📄 mathml.dtd
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<!ENTITY numsp ' '><!ENTITY puncsp ' '><!ENTITY ThinSpace ' '> <!ENTITY thinsp ' '><!ENTITY ThickSpace ''><!ENTITY NegativeThinSpace ''><!ENTITY VeryThinSpace ' '> <!ENTITY hairsp ' '><!ENTITY NegativeVeryThinSpace ''><!ENTITY InvisibleComma '​'> <!ENTITY ZeroWidthSpace '​'> <!ENTITY ic '​'><!ENTITY zwnj '‌'><!ENTITY zwj '‍'><!ENTITY lrm '‎'><!ENTITY rlm '‏'><!ENTITY dash '‐'> <!ENTITY hyphen '‐'><!ENTITY ndash '–'><!ENTITY mdash '—'><!ENTITY horbar '―'><!ENTITY Verbar '‖'> <!ENTITY Vert '‖'><!ENTITY OpenCurlyQuote '‘'> <!ENTITY lsquo '‘'><!ENTITY CloseCurlyQuote '’'> <!ENTITY rsquo '’'> <!ENTITY rsquor '’'><!ENTITY lsquor '‚'> <!ENTITY sbquo '‚'><!ENTITY OpenCurlyDoubleQuote '“'> <!ENTITY ldquo '“'><!ENTITY CloseCurlyDoubleQuote '”'> <!ENTITY rdquo '”'> <!ENTITY rdquor '”'><!ENTITY bdquo '„'> <!ENTITY ldquor '„'><!ENTITY dagger '†'><!ENTITY Dagger '‡'> <!ENTITY ddagger '‡'><!ENTITY bull '•'> <!ENTITY bullet '•'><!ENTITY nldr '‥'><!ENTITY hellip '…'> <!ENTITY mldr '…'><!ENTITY permil '‰'><!ENTITY pertenk '‱'><!ENTITY prime '′'><!ENTITY Prime '″'><!ENTITY tprime '‴'><!ENTITY backprime '‵'> <!ENTITY bprime '‵'><!ENTITY lsaquo '‹'><!ENTITY rsaquo '›'><!ENTITY oline '‾'><!ENTITY caret '⁁'><!ENTITY hybull '⁃'><!ENTITY frasl '⁄'><!ENTITY bsemi '⁏'><!ENTITY qprime '⁗'><!ENTITY MediumSpace ' '><!ENTITY NegativeMediumSpace ''><!ENTITY ApplyFunction '⁡'> <!ENTITY af '⁡'><!ENTITY InvisibleTimes '⁢'> <!ENTITY it '⁢'><!ENTITY euro '€'><!ENTITY TripleDot '⃛'> <!ENTITY tdot '⃛'><!ENTITY DotDot '⃜'><!ENTITY Copf 'ℂ'> <!ENTITY complexes 'ℂ'><!ENTITY incare '℅'><!ENTITY gscr 'ℊ'><!ENTITY HilbertSpace 'ℋ'> <!ENTITY Hscr 'ℋ'> <!ENTITY hamilt 'ℋ'><!ENTITY Hfr 'ℌ'> <!ENTITY Poincareplane 'ℌ'><!ENTITY Hopf 'ℍ'> <!ENTITY quaternions 'ℍ'><!ENTITY planckh 'ℎ'><!ENTITY hslash 'ℏ'> <!ENTITY plankv 'ℏ'><!ENTITY hbar ''> <!ENTITY planck ''><!ENTITY Iscr 'ℐ'> <!ENTITY imagline 'ℐ'><!ENTITY Ifr 'ℑ'> <!ENTITY Im 'ℑ'> <!ENTITY image 'ℑ'> <!ENTITY imagpart 'ℑ'><!ENTITY Laplacetrf 'ℒ'> <!ENTITY Lscr 'ℒ'> <!ENTITY lagran 'ℒ'><!ENTITY ell 'ℓ'> <!ENTITY lscr 'ℓ'><!ENTITY Nopf 'ℕ'> <!ENTITY naturals 'ℕ'><!ENTITY numero '№'><!ENTITY copysr '℗'><!ENTITY weierp '℘'> <!ENTITY wp '℘'><!ENTITY Popf 'ℙ'> <!ENTITY primes 'ℙ'><!ENTITY Qopf 'ℚ'> <!ENTITY rationals 'ℚ'><!ENTITY Rscr 'ℛ'> <!ENTITY realine 'ℛ'><!ENTITY Re 'ℜ'> <!ENTITY Rfr 'ℜ'> <!ENTITY real 'ℜ'> <!ENTITY realpart 'ℜ'><!ENTITY Ropf 'ℝ'> <!ENTITY reals 'ℝ'><!ENTITY rx '℞'><!ENTITY trade '™'><!ENTITY Zopf 'ℤ'> <!ENTITY integers 'ℤ'><!ENTITY ohm 'Ω'><!ENTITY mho '℧'><!ENTITY Zfr 'ℨ'> <!ENTITY zeetrf 'ℨ'><!ENTITY iiota '℩'><!ENTITY angst 'Å'><!ENTITY Bernoullis 'ℬ'> <!ENTITY Bscr 'ℬ'> <!ENTITY bernou 'ℬ'><!ENTITY Cayleys 'ℭ'> <!ENTITY Cfr 'ℭ'><!ENTITY escr 'ℯ'><!ENTITY Escr 'ℰ'> <!ENTITY expectation 'ℰ'><!ENTITY Fouriertrf 'ℱ'> <!ENTITY Fscr 'ℱ'><!ENTITY Mellintrf 'ℳ'> <!ENTITY Mscr 'ℳ'> <!ENTITY phmmat 'ℳ'><!ENTITY order 'ℴ'> <!ENTITY orderof 'ℴ'> <!ENTITY oscr 'ℴ'><!ENTITY alefsym 'ℵ'> <!ENTITY aleph 'ℵ'><!ENTITY beth 'ℶ'><!ENTITY gimel 'ℷ'><!ENTITY daleth 'ℸ'><!ENTITY CapitalDifferentialD 'ⅅ'> <!ENTITY DD 'ⅅ'><!ENTITY DifferentialD 'ⅆ'> <!ENTITY dd 'ⅆ'><!ENTITY ExponentialE 'ⅇ'> <!ENTITY ee 'ⅇ'> <!ENTITY exponentiale 'ⅇ'><!ENTITY ImaginaryI 'ⅈ'> <!ENTITY ii 'ⅈ'><!ENTITY frac13 '⅓'><!ENTITY frac23 '⅔'><!ENTITY frac15 '⅕'><!ENTITY frac25 '⅖'><!ENTITY frac35 '⅗'><!ENTITY frac45 '⅘'><!ENTITY frac16 '⅙'><!ENTITY frac56 '⅚'><!ENTITY frac18 '⅛'><!ENTITY frac38 '⅜'><!ENTITY frac58 '⅝'><!ENTITY frac78 '⅞'><!ENTITY LeftArrow '←'> <!ENTITY larr '←'> <!ENTITY leftarrow '←'><!ENTITY ShortLeftArrow ''> <!ENTITY slarr ''><!ENTITY UpArrow '↑'> <!ENTITY uarr '↑'> <!ENTITY uparrow '↑'><!ENTITY RightArrow '→'> <!ENTITY rarr '→'> <!ENTITY rightarrow '→'><!ENTITY ShortRightArrow ''> <!ENTITY srarr ''><!ENTITY DownArrow '↓'> <!ENTITY darr '↓'> <!ENTITY downarrow '↓'><!ENTITY LeftRightArrow '↔'> <!ENTITY harr '↔'> <!ENTITY leftrightarrow '↔'><!ENTITY UpDownArrow '↕'> <!ENTITY updownarrow '↕'> <!ENTITY varr '↕'><!ENTITY UpperLeftArrow '↖'> <!ENTITY nwarr '↖'> <!ENTITY nwarrow '↖'><!ENTITY UpperRightArrow '↗'> <!ENTITY nearr '↗'> <!ENTITY nearrow '↗'><!ENTITY LowerRightArrow '↘'> <!ENTITY searr '↘'> <!ENTITY searrow '↘'><!ENTITY LowerLeftArrow '↙'> <!ENTITY swarr '↙'> <!ENTITY swarrow '↙'><!ENTITY nlarr '↚'> <!ENTITY nleftarrow '↚'><!ENTITY nrarr '↛'> <!ENTITY nrightarrow '↛'><!ENTITY rarrw '↝'> <!ENTITY rightsquigarrow '↝'><!ENTITY nrarrw ''><!ENTITY Larr '↞'> <!ENTITY twoheadleftarrow '↞'><!ENTITY Uarr '↟'><!ENTITY Rarr '↠'> <!ENTITY twoheadrightarrow '↠'><!ENTITY Darr '↡'><!ENTITY larrtl '↢'> <!ENTITY leftarrowtail '↢'><!ENTITY rarrtl '↣'> <!ENTITY ratail '↣'> <!ENTITY rightarrowtail '↣'><!ENTITY LeftTeeArrow '↤'> <!ENTITY mapstoleft '↤'><!ENTITY UpTeeArrow '↥'> <!ENTITY mapstoup '↥'><!ENTITY RightTeeArrow '↦'> <!ENTITY map '↦'> <!ENTITY mapsto '↦'><!ENTITY DownTeeArrow '↧'> <!ENTITY mapstodown '↧'><!ENTITY hookleftarrow '↩'> <!ENTITY larrhk '↩'><!ENTITY hookrightarrow '↪'> <!ENTITY rarrhk '↪'><!ENTITY larrlp '↫'> <!ENTITY looparrowleft '↫'><!ENTITY looparrowright '↬'> <!ENTITY rarrlp '↬'><!ENTITY harrw '↭'> <!ENTITY leftrightsquigarrow '↭'><!ENTITY nharr '↮'> <!ENTITY nleftrightarrow '↮'><!ENTITY Lsh '↰'> <!ENTITY lsh '↰'><!ENTITY Rsh '↱'> <!ENTITY rsh '↱'><!ENTITY ldsh '↲'><!ENTITY rdsh '↳'><!ENTITY crarr '↵'><!ENTITY cularr '↶'> <!ENTITY curvearrowleft '↶'><!ENTITY curarr '↷'> <!ENTITY curvearrowright '↷'><!ENTITY circlearrowleft '↺'> <!ENTITY olarr '↺'><!ENTITY circlearrowright '↻'> <!ENTITY orarr '↻'><!ENTITY LeftVector '↼'> <!ENTITY leftharpoonup '↼'> <!ENTITY lharu '↼'><!ENTITY DownLeftVector '↽'> <!ENTITY leftharpoondown '↽'> <!ENTITY lhard '↽'><!ENTITY RightUpVector '↾'> <!ENTITY uharr '↾'> <!ENTITY upharpoonright '↾'><!ENTITY LeftUpVector '↿'> <!ENTITY uharl '↿'> <!ENTITY upharpoonleft '↿'><!ENTITY RightVector '⇀'> <!ENTITY rharu '⇀'> <!ENTITY rightharpoonup '⇀'><!ENTITY DownRightVector '⇁'> <!ENTITY rhard '⇁'> <!ENTITY rightharpoondown '⇁'><!ENTITY RightDownVector '⇂'> <!ENTITY dharr '⇂'> <!ENTITY downharpoonright '⇂'><!ENTITY LeftDownVector '⇃'> <!ENTITY dharl '⇃'> <!ENTITY downharpoonleft '⇃'><!ENTITY RightArrowLeftArrow '⇄'> <!ENTITY rightleftarrows '⇄'> <!ENTITY rlarr '⇄'><!ENTITY UpArrowDownArrow '⇅'> <!ENTITY udarr '⇅'><!ENTITY LeftArrowRightArrow '⇆'> <!ENTITY leftrightarrows '⇆'> <!ENTITY lrarr '⇆'><!ENTITY leftleftarrows '⇇'> <!ENTITY llarr '⇇'><!ENTITY upuparrows '⇈'> <!ENTITY uuarr '⇈'><!ENTITY rightrightarrows '⇉'> <!ENTITY rrarr '⇉'><!ENTITY ddarr '⇊'> <!ENTITY downdownarrows '⇊'><!ENTITY ReverseEquilibrium '⇋'> <!ENTITY leftrightharpoons '⇋'> <!ENTITY lrhar '⇋'><!ENTITY Equilibrium '⇌'> <!ENTITY rightleftharpoons '⇌'> <!ENTITY rlhar '⇌'><!ENTITY nLeftarrow '⇍'> <!ENTITY nlArr '⇍'> <!ENTITY nvlArr '⇍'><!ENTITY nLeftrightarrow '⇎'> <!ENTITY nhArr '⇎'> <!ENTITY nvHarr '⇎'><!ENTITY nRightarrow '⇏'> <!ENTITY nrArr '⇏'> <!ENTITY nvrArr '⇏'><!ENTITY DoubleLeftArrow '⇐'> <!ENTITY Leftarrow '⇐'> <!ENTITY lArr '⇐'><!ENTITY DoubleUpArrow '⇑'> <!ENTITY Uparrow '⇑'> <!ENTITY uArr '⇑'><!ENTITY DoubleRightArrow '⇒'> <!ENTITY Implies '⇒'> <!ENTITY Rightarrow '⇒'> <!ENTITY rArr '⇒'><!ENTITY DoubleDownArrow '⇓'> <!ENTITY Downarrow '⇓'> <!ENTITY dArr '⇓'><!ENTITY DoubleLeftRightArrow '⇔'> <!ENTITY Leftrightarrow '⇔'> <!ENTITY hArr '⇔'> <!ENTITY iff '⇔'><!ENTITY DoubleUpDownArrow '⇕'> <!ENTITY Updownarrow '⇕'> <!ENTITY vArr '⇕'><!ENTITY nwArr '⇖'><!ENTITY neArr '⇗'><!ENTITY seArr '⇘'><!ENTITY swArr '⇙'><!ENTITY Lleftarrow '⇚'> <!ENTITY lAarr '⇚'><!ENTITY Rrightarrow '⇛'> <!ENTITY rAarr '⇛'><!ENTITY zigrarr '⇝'><!ENTITY LeftArrowBar '⇤'> <!ENTITY larrb '⇤'><!ENTITY RightArrowBar '⇥'> <!ENTITY rarrb '⇥'><!ENTITY DownArrowUpArrow '⇵'> <!ENTITY duarr '⇵'><!ENTITY loarr '⇽'><!ENTITY roarr '⇾'><!ENTITY hoarr '⇿'><!ENTITY ForAll '∀'> <!ENTITY forall '∀'><!ENTITY comp '∁'> <!ENTITY complement '∁'><!ENTITY PartialD '∂'> <!ENTITY part '∂'><!ENTITY npart ''><!ENTITY Exists '∃'> <!ENTITY exist '∃'><!ENTITY NotExists '∄'> <!ENTITY nexist '∄'> <!ENTITY nexists '∄'><!ENTITY empty '∅'> <!ENTITY emptyv '∅'> <!ENTITY varnothing '∅'><!ENTITY empty ''> <!ENTITY emptyset ''><!ENTITY Del '∇'> <!ENTITY nabla '∇'><!ENTITY Element '∈'> <!ENTITY in '∈'> <!ENTITY isin '∈'> <!ENTITY isinv '∈'><!ENTITY NotElement '∉'> <!ENTITY notin '∉'><!ENTITY notinva ''><!ENTITY ReverseElement '∋'> <!ENTITY SuchThat '∋'> <!ENTITY ni '∋'> <!ENTITY niv '∋'><!ENTITY NotReverseElement '∌'> <!ENTITY notni '∌'> <!ENTITY notniva '∌'><!ENTITY Product '∏'> <!ENTITY prod '∏'><!ENTITY Coproduct '∐'> <!ENTITY coprod '∐'><!ENTITY Sum '∑'> <!ENTITY sum '∑'><!ENTITY minus '−'><!ENTITY MinusPlus '∓'> <!ENTITY mnplus '∓'> <!ENTITY mp '∓'><!ENTITY dotplus '∔'> <!ENTITY plusdo '∔'><!ENTITY Backslash '∖'> <!ENTITY setminus '∖'> <!ENTITY setmn '∖'><!ENTITY smallsetminus ''> <!ENTITY ssetmn ''><!ENTITY lowast '∗'><!ENTITY SmallCircle '∘'> <!ENTITY compfn '∘'><!ENTITY Sqrt '√'> <!ENTITY radic '√'><!ENTITY Proportional '∝'> <!ENTITY prop '∝'> <!ENTITY propto '∝'> <!ENTITY varpropto '∝'> <!ENTITY vprop '∝'><!ENTITY infin '∞'><!ENTITY angrt '∟'><!ENTITY ang '∠'> <!ENTITY angle '∠'><!ENTITY nang ''><!ENTITY angmsd '∡'> <!ENTITY measuredangle '∡'><!ENTITY angsph '∢'><!ENTITY VerticalBar '∣'> <!ENTITY mid '∣'><!ENTITY shortmid ''> <!ENTITY smid ''><!ENTITY NotVerticalBar '∤'> <!ENTITY nmid '∤'><!ENTITY nshortmid ''> <!ENTITY nsmid ''><!ENTITY DoubleVerticalBar '∥'> <!ENTITY par '∥'> <!ENTITY parallel '∥'><!ENTITY parsl ''> <!ENTITY shortparallel ''> <!ENTITY spar ''><!ENTITY nparsl ''><!ENTITY NotDoubleVerticalBar '∦'> <!ENTITY npar '∦'> <!ENTITY nparallel '∦'><!ENTITY nshortparallel ''> <!ENTITY nspar ''><!ENTITY and '∧'> <!ENTITY wedge '∧'><!ENTITY or '∨'> <!ENTITY vee '∨'><!ENTITY cap '∩'><!ENTITY caps ''><!ENTITY cup '∪'><!ENTITY cups ''><!ENTITY Integral '∫'> <!ENTITY int '∫'><!ENTITY Int '∬'><!ENTITY iiint '∭'> <!ENTITY tint '∭'><!ENTITY ContourIntegral '∮'> <!ENTITY conint '∮'> <!ENTITY oint '∮'><!ENTITY Conint '∯'> <!ENTITY DoubleContourIntegral '∯'><!ENTITY Cconint '∰'><!ENTITY cwint '∱'><!ENTITY ClockwiseContourIntegral '∲'> <!ENTITY cwconint '∲'><!ENTITY CounterClockwiseContourIntegral '∳'> <!ENTITY awconint '∳'><!ENTITY Therefore '∴'> <!ENTITY there4 '∴'> <!ENTITY therefore '∴'><!ENTITY Because '∵'> <!ENTITY becaus '∵'> <!ENTITY because '∵'><!ENTITY ratio '∶'><!ENTITY Colon '∷'> <!ENTITY Proportion '∷'><!ENTITY dotminus '∸'> <!ENTITY minusd '∸'><!ENTITY mDDot '∺'><!ENTITY homtht '∻'><!ENTITY Tilde '∼'> <!ENTITY sim '∼'><!ENTITY thicksim ''> <!ENTITY thksim ''><!ENTITY backsim '∽'> <!ENTITY bsim '∽'><!ENTITY mstpos '∾'><!ENTITY acd '∿'><!ENTITY VerticalTilde '≀'> <!ENTITY wr '≀'> <!ENTITY wreath '≀'><!ENTITY NotTilde '≁'> <!ENTITY nsim '≁'><!ENTITY nvsim ''><!ENTITY EqualTilde '≂'> <!ENTITY eqsim '≂'> <!ENTITY esim '≂'><!ENTITY NotEqualTilde ''> <!ENTITY nesim ''><!ENTITY TildeEqual '≃'> <!ENTITY sime '≃'> <!ENTITY simeq '≃'><!ENTITY NotTildeEqual '≄'> <!ENTITY nsime '≄'> <!ENTITY nsimeq '≄'><!ENTITY TildeFullEqual '≅'> <!ENTITY cong '≅'><!ENTITY simne '≆'><!ENTITY NotTildeFullEqual '≇'> <!ENTITY ncong '≇'><!ENTITY TildeTilde '≈'> <!ENTITY ap '≈'> <!ENTITY approx '≈'> <!ENTITY asymp '≈'><!ENTITY thickapprox ''> <!ENTITY thkap ''><!ENTITY NotTildeTilde '≉'> <!ENTITY nap '≉'> <!ENTITY napprox '≉'><!ENTITY nvap ''><!ENTITY apE '≊'> <!ENTITY ape '≊'> <!ENTITY approxeq '≊'><!ENTITY apid '≋'><!ENTITY napid ''><!ENTITY backcong '≌'> <!ENTITY bcong '≌'><!ENTITY CupCap '≍'> <!ENTITY asymp '≍'><!ENTITY Bumpeq '≎'> <!ENTITY HumpDownHump '≎'> <!ENTITY bump '≎'><!ENTITY NotHumpDownHump ''> <!ENTITY nbump ''><!ENTITY HumpEqual '≏'> <!ENTITY bumpe '≏'> <!ENTITY bumpeq '≏'><!ENTITY NotHumpEqual ''> <!ENTITY nbumpe ''><!ENTITY DotEqual '≐'> <!ENTITY doteq '≐'> <!ENTITY esdot '≐'><!ENTITY doteqdot '≑'> <!ENTITY eDot '≑'><!ENTITY efDot '≒'> <!ENTITY fallingdotseq '≒'><!ENTITY erDot '≓'> <!ENTITY risingdotseq '≓'><!ENTITY Assign '≔'> <!ENTITY colone '≔'> <!ENTITY coloneq '≔'><!ENTITY ecolon '≕'> <!ENTITY eqcolon '≕'><!ENTITY ecir '≖'> <!ENTITY eqcirc '≖'><!ENTITY circeq '≗'> <!ENTITY cire '≗'><!ENTITY wedgeq '≙'><!ENTITY veeeq '≚'><!ENTITY easter '≛'><!ENTITY triangleq '≜'> <!ENTITY trie '≜'><!ENTITY equest '≟'> <!ENTITY questeq '≟'><!ENTITY NotEqual '≠'> <!ENTITY ne '≠'><!ENTITY nedot ''><!ENTITY Congruent '≡'> <!ENTITY equiv '≡'><!ENTITY bnequiv ''><!ENTITY NotCongruent '≢'> <!ENTITY nequiv '≢'><!ENTITY le '≤'> <!ENTITY leq '≤'><!ENTITY GreaterEqual '≥'> <!ENTITY ge '≥'> <!ENTITY geq '≥'><!ENTITY LessFullEqual '≦'> <!ENTITY lE '≦'> <!ENTITY leqq '≦'><!ENTITY GreaterFullEqual '≧'> <!ENTITY gE '≧'> <!ENTITY geqq '≧'><!ENTITY lnE '≨'> <!ENTITY lne '≨'> <!ENTITY lneq '≨'> <!ENTITY lneqq '≨'><!ENTITY lvertneqq ''> <!ENTITY lvnE ''><!ENTITY gnE '≩'> <!ENTITY gne '≩'> <!ENTITY gneq '≩'> <!ENTITY gneqq '≩'><!ENTITY gvertneqq ''> <!ENTITY gvnE ''><!ENTITY Lt '≪'> <!ENTITY NestedLessLess '≪'> <!ENTITY ll '≪'><!ENTITY nLt ''><!ENTITY NotLessLess ''> <!ENTITY nLtv ''><!ENTITY Gt '≫'> <!ENTITY NestedGreaterGreater '≫'> <!ENTITY gg '≫'><!ENTITY nGt ''><!ENTITY NotGreaterGreater ''> <!ENTITY nGtv ''><!ENTITY between '≬'> <!ENTITY twixt '≬'><!ENTITY NotCupCap '≭'>⌨️ 快捷键说明
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