msa 72 0 mathord x blacktriangleright msa 73 0 mathrel x blacktriangleleft msa 74 0 mathrel x vartriangle msa 77 0 mathrel x blacktriangle msa 78 0 mathord x triangledown msa 79 0 mathord x eqcirc msa 80 0 mathrel x lesseqgtr msa 81 0 mathrel x gtreqless msa 82 0 mathrel x lesseqqgtr msa 83 0 mathrel x gtreqqless msa 84 0 mathrel x Rrightarrow msa 86 0 mathrel x Lleftarrow msa 87 0 mathrel x veebar msa 89 0 mathbin x barwedge msa 90 0 mathbin x doublebarwedge msa 91 0 mathbin x measuredangle msa 93 0 mathord x sphericalangle msa 94 0 mathord x varpropto msa 95 0 mathrel x smallsmile msa 96 0 mathrel x smallfrown msa 97 0 mathrel x Subset msa 98 0 mathrel x Supset msa 99 0 mathrel x Cup msa 100 0 mathbin x doublecup msa 100 0 mathbin x Cap msa 101 0 mathbin x doublecap msa 101 0 mathbin x curlywedge msa 102 0 mathbin x curlyvee msa 103 0 mathbin x leftthreetimes msa 104 0 mathbin x rightthreetimes msa 105 0 mathbin x subseteqq msa 106 0 mathrel x supseteqq msa 107 0 mathrel x bumpeq msa 108 0 mathrel x Bumpeq msa 109 0 mathrel x lll msa 110 0 mathrel x llltr msa 110 0 mathrel x ggg msa 111 0 mathrel x gggtr msa 111 0 mathrel x circledS msa 115 0 mathord x pitchfork msa 116 0 mathrel x dotplus msa 117 0 mathbin x backsim msa 118 0 mathrel x backsimeq msa 119 0 mathrel x complement msa 123 0 mathord x intercal msa 124 0 mathbin x circledcirc msa 125 0 mathbin x circledast msa 126 0 mathbin x circleddash msa 127 0 mathbin x lvertneqq msb 161 0 mathrel x gvertneqq msb 162 0 mathrel x nleq msb 163 0 mathrel x ngeq msb 164 0 mathrel x nless msb 165 0 mathrel x ngtr msb 166 0 mathrel x nprec msb 167 0 mathrel x nsucc msb 168 0 mathrel x lneqq msb 169 0 mathrel x gneqq msb 170 0 mathrel x nleqslant msb 173 0 mathrel x ngeqslant msb 174 0 mathrel x lneq msb 175 0 mathrel x gneq msb 176 0 mathrel x npreceq msb 177 0 mathrel x nsucceq msb 178 0 mathrel x precnsim msb 179 0 mathrel x succnsim msb 180 0 mathrel x lnsim msb 181 0 mathrel x gnsim msb 182 0 mathrel x nleqq msb 183 0 mathrel x ngeqq msb 184 0 mathrel x precneqq msb 185 0 mathrel x succneqq msb 186 0 mathrel x precnapprox msb 187 0 mathrel x succnapprox msb 188 0 mathrel x lnapprox msb 189 0 mathrel x gnapprox msb 190 0 mathrel x nsim msb 191 0 mathrel x ncong msb 192 0 mathrel x diagup msb 193 0 mathord x diagdown msb 194 0 mathord x varsubsetneq msb 32 0 mathrel x varsupsetneq msb 33 0 mathrel x nsubseteqq msb 34 0 mathrel x nsupseteqq msb 35 0 mathrel x subsetneqq msb 36 0 mathrel x supsetneqq msb 37 0 mathrel x varsubsetneqq msb 38 0 mathrel x varsupsetneqq msb 39 0 mathrel x subsetneq msb 40 0 mathrel x supsetneq msb 41 0 mathrel x nsubseteq msb 42 0 mathrel x nsupseteq msb 43 0 mathrel x nparallel msb 44 0 mathrel x nmid msb 45 0 mathrel x nshortmid msb 46 0 mathrel x nshortparallel msb 47 0 mathrel x nvdash msb 48 0 mathrel x nVdash msb 49 0 mathrel x nvDash msb 50 0 mathrel x nVDash msb 51 0 mathrel x ntrianglerighteq msb 52 0 mathrel x ntrianglelefteq msb 53 0 mathrel x ntriangleleft msb 54 0 mathrel x ntriangleright msb 55 0 mathrel x nleftarrow msb 56 0 mathrel x nrightarrow msb 57 0 mathrel x nLeftarrow msb 58 0 mathrel x nRightarrow msb 59 0 mathrel x nLeftrightarrow msb 60 0 mathrel x nleftrightarrow msb 61 0 mathrel x divideontimes msb 62 0 mathbin x varnothing msb 63 0 mathord x nexists msb 64 0 mathord x Finv msb 96 0 mathord x Game msb 97 0 mathord x eth msb 103 0 mathord x eqsim msb 104 0 mathrel x beth msb 105 0 mathord x gimel msb 106 0 mathord x daleth msb 107 0 mathord x lessdot msb 108 0 mathbin x gtrdot msb 109 0 mathbin x ltimes msb 110 0 mathbin x rtimes msb 111 0 mathbin x shortmid msb 112 0 mathrel x shortparallel msb 113 0 mathrel x smallsetminus msb 114 0 mathbin x thicksim msb 115 0 mathrel x thickapprox msb 116 0 mathrel x approxeq msb 117 0 mathrel x succapprox msb 118 0 mathrel x precapprox msb 119 0 mathrel x curvearrowleft msb 120 0 mathrel x curvearrowright msb 121 0 mathrel x digamma msb 122 0 mathord x varkappa msb 123 0 mathord x Bbbk msb 124 0 mathord x hslash msb 125 0 mathord x hbar msb 126 0 mathord x backepsilon msb 127 0 mathrel x lyxbar cmsy 161 0 mathord x lyxeq cmr 61 0 mathord x lyxdabar msa 57 0 mathord x lyxright msa 75 0 mathord x lyxleft msa 76 0 mathord x male wasy 26 0 x x female wasy 25 0 x x currency wasy 27 0 x x phone wasy 7 0 x x recorder wasy 6 0 x x clock wasy 28 0 x x lightning wasy 18 0 x x pointer wasy 9 0 x x RIGHTarrow wasy 17 0 x x LEFTarrow wasy 16 0 x x UParrow wasy 75 0 x x DOWNarrow wasy 76 0 x x #AC wasy n0.5pt\wasyfamily\char58\kern0.5pt}} #HF {\leavevmode # \lower0.9pt\hbox to 0pt{\kern0.5pt\wasyfamily\char58\hss}% # \raise0.9pt\hbox{\kern0.5pt\wasyfamily\char58\kern0.5pt}} #VHF wasy 64 0 x x Square wasy 50 0 x x #CheckedBox wasy 50\hss}\hbox{\wasyfamily\char8 0 x XBox wasy 52 0 x x hexagon wasy 55 0 x x pentagon wasy 68 0 x x octagon wasy 56 0 x x varhexagon wasy 57 0 x x hexstar wasy 65 0 x x varhexstar wasy 66 0 x x davidsstar wasy 67 0 x x diameter wasy 31 0 x x invdiameter wasy 21 0 x x varangle wasy 30 0 x x wasylozenge wasy 53 0 x x kreuz wasy 54 0 x x smiley wasy 44 0 x x frownie wasy 47 0 x x blacksmiley wasy 45 0 x x sun wasy 46 0 x x checked wasy 8 0 x x bell wasy 10 0 x x eighthnote wasy 11 0 x x quarternote wasy 12 0 x x halfnote wasy 13 0 x x fullnote wasy 14 0 x x twonotes wasy 15 0 x x brokenvert wasy 124 0 x x ataribox wasy 109 0 x x wasytherefore wasy 5 0 x x Circle wasy 35 0 x x CIRCLE wasy 32 0 x x Leftcircle wasy 73 0 x x LEFTCIRCLE wasy 71 0 x x Rightcircle wasy 74 0 x x RIGHTCIRCLE wasy 72 0 x x #LEFTcircle {\hbox to 0pt{\wasyfamily\char71\hss}\hbox{\wasyfamily\char35}} #RIGHTcircle{\hbox to 0pt{\wasyfamily\char72\hss}\hbox{\wasyfamily\char35}} # # wasy astronomy # vernal wasy 23 0 x x ascnode wasy 19 0 x x descnode wasy 20 0 x x fullmoon wasy 35 0 x x newmoon wasy 32 0 x x leftmoon wasy 36 0 x x rightmoon wasy 37 0 x x astrosun cmsy 175 0 mathbin x mercury wasy 39 0 x x venus wasy 25 0 x x earth wasy 38 0 x x mars wasy 26 0 x x jupiter wasy 88 0 x x saturn wasy 89 0 x x uranus wasy 90 0 x x neptune wasy 91 0 x x pluto wasy 92 0 x x # # wasy zodiac # aries wasy 23 0 x x taurus wasy 93 0 x x gemini wasy 94 0 x x cancer wasy 95 0 x x leo wasy 19 0 x x virgo wasy 96 0 x x libra wasy 97 0 x x scorpio wasy 98 0 x x sagittarius wasy 99 0 x x capricornus wasy 100 0 x x aquarius wasy 101 0 x x pisces wasy 102 0 x x conjunction wasy 86 0 x x opposition wasy 87 0 x x # APL characters APLstar wasy 69 0 x x APLlog wasy 22 0 x x APLbox wasy 126 0 x x APLup wasy 0 0 x x APLdown wasy 70 0 x x APLinput wasy 125 0 x x APLcomment wasy 127 0 x x #APLinv {{\hbox to 0pt{$\div$\hss}\APLbox}} APLuparrowbox wasy 110 0 x x APLdownarrowbox wasy 111 0 x x APLleftarrowbox wasy 112 0 x x APLrightarrowbox wasy 113 0 x x # math characters Bowtie wasy 49 0 x x leftturn wasy 34 0 x x rightturn wasy 33 0 x x # diagrams #photon wasy 58\char58\char58\char58}} #gluon wasy 81\char80\char80\char80% #char80\char80\char80\char82}} # special characters cent wasy 103 0 x x permil wasy 104 0 x x agemO wasy 48 0 x x thorn wasy 105 0 x x Thorn wasy 106 0 x x openo wasy 108 0 x x inve wasy 85 0 x x #mho wasy 48 0 mathord x Join wasy 49 0 mathrel x Box wasy 50 0 mathord x Diamond wasy 51 0 mathord x leadsto wasy 59 0 mathrel x #sqsubset wasy 60 0 mathrel x #sqsupset wasy 61 0 mathrel x #lhd wasy 1 0 mathbin x #unlhd wasy 2 0 mathbin x LHD wasy 16 0 mathbin x #rhd wasy 3 0 mathbin x #unrhd wasy 4 0 mathbin x RHD wasy 17 0 mathbin x apprle wasy 62 0 mathrel x apprge wasy 63 0 mathrel x wasypropto wasy 29 0 mathrel x invneg wasy 24 0 mathrel x ocircle wasy 35 0 mathbin x logof wasy 22 0 mathrel x varint wasy 114 0 mathop x iint wasy 115 0 mathop x iiint wasy 116 0 mathop x varoint wasy 117 0 mathop x oiint wasy 118 0 mathop x log lyxblacktext 0 0 func x lg lyxblacktext 0 0 func x ln lyxblacktext 0 0 func x lim lyxblacktext 0 0 funclim x limsup lyxblacktext 0 0 funclim x liminf lyxblacktext 0 0 funclim x sin lyxblacktext 0 0 func x arcsin lyxblacktext 0 0 func x sinh lyxblacktext 0 0 func x cos lyxblacktext 0 0 func x arccos lyxblacktext 0 0 func x cosh lyxblacktext 0 0 func x tan lyxblacktext 0 0 func x arctan lyxblacktext 0 0 func x tanh lyxblacktext 0 0 func x cot lyxblacktext 0 0 func x coth lyxblacktext 0 0 func x sec lyxblacktext 0 0 func x csc lyxblacktext 0 0 func x max lyxblacktext 0 0 funclim x min lyxblacktext 0 0 funclim x sup lyxblacktext 0 0 funclim x inf lyxblacktext 0 0 funclim x arg lyxblacktext 0 0 func x ker lyxblacktext 0 0 func x dim lyxblacktext 0 0 func x hom lyxblacktext 0 0 func x det lyxblacktext 0 0 funclim x exp lyxblacktext 0 0 func x Pr lyxblacktext 0 0 funclim x gcd lyxblacktext 0 0 funclim x deg lyxblacktext 0 0 func x { mathnormal 0 0 special x } mathnormal 0 0 special x $ mathnormal 0 0 special x % mathnormal 0 0 special x # don't remove the space from the beginning of the next line # mathnormal 0 0 special x # # pre-defined macros # \def\notin{\not\in} \def\slash{/} \def\longleftrightarrow{\leftarrow\kern-15mu\rightarrow} \def\Longleftrightarrow{\Leftarrow\kern-15mu\Rightarrow} \def\doteq{\stackrel{\cdot}{=}} iffont cmsy \def\longrightarrow{\lyxbar\kern-11mu\rightarrow} \def\longleftarrow{\leftarrow\kern-11mu\lyxbar} \def\Longrightarrow{\lyxeq\kern-9mu\Rightarrow} \def\Longleftarrow{\Leftarrow\kern-9mu\lyxeq} \def\mapsto{\mapstochar\kern-12mu\rightarrow} \def\longmapsto{\mapstochar\kern-9mu\lyxbar\kern-11mu\rightarrow} \def\models{\vert\kern-7.5mu\lyxeq} endif iffont cmm \def\hookrightarrow{\lhook\kern-13mu\rightarrow} \def\hookleftarrow{\leftarrow\kern-13mu\rhook} \def\bowtie{\triangleright\kern-6mu\triangleleft} endif iffont msa \def\dashrightarrow{\lyxdabar\lyxdabar\lyxright} \def\dashleftarrow{\lyxleft\lyxdabar\lyxdabar} \def\dasharrow{\dashrightarrow} endif iffont msb \def\Join{\ltimes\kern-12mu\rtimes} endif \def\mathcircumflex{\mbox{\^{}}} neq lyxsymbol 185 0 mathrel x ne lyxsymbol 185 0 mathrel x textdegree lyxsymbol 176 0 mathord x cong lyxsymbol 64 0 mathrel x surd lyxsymbol 214 0 mathord x #"{\hat{}}