This run took 72 seconds.
$ date
Mon Dec 6 07:28:56 UTC 2021
$ git clone file:///srv/git/mediawiki-services-texvcjs.git repo --depth=1 -b master
Cloning into 'repo'...
$ git config user.name libraryupgrader
$ git config user.email tools.libraryupgrader@tools.wmflabs.org
$ git submodule update --init
$ grr init
Installed commit-msg hook.
$ git show-ref refs/heads/master
3255e8023610b15effe8941c9aaca0749cbc1554 refs/heads/master
Attempting to npm audit fix
$ npm audit fix --only=dev
> core-js@3.10.1 postinstall /src/repo/node_modules/core-js
> node -e "try{require('./postinstall')}catch(e){}"
[96mThank you for using core-js ([94m https://github.com/zloirock/core-js [96m) for polyfilling JavaScript standard library![0m
[96mThe project needs your help! Please consider supporting of core-js on Open Collective or Patreon: [0m
[96m>[94m https://opencollective.com/core-js [0m
[96m>[94m https://www.patreon.com/zloirock [0m
[96mAlso, the author of core-js ([94m https://github.com/zloirock [96m) is looking for a good job -)[0m
npm WARN optional SKIPPING OPTIONAL DEPENDENCY: fsevents@2.1.3 (node_modules/fsevents):
npm WARN notsup SKIPPING OPTIONAL DEPENDENCY: Unsupported platform for fsevents@2.1.3: wanted {"os":"darwin","arch":"any"} (current: {"os":"linux","arch":"x64"})
added 425 packages from 263 contributors in 10.441s
64 packages are looking for funding
run `npm fund` for details
fixed 0 of 9 vulnerabilities in 427 scanned packages
1 package update for 9 vulnerabilities involved breaking changes
(use `npm audit fix --force` to install breaking changes; or refer to `npm audit` for steps to fix these manually)
$ npm audit fix --only=dev
npm WARN optional SKIPPING OPTIONAL DEPENDENCY: fsevents@2.1.3 (node_modules/fsevents):
npm WARN notsup SKIPPING OPTIONAL DEPENDENCY: Unsupported platform for fsevents@2.1.3: wanted {"os":"darwin","arch":"any"} (current: {"os":"linux","arch":"x64"})
up to date in 2.425s
64 packages are looking for funding
run `npm fund` for details
fixed 0 of 9 vulnerabilities in 427 scanned packages
1 package update for 9 vulnerabilities involved breaking changes
(use `npm audit fix --force` to install breaking changes; or refer to `npm audit` for steps to fix these manually)
$ npm audit fix --only=dev
npm WARN optional SKIPPING OPTIONAL DEPENDENCY: fsevents@2.1.3 (node_modules/fsevents):
npm WARN notsup SKIPPING OPTIONAL DEPENDENCY: Unsupported platform for fsevents@2.1.3: wanted {"os":"darwin","arch":"any"} (current: {"os":"linux","arch":"x64"})
up to date in 2.498s
64 packages are looking for funding
run `npm fund` for details
fixed 0 of 9 vulnerabilities in 427 scanned packages
1 package update for 9 vulnerabilities involved breaking changes
(use `npm audit fix --force` to install breaking changes; or refer to `npm audit` for steps to fix these manually)
$ package-lock-lint package-lock.json
Checking package-lock.json
Verifying that tests still pass
$ npm ci
npm WARN prepare removing existing node_modules/ before installation
> core-js@3.10.1 postinstall /src/repo/node_modules/core-js
> node -e "try{require('./postinstall')}catch(e){}"
added 427 packages in 7.258s
$ npm test
> mathoid-texvcjs@0.3.10 test /src/repo
> node -e 'require("./lib/build-parser")' && npm run lint && mocha
> mathoid-texvcjs@0.3.10 lint /src/repo
> eslint --max-warnings 0 --ext .js .
Comprehensive test cases
Box functions
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Box functions (2)
✓ output should be correct
✓ should parse its own output
LaTeX functions
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Mediawiki functions
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Literals (1)
✓ output should be correct
✓ should parse its own output (76ms)
✓ should match ocaml output
Literals (2)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Literals (2')
✓ output should be correct
✓ should parse its own output
Literals (2) MJ
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Literals (2') MJ
✓ output should be correct
✓ should parse its own output
Literals (3)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Big
✓ output should be correct (48ms)
✓ should parse its own output (309ms)
✓ should match ocaml output
Delimiters (1)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Delimiters (2)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Delimiters (3)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Delimiters (4)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Delimiters (5)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
FUN_AR1
✓ output should be correct
✓ should parse its own output
FUN_AR1 (2)
✓ output should be correct
✓ should match ocaml output (except for spacing)
FUN_AR1NB (1)
✓ output should be correct
✓ should parse its own output
FUN_AR1NB (2)
✓ output should be correct
✓ should parse its own output
FUN_AR1NB (3)
✓ output should be correct
✓ should parse its own output
FUN_AR1NB (4)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
FUN_AR1NB (5)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
FUN_AR1OPT
✓ output should be correct
✓ should parse its own output
FUN_AR2
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output (except for spacing)
FUN_AR2nb
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
FUN_INFIX (1)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
FUN_INFIX (2)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
FUN_INFIX (3)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
FUN_INFIX (4)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
DECLh
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
litsq_zq
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Matrices (1)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Matrices (2)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Matrices (3)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Color (1)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Color (2)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Color (3)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Color (4)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Color (5)
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
Unicode
✓ output should be correct
✓ should parse its own output
✓ should match ocaml output
API
✓ should return success (1)
✓ should return success (2)
✓ should report undefined functions (1)
✓ should report undefined functions (2)
✓ should report undefined parser errors
✓ should throw an exception in debug mode
✓ should accept parsed input
✓ should check "\\newcommand{\\text{do evil things}}"
✓ should check "\\sin\\left(\\frac12x\\right)"
✓ should check "\\reals"
✓ should check "\\lbrack"
✓ should check "\\figureEightIntegral"
✓ should check "\\diamondsuit "
✓ should check "\\sinh x"
✓ should check "\\begin{foo}\\end{foo}"
✓ should check "\\hasOwnProperty"
✓ should check "\\hline"
✓ should check "\\begin{array}{c}\\hline a \\\\ \\hline\\hline b \\end{array}"
✓ should check "\\Diamond "
✓ should check "{\\begin{matrix}a\\ b\\end{matrix}}"
✓ should check "{\\cancel {x}}"
✓ should check "\\color {red}"
✓ should check "\\euro"
✓ should check "\\coppa"
✓ should check "\\mathbb {R}"
✓ should check "\\reals"
✓ should check "{\\color [rgb]{1,0,0}{\\mbox{This text is red.}}}"
✓ should check "{\\color[rgb]{1.5,0,0}{\\mbox{This text is bright red.}}}"
✓ should check "{\\color [RGB]{51,0,0}{\\mbox{This text is dim red.}}}"
✓ should check "{\\color[RGB]{256,0,0}{\\mbox{This text is bright red.}}}"
✓ should check "\\ce{ H2O }"
✓ should check "\\ce{[Zn(OH)4]^2-}"
✓ should retry parsing if oldmhchem is not set
✓ should not retry parsing if oldmhchem is set
AST
✓ should construct and stringify
All formulae from chem regression dataset:
✓ {\displaystyle {\ce {H2SO4\;->[P_{2}O5]\;H2O\;+\;SO3}}} ... {\displaystyle {\ce {AgNO3\;+\;H2S\;->\;Ag2S\;+\;}}} (1971ms)
✓ {\displaystyle {\ce {[A]=[B]The'''integratedsecondorderratelaws'''arerespectively:<ce>{\frac {1}{[A]}}={\frac {1}{[A]0}}+{\mathit {kt}}}}} ... {\displaystyle {\ce {3RuCl3\cdot {\mathit {x}}H2O\ +\mathrm {4.5} Zn\ +12CO{\mathit {(highpressure)}}]->Ru3(CO)12\ +3H2O\ +\mathrm {4.5} ZnCl2}}} (1990ms)
✓ {\displaystyle {\ce {1/8SO3\;+\;H2O\;->\;H2SO4\quad \quad \Delta H=-73,69\;kJ/mol}}} ... {\displaystyle {\ce {6Al\;+\;3CO\;->\;Al4C3\;+\;6CO}}} (1969ms)
✓ {\displaystyle {\ce {C6H2(NO2)3OH->{(NH4)2S2O3}+{CO<sub>2</sub>}+{HNO<sub>3</sub>}+{HCN}}}} ... {\displaystyle {\ce {{ClO4^{-}(aq)}+{2H^{+}(aq)}+{2e^{-}}\ =\ {ClO3^{-}(aq)}+{H2O(l)}\ ,\ {\mathit {E}}^{\circ }\ =}}} (1817ms)
✓ {\displaystyle {\ce {\underbrace {S\ {+}\ O2->SO_{2}} _{ReaktionvonSchwefelmitSauerstoff}}}} ... {\displaystyle {\ce {E\ +\ S\ {\underset {{\mathit {k}}_{-1}}{\overset {{\mathit {k}}_{1}}{\rightleftarrows }}}\ ES\ {\underset {{\mathit {k}}_{-2}}{\overset {{\mathit {k}}_{2}}{\rightleftarrows }}}\ EP\ {\underset {{\mathit {k}}_{-3}}{\overset {{\mathit {k}}_{1}}{\rightleftarrows }}}\ E\ +\ P}}} (1880ms)
✓ {\displaystyle {\ce {{[{M}+H]^{1}+}+He+->}}\left[{\ce {[{M}+H]^{2}+}}\right]^{*}+{\ce {He^{0}->fragments}}} ... {\displaystyle {\ce {Al2O3\cdot nH2O(0<n<0,6)}}} (1569ms)
✓ {\displaystyle {\ce {oiiornjgre9tjhgbrwemnfmgooir.ifgrjigkwjhrkjhewhfdseweiudfoi;jw3jfgmwendfnbvbwefknowkskjnlweknv.kwnbfjbwehemdfmnbvqnuebcomuincnwldjbhc9j0chiinonweoondoofnrjmk,.wlmomj,odpkp,dsjporxpojrmmkmown111111iednbxudbdfefuhjdjbhidjopejmiomniepopd.,wjciwdhdbccjca9shdbnbbjbchdcnmwjjnq9ksiouniookiooijsioxihiiwncpodopbupif9mpombhcnod,dsjporxpojrmmkmown111111iednbxudbdfefuhCO2+C->2COHg^{2}+->[I-]HgI2->[I-]{[Hg^{II}I4]^{2}-}}}} ... {\displaystyle {\ce {2Na2HAsO4\ {\overset {\mathit {\rm {\Delta }}}{\longrightarrow }}\ {Na4As2O7}+H_{2}O}}} (1729ms)
✓ {\displaystyle {\ce {2Na{+}Cl2={\Delta }}}} ... {\displaystyle {\ce {{2MgO_{(s)}}+{Si_{(s)}}+{2CaO_{(s)}}->{2Mg_{(}g)}+Ca2SiO4(s)}}} (1535ms)
✓ {\displaystyle {\ce {H-{\overset {\displaystyle {H2-CH3-T5} \atop |}{\underset {| \atop \displaystyle H}{C}}}}}} ... {\displaystyle {\ce {[A]_{\mathit {t}}=[A]_{0}-[B]_{\mathit {t}}}}} (1601ms)
✓ {\displaystyle {\ce {Ni+4CO{\xrightarrow[{}]{25deg.C}}\mathrm {Ni(CO)} _{4}{\xrightarrow[{}]{>100deg.C}}\mathrm {Ni} +4\mathrm {CO} }}} ... {\displaystyle {\ce {{CO_{2}}+{H_{2}O}\longrightarrow {H+}+{2HCO_{3}^{-}}}}} (1745ms)
✓ {\displaystyle {\ce {2NO3^{-}\;+\;2CH2O\;+\;H3O^{+}\;+\;->\;N2O\;+\;2CO2\;+\;5}}} ... {\displaystyle {\ce {S\;+\;1/2O2\;->\;SO\quad \quad \Delta H_{f}=+7\;kJ/mol}}} (1744ms)
✓ {\displaystyle {\ce {{\Pi \rho {\acute {\mathrm {o} }}\delta \rho \mathrm {o} \mu \mathrm {o} ~\mu {\acute {\mathrm {o} }}\rho \iota \mathrm {o} }+ATP<=>{\pi \rho \mathrm {o} {\ddot {\iota }}{\acute {\mathrm {o} }}\nu ~AMP}+PP_{i}}}} ... {\displaystyle {\ce {{[A]_{0}}-[C]\approx [A]_{0}}}} (1612ms)
✓ {\displaystyle {\ce {NH4NO3(s)\;->\;N2O(g)}}} ... {\displaystyle {\begin{array}{l}{}\\{\ce {^{238}_{92}U->[\alpha ][4.468\times 10^{9}\ {\ce {y}}]_{90}^{234}Th->[\beta ^{-}][24.1\ {\ce {d}}]_{91}^{234\!m}Pa}}{\begin{Bmatrix}{\ce {->[0.16\%][1.17\ {\ce {min}}]_{91}^{234}Pa->[\beta ^{-}][6.7\ {\ce {h}}]}}\\{\ce {->[99.84\%\ \beta ^{-}][1,17\ {\ce {min}}]}}\end{Bmatrix}}{\ce {^{234}_{92}U->[\alpha ][2.445\times 10^{5}\ {\ce {y}}]_{90}^{230}Th->[\alpha ][7.7\times 10^{4}\ {\ce {y}}]_{88}^{226}Ra->[\alpha ][1600\ y]_{86}^{222}Rn}}\\{\ce {^{222}_{86}Rn->[\alpha ][3.8235\ {\ce {d}}]_{84}^{218}Po->[\alpha ][3.05\ {\ce {min}}]_{82}^{214}Pb->[\beta ^{-}][26,8\ {\ce {min}}]_{83}^{214}Bi->[\beta ^{-}][19.9\ {\ce {min}}]_{84}^{214}Po->[\alpha ][164.3\ \mu {\ce {s}}]_{82}^{210}Pb->[\beta ^{-}][22.26\ {\ce {y}}]_{83}^{210}Bi->[\beta ^{-}][5,013\ {\ce {d}}]_{84}^{210}Po->[\alpha ][138.38\ {\ce {d}}]_{82}^{206}Pb}}\end{array}}} (1884ms)
✓ {\displaystyle {\ce {N_{2}O\;+\;O_{2}\;->\;2NO}}} ... {\displaystyle {\ce {HSo3^{-}\;->\;H2O2\;+\;O2}}} (1692ms)
✓ {\displaystyle {\ce {NaCl\;+\;NaSO4\;->[200\;{}^{\circ }C]\;HCl\;+\;NaHSO4}}} ... {\displaystyle {\ce {S^{IV}O2\;+\;H2O2\;->\;H2SO4}}} (466ms)
ast.Tex.contains_func
✓ should not find \foo in \left(abc\right)
✓ should not find \begin{foo} in \left(abc\right)
✓ should find \left in \left(abc\right)
✓ should find \right in \left(abc\right)
✓ should not find \foo in \sin(x)+\cos(x)^2
✓ should not find \begin{foo} in \sin(x)+\cos(x)^2
✓ should find \sin in \sin(x)+\cos(x)^2
✓ should find \cos in \sin(x)+\cos(x)^2
✓ should not find \foo in \big\langle
✓ should not find \begin{foo} in \big\langle
✓ should find \big in \big\langle
✓ should find \langle in \big\langle
✓ should not find \arccot in \arccot(x) \atop \aleph
✓ should not find \foo in \arccot(x) \atop \aleph
✓ should not find \begin{foo} in \arccot(x) \atop \aleph
✓ should find \operatorname in \arccot(x) \atop \aleph
✓ should find \atop in \arccot(x) \atop \aleph
✓ should find \aleph in \arccot(x) \atop \aleph
✓ should not find \alef in \acute{\euro\alef}
✓ should not find \foo in \acute{\euro\alef}
✓ should not find \begin{foo} in \acute{\euro\alef}
✓ should find \acute in \acute{\euro\alef}
✓ should find \euro in \acute{\euro\alef}
✓ should find \aleph in \acute{\euro\alef}
✓ should find \mbox in \acute{\euro\alef}
✓ should not find \darr in \sqrt[\backslash]{\darr}
✓ should not find \foo in \sqrt[\backslash]{\darr}
✓ should not find \begin{foo} in \sqrt[\backslash]{\darr}
✓ should find \sqrt in \sqrt[\backslash]{\darr}
✓ should find \backslash in \sqrt[\backslash]{\darr}
✓ should find \downarrow in \sqrt[\backslash]{\darr}
✓ should not find \foo in \mbox{abc}
✓ should not find \begin{foo} in \mbox{abc}
✓ should find \mbox in \mbox{abc}
✓ should not find \foo in x_\aleph^\sqrt{2}
✓ should not find \begin{foo} in x_\aleph^\sqrt{2}
✓ should find \aleph in x_\aleph^\sqrt{2}
✓ should find \sqrt in x_\aleph^\sqrt{2}
✓ should not find \foo in {abc \rm def \it ghi}
✓ should not find \begin{foo} in {abc \rm def \it ghi}
✓ should find \rm in {abc \rm def \it ghi}
✓ should find \it in {abc \rm def \it ghi}
✓ should not find \bold in {\frac{\sideset{_\dagger}{^\bold{x}}\prod}{\hat{a}}}
✓ should not find \foo in {\frac{\sideset{_\dagger}{^\bold{x}}\prod}{\hat{a}}}
✓ should not find \begin{foo} in {\frac{\sideset{_\dagger}{^\bold{x}}\prod}{\hat{a}}}
✓ should find \frac in {\frac{\sideset{_\dagger}{^\bold{x}}\prod}{\hat{a}}}
✓ should find \sideset in {\frac{\sideset{_\dagger}{^\bold{x}}\prod}{\hat{a}}}
✓ should find \dagger in {\frac{\sideset{_\dagger}{^\bold{x}}\prod}{\hat{a}}}
✓ should find \mathbf in {\frac{\sideset{_\dagger}{^\bold{x}}\prod}{\hat{a}}}
✓ should find \prod in {\frac{\sideset{_\dagger}{^\bold{x}}\prod}{\hat{a}}}
✓ should find \hat in {\frac{\sideset{_\dagger}{^\bold{x}}\prod}{\hat{a}}}
✓ should not find \begin in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should not find \end in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should not find \hline in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should not find \foo in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should not find \begin{foo} in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should find \begin{array} in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should find \end{array} in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should find \alpha in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should find \beta in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should find \gamma in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should find \delta in \begin{array}{l|r} \alpha & \beta \\ \gamma & \delta \end{array}
✓ should not find \foo in \begin{array}{l|r}\hline a & b\end{array}
✓ should not find \begin{foo} in \begin{array}{l|r}\hline a & b\end{array}
✓ should find \begin{array} in \begin{array}{l|r}\hline a & b\end{array}
✓ should find \end{array} in \begin{array}{l|r}\hline a & b\end{array}
✓ should find \hline in \begin{array}{l|r}\hline a & b\end{array}
✓ should not find \c in \color[rgb]{0,1,.2}
✓ should not find rgb in \color[rgb]{0,1,.2}
✓ should not find \pagecolor in \color[rgb]{0,1,.2}
✓ should not find \definecolor in \color[rgb]{0,1,.2}
✓ should not find \foo in \color[rgb]{0,1,.2}
✓ should not find \begin{foo} in \color[rgb]{0,1,.2}
✓ should find \color in \color[rgb]{0,1,.2}
✓ should not find \color in \definecolor{blue}{cmyk}{1,0,0,0}\pagecolor{blue}
✓ should not find cmyk in \definecolor{blue}{cmyk}{1,0,0,0}\pagecolor{blue}
✓ should not find blue in \definecolor{blue}{cmyk}{1,0,0,0}\pagecolor{blue}
✓ should not find \blue in \definecolor{blue}{cmyk}{1,0,0,0}\pagecolor{blue}
✓ should not find \foo in \definecolor{blue}{cmyk}{1,0,0,0}\pagecolor{blue}
✓ should not find \begin{foo} in \definecolor{blue}{cmyk}{1,0,0,0}\pagecolor{blue}
✓ should find \definecolor in \definecolor{blue}{cmyk}{1,0,0,0}\pagecolor{blue}
✓ should find \pagecolor in \definecolor{blue}{cmyk}{1,0,0,0}\pagecolor{blue}
✓ should not find R in \mathbb{R}
✓ should not find \foo in \mathbb{R}
✓ should not find \begin{foo} in \mathbb{R}
✓ should find \mathbb in \mathbb{R}
✓ should not find a in \ce{\underbrace{a}_{b}}
✓ should not find b in \ce{\underbrace{a}_{b}}
✓ should not find \foo in \ce{\underbrace{a}_{b}}
✓ should not find \begin{foo} in \ce{\underbrace{a}_{b}}
✓ should find \underbrace in \ce{\underbrace{a}_{b}}
✓ should not find A in \AA
✓ should not find \foo in \AA
✓ should not find \begin{foo} in \AA
✓ should find \mbox in \AA
✓ should process string input
✓ should process mathrm
✓ should process partial trees
✓ should process parsed search input
All formulae from en-wiki:
- P=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)} ... Opex_t
- S_\ell=e^{2i\delta_\ell} ... \scriptstyle W[k] = (-1)^k\cdot W_0[k].
-
\psi(x)=\sum_{n\le x}\Lambda(n). \;
... \quad k(\phi)\;=\;\frac{P'M'}{PM}\;=\;\frac{\delta x}{R\cos\phi\,\delta\lambda},
- B = { I_0 \over 2 } e^{ -j \phi } ... \cos\left(\tfrac{\pi}{2}\,(2k+1)\right)=0
- \ \mathcal{L}_\mathrm{gf} = - \frac{1}{2} \operatorname{Tr}(F^{\mu \nu} F_{\mu \nu}) ... \begin{align}
x1 &= 1x = x \quad\text{(two-sided identity)} \\
x^0 &= 1
\end{align}
- \scriptstyle Z=A ... \psi(\alpha+1)=\psi(\alpha)=\delta
- p_w(\theta)=\frac{1}{2\pi}\,\sum_{n=-\infty}^{\infty} \phi(-n)\,e^{in\theta} = \frac{1}{2\pi}\,\sum_{n=-\infty}^{\infty} \phi(-n)\,z^n ... q_\mathrm{net} = \sum_{i=1}^N q_i \,\!
- y_3=Ay_2=AA^{2}y_0=A^{3}y_0, ... d J/d x = d A \rho v/dx = k r \rho v
- 0.0\dot{7} ... E_\text{cm}
- \ M_{heel} = pressure \times S \times A {cos(\phi)}^n ... x^3-x^2+(3x+1)y^2=0\,
- a(b + c + d) = ab + ac + ad ...
\left\{\begin{matrix} \ln\ \gamma_1=x^2_2\left[\tau_{21}\left(\frac{G_{21}}{x_1+x_2 G_{21}}\right)^2 +\frac{\tau_{12} G_{12}} {(x_2+x_1 G_{12})^2 }\right] \\
\\ \ln\ \gamma_2=x^2_1\left[\tau_{12}\left(\frac{G_{12}}{x_2+x_1 G_{12}}\right)^2 +\frac{\tau_{21} G_{21}} {(x_1+x_2 G_{21})^2 }\right]
\end{matrix}\right.
- a_{5}+b_{5}+c_{5}=2a_{1} ... \int_0^1 \left[xy + \frac{y^2}{2}\right]^1_{x^2} \, dx = \int_0^1 \left(x + \frac{1}{2} - x^3 - \frac{x^4}{2} \right) dx = \cdots = \frac{13}{20}.
- \frac{6}{r} + \frac{(1-p)^2}{pr} ... f*g=fg+\mathcal{O}(\hbar),
- \sigma_{zz} - \sigma_{yz} + \sigma_{xz} ... f\left( \frac{x+y}2 \right) \ge \frac{f(x) + f(y)}2
- N_W = {\text{Transient Inertial Force}\over \text{Shear Force}}\,\! ... return: fail
- \frac x{\cos\gamma} + \frac y{\sin\gamma} = 1, ... m_{solvent}
- \frac {x}{\ln x + 2} < \pi(x) < \frac {x}{\ln x - 4} ...
\sigma _1 ^2 = \sigma _3 ^2 = I, \; \sigma _1 \sigma _3 = - \sigma _3 \sigma _1 = e^{\pi i} \sigma _3 \sigma_1.
- \scriptstyle x \;\in\; [0,\, \infty)\! ... _{p}
- \lim_{x\to\infty}N^{-x}=\lim_{x\to\infty}1/N^{x}=0 \text{ for any } N > 1 ... \displaystyle{f_z(x) = e^{izx^2/2}}
- \scriptstyle G=\langle H, t | t^{-1}Kt=L\rangle ... \frac{}{}-I \, \delta
- \Re(z)>2 ... r_i = \frac{\varphi^2 a}{2 \sqrt{3}} = \frac{\sqrt{3}}{12} \left(3+ \sqrt{5} \right) a \approx 0.7557613141\cdot a
-
\mathcal F_\infty^* = \sigma\left\{ X_s^{-1}(B) : s\in[0,\infty), B \in \mathcal E^*\right\}.
... SubCipher_{n+1}=DEC_{b_{n+1}}(k_{b_{n+1}},C)
- c_{\text{fil}} ... \frac{(\log g)^2}{\pi g},
- g' \in G ... (n,k)
- \tbinom mr. ... \delta E/\delta x
- \Lambda(x,y,0) ...
I:\{\mathbb{X}\subseteq\mathbb{R}^n\}\rightarrow\{\mathbb{Y}\subseteq\mathbb{R}^m\}
- e\colon G\times G\rightarrow G_T ... (L_1 \times L_2) \cdot L_3 = \langle L_1,L_2,L_3 \rangle = 0.
- \dot S ... ~\epsilon_{t-1} > 0
- X \backslash E ... D_1(P \| Q) = \sum_{i=1}^n p_i \log \frac{p_i}{q_i}
- \frac{\text{d} f(x_1^*(c_1, c_2, \dots), x_2^*(c_1, c_2, \dots), ...)}{\text{d} c_k} = \lambda_k^*. ... \mathbf{r}
- \Delta_{\alpha} ... \mathbf{x} = \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix}^{\rm T}
- c = \pm 1 ... (\partial V)_T=-(\partial T)_V=-\left(\frac{\partial V}{\partial P}\right)_T
- - \hbar^2 c^2 \mathbf{\nabla}^2 \psi + m^2 c^4 \psi = - \hbar^2 \frac{\partial^2}{(\partial t)^2} \psi. ... M_v-N_u=L\Gamma^1{}_{22} + M(\Gamma^2{}_{22}-\Gamma^1{}_{12}) - N\Gamma^2{}_{12}
- \beta = -\eta_2, ... S(\theta_0 , \theta_i) = \frac{(\theta_0 - \theta_i) L_f}{t^{1/2}}
- \{f_i\}_{0}^{N-1} ... \alpha\,=\,\sum_{j=1}^{n}\,\frac{\sigma - \sigma_e}{\sigma_e + L_j(\sigma - \sigma_e)}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3)
- \gamma_{xy}=\frac{\partial u_x}{\partial y}+\frac{\partial u_y}{\partial x}\,\! ... \tfrac5{36} - \tfrac1{24} \sqrt{15}
- \varepsilon(w,z) = \overline{\mathbf{w}}^T \mathbf{Az}. ... (2 f(x))^{-2}
- \mathrm{R{-}COOH\ +\ H_2O_2\longrightarrow\ R{-}COOOH\ +\ H_2O} ... (t_1,t_0,p) \in D(X)
- A\mathbf{x} ... x_k,y_l
- A = \frac{M_{ssd}-M_{dry}}{M_{dry}} ... H_{\frac{1}{4},2}=16-8G-\tfrac{5}{6}\pi^2
- \rho= \frac{s}{1+c} , ... \begin{align}
\operatorname{Cov}(z',z'A') &= E\left[\left(z' - E(z') \right)\left(z'A' - E\left(z'A'\right) \right)' \right] \\
&= E\left[ (z' - \mu') (z'A' - \mu' A' )' \right]\\
&= E\left[ (z - \mu)' (Az - A\mu) \right].
\end{align}
- 0\le p_i \le 1 ... I^\pm(x)
- g=\prod_{i=1}^k p_i^{n_i}. ... \ x^2 - 92y^2=1
- LP ... \scriptstyle r(\boldsymbol{r}_i,\, \boldsymbol{r}_{\text{rec}}) / c \,+\, (t_i \,-\, t_{\text{rec}}) \,+\, \delta t_{\text{atmos},i} \,-\, \delta t_{\text{meas-err},i} \;=\; 0
- R_1 = \frac{1}{2!}f^{\prime\prime}(\xi_n)(\alpha - x_n)^{2} \,, ... u-u_h
- (a,b)=\begin{cases}1,&\mbox{ if }z^2=ax^2+by^2\mbox{ has a non-zero solution }(x,y,z)\in F^3;\\-1,&\mbox{ if not.}\end{cases} ... \Delta G_{ad} = \Delta G_{p} + \Delta G_{c}
- \frac {C_{13}^2 C_4^2 C_4^2 \cdot C_{11}^1 C_{4}^1} {C_{52}^5} = \frac {78 \cdot 6 \cdot 6 \cdot 11 \cdot 4} {2{,}598{,}960} = \frac {123{,}552} {2{,}598{,}960} \approx 4.75\% ...
u_{n,i+1/2} = \frac{u_{n,i}+u_{n,i+1}}{2}, \quad u_{n+1/2,i} = \frac{u_{n,i}+u_{n+1,i}}{2},
u_{n+1/2,i+1/2} = \frac{u_{n,i}+u_{n,i+1}+u_{n+1,i}+u_{n+1,i+1}}{4}.
- -Q_{Coble} ... \Gamma^\mu {}_{\alpha \beta}\
- \chi = B \rightarrow A ... \alpha=\frac{d\log(\lambda F_\lambda)}{d\log(\lambda)}
-
\Omega_{n,\mu\nu}(\mathbf R)=i\sum_{n'\neq n}{\langle n|(\partial H/\partial R_\mu) |n'\rangle\langle n'|(\partial H/\partial R_\nu) | n\rangle-(\nu\leftrightarrow\mu)\over(\varepsilon_n-\varepsilon_{n'})^2}.
... \phi_2
- s_{i+1}:=s_{i-1}-qs_{i}; ... R= 1 + \frac{\Delta W}{2 U^2} - \frac{C_{y2}}{U}
-
\lim_{\tau \rightarrow \infty} \left| \left\langle \frac{dG^{\mathrm{bound}}}{dt} \right\rangle_\tau \right| =
\lim_{\tau \rightarrow \infty} \left| \frac{G(\tau) - G(0)}{\tau} \right| \le
\lim_{\tau \rightarrow \infty} \frac{G_\max - G_\min}{\tau} = 0.
... c=\frac{\sigma_{\varepsilon}}{V}=\frac{\varepsilon}{d}
- b_1,b_2\in \mathcal{B} ... \mathrm{spark}(A) = \min_{d \ne 0} \|d\|_0 \text{ s.t. } A d = 0.
- X\times V ... P(y) \ge 0
- \vec{S}_t=\vec{S}\wedge \vec{S}_{xx}. \qquad ... X_1, X_2, X_3\ldots
- \rho \frac{\partial u}{\partial t} = -\frac{\partial p}{\partial x} + \mu \left(\frac{\partial^2 u}{\partial r^2} + \frac{1}{r} \frac{\partial u}{\partial r}\right) \, ... A(k) = \frac{1}{\sqrt{2}} e^{-\frac{(k-k_0)^2}{4}},
- (-\infty, 0) ... E=\frac{1}{8}\rho g H^2=\frac{1}{2}\rho g a^2.
- f : \mathbb R^2 \to \mathbb R^2 ... M = E - \epsilon \cdot \sin E
- SP(n)/P ... {\tilde K}_1(\mathbf{Z}[G])
- E(\bar{x})= c. \, ... \forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc
- U \subset \mathbb{R}^2 \times \mathbb{R}_{+} ... \nu = \frac{\tau-1}{\sigma d}\,\!
- B_i\subset\{1,2,\dots,n\} ... g_n > \frac{c\log n\log\log n\log\log\log\log n}{(\log\log\log n)^2}
- \Delta y=f(x+\Delta x)-f(x) ... g_8=-x+119x^2-490x^3+105x^4;
- =\left(\frac{1}{4} + \frac{1}{5}\right) ... (a_0, a_1, a_2, \ldots)
- \sum_ {} \vec{F} = 0 ... \ PV \ = \ {A \over e^r - 1}
-
\begin{bmatrix}
1 & 0\\
0 & 0\\
\end{bmatrix}
\begin{bmatrix}
0 & 0\\
0 & 1\\
\end{bmatrix}
\begin{bmatrix}
0 & 1\\
0 & 0\\
\end{bmatrix}
\begin{bmatrix}
0 & 0\\
1 & 0\\
\end{bmatrix}
... F_2(a, b) = a^b
-
\begin{align}
& \left(\csc\left(A + \frac{\pi}{6}\right), \csc\left(B + \frac{\pi}{6}\right), \csc\left(C + \frac{\pi}{6}\right)\right) \\
& = \left( \sec\left(A -\frac{\pi}{3}\right), \sec\left(B -\frac{\pi}{3}\right), \sec\left(C - \frac{\pi}{3}\right)\right)
\end{align}
... \ell^*(t)
- F(x)=\mu(-\infty,x] ... F_n(a, 0) = 0
- \quad A \cdot (A + B) = A ... = [(p_1,0,0,p_1)+(p_2,0,p_2\sin\theta, p_2\cos\theta)]^2 = (p_1+p_2)^2 -p_2^2\sin^2\theta -(p_1 + p_2\cos\theta)^2 \,
- \langle a, b \mid a^2, b^3, (ab)^{13}, [a, b]^5, [a, bab]^4, (ababababab^{-1})^6 \rangle ... \; [R_\pi(\varrho_{A_1\ldots A_m})]_{i_1j_1,i_2j_2,\ldots,i_nj_n}\equiv\varrho_{\pi(i_1j_1,i_2j_2,\ldots,i_nj_n)}
- \mathbf{K}=h\hat{x}^* + k\hat{y}^* + l\hat{z}^*=(2\pi/a)(h\hat{x} + k\hat{y} + l\hat{z}) ... m_\text{red} \leq m_1, \quad m_\text{red} \leq m_2 \!\,
- \left| \left\langle f,{{g}_{m}} \right\rangle \right| ... Q=\frac{\pi L}{2\lambda (1-r)}
-
\begin{align}
df(x_t,t) & = \theta x_t e^{\theta t}\, dt + e^{\theta t}\, dx_t \\[6pt]
& = e^{\theta t}\theta \mu \, dt + \sigma e^{\theta t}\, dW_t.
\end{align}
... x(0) = \left. {\frac{{dx}}{{dt}}} \right|_{t = 0} = 0
- X_n\ \xrightarrow{d}\ X,\ \ Y_n\ \xrightarrow{d}\ c\ \quad\Rightarrow\quad (X_n,Y_n)\ \xrightarrow{d}\ (X,c)
... \mu_n(E)\to \mu(E),~\forall E\in \Sigma.
- \alpha >1 ... \frac{\pi^5}{120} R^{10}
- \textbf{G}(\textbf{r}, \textbf{r}^{\prime}) = \frac{1}{4 \pi} \left[ \textbf{I}+\frac{\nabla \nabla}{k^2} \right] G(\textbf{r}, \textbf{r}^{\prime}) \, ... \; 0 \log_2 0 = 0
- \mbox{M} = \frac{100%}{n}\sum_{t=1}^n \left| \frac{A_t-F_t}{A_t}\right|, ... (\tilde{\nu})
- [\mathfrak{g},I]\subseteq I, ...
C_{4,3/4}=
\begin{bmatrix}
c_1&c_2&c_3&0\\
-c_2^*&c_1^*&0&c_3\\
-c_3^*&0&c_1^*&-c_2\\
0&-c_3^*&c_2^*&c_1
\end{bmatrix},
- a = b \times c ... \int_{\mathbf{R}} \psi_{n_1, k_1}(t) \psi_{n_2, k_2}(t) \, d t = \delta_{n_1, n_2} \delta_{k_1, k_2},
- w=Az^n, \, ... V(r,t) = \frac {1}{4 \pi} \int_{S} \left\{[V] \frac {\partial}{\partial n} \left(\frac {1}{s}\right) - \frac {1}{cs} \frac {\partial s}{\partial n} \left[\frac{\partial V}{\partial t}\right] - \frac{1}{s} \left[\frac{\partial V}{\partial n} \right] \right\} dS
- T_v = \log_2 ... 0 = x r \cos \varphi + y r \sin \varphi - z \sqrt{R^2-r^2} \,\!
- \dot{v}_4 = -({1 \over {C_4 R_6}} + {1 \over {C_4 R_2}}) v_4 + {1 \over {C_4 R_2}} v_3 + { 1 \over {C_4 R_6}} v_1 ... COP_{heating}=\frac{T_{hot}}{T_{hot}-T_{cold}}
- V_G = V_{ch} + E \ t_{ins} = V_{ch} + \frac {Q t_{ins}}{\kappa \epsilon_0}, ... \begin{align}\operatorname{MSE}(S^2_{n-1})&= \frac{1}{n} \left(\mu_4-\frac{n-3}{n-1}\sigma^4\right) \\
&=\frac{1}{n} \left(\gamma_2+\frac{2n}{n-1}\right)\sigma^4,\end{align}
- \mu^\circ_{solid} = \mu^\circ_{solution}\, ... = 2(2\eta^{\rho \sigma} - \gamma^\sigma \gamma^\rho) \gamma^\nu - 4 \gamma^\nu \eta^{\rho \sigma} \,
- n_1=\pm\frac{1}{\sqrt 2},\,\,n_2=\pm\frac{1}{\sqrt 2},\,\,n_3=0,\,\,\tau_\mathrm{n}=\pm\frac{\sigma_2-\sigma_3}{2}\,\! ... \left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil
- {\mathbf{f}} ... \mathrm{N}(n,S) = \#\{ m \in S : m \le n \} .
- K_2 = {{}^\star R}_{abcd} \, R^{abcd} ... Ax^2 + Bxy + Cy^2 = -(Dx + Ey + F). \,
- S_{n-1} ... S_1 := \emptyset
- \nabla \times \frac{1}{\mu} \nabla \times - (\omega^2/c^2) \varepsilon ... x \leftarrow x+lb_{computed}
- V_n(R) = \frac{\pi^{n/2}}{\Gamma(\frac{n}{2} + 1)}R^n, ... \sqrt{\frac{1}{8}}\!\,
- m(\varphi) = \int_0^\varphi\frac{a(1-n)^2(1+n)}{\left (1 + 2n \cos 2\varphi + n^2 \right )^{3/2}} \, d\varphi. ... \lambda_{12}=7.01559
-
\omega_{r}^{2} = \frac{1}{m} \left[ \frac{d^{2}V}{dr^{2}} \right]_{r=r_{\mathrm{outer}}}
... \mathbb{P} \left( \max_{1 \leq k \leq n} | S_{k} | \geq \alpha \right) \leq \frac{27}{\alpha^{2}} \mathrm{Var} (S_{n}).
- \sin(\theta) = \sin(\arcsin x) ... u v \, \partial_u + \frac{1-u^2+v^2}{2} \partial_v
- \scriptstyle E^{0}_n ... S_g+S_m=0
- M = \alpha \cdot u v^*, \quad \mbox{where} \quad \|u \| = \|v\| = 1 \quad \mbox{and} \quad \alpha \geq 0 . ... F'_{-}
- a_k(0) ... \frac{A}{x - 1}
- \psi_k(x) = \sqrt{2/\pi}\sin(k x) ... while X\ne Y
- c({\alpha}) ... k \leq 3
- \dfrac{d^a}{dx^a}x^k=\dfrac{\Gamma(k+1)}{\Gamma(k-a+1)}x^{k-a}\;. ... \sum_{P \in C}{c_P [P]} + \sum_{P \in C}{d_P [P]} = \sum_{P \in C}{(c_P + d_P)[P]}
- \operatorname{Tr } \Lambda^n(K) = \frac{1}{n!}\int\cdots\int \det K(x_i,x_j)|_{1\leq i,j\leq n}\,dx_1\cdots dx_n ... \{ \mathfrak{p} \in \operatorname{Spec}A | A_\mathfrak{p} \text{ is integrally closed} \}
- 1^1 \cdot 2^2 \cdot 3^3 ... [Z]_i
- \frac{\sum_{k=1}^\eta d(k)}{\eta} \approx \ln \eta + 2\gamma - 1, ... b_1, b_2, \dots,b_d
- \Phi(\eta, \tau) = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \Pi(t,f) \exp (-j2\pi(t\,\eta-f\,\tau))\, dt\, df, ... y = r \sin \left ( \theta + \omega t \right )
- \textstyle\rho = |i\rang\lang i| ... x^n,
- y^2-z^2=1, ... a_i,
- (6k + 1)(12k + 1)(18k + 1) ... 2\ f\ x = f\ (f\ x)
- \mathbb{N} = \left\{0, 1, 2, 3, \dots\right\} ... {17 + 20 + 22 + 21 + 2 + 6 + 10 + 14 + 3 + 16 + 12 + 7}
- (P \wedge (P \to \bot)) ... C\ge 0
-
\begin{bmatrix}
\omega^2 m - 2 k & k \\
k & \omega^2 m - 2 k
\end{bmatrix} \begin{pmatrix} A_1 \\ A_2 \end{pmatrix} = 0
... x^2 + y^2 + 10 = 0
- {x\!:\!\sigma \in \Gamma}\over{\Gamma \vdash x \Rightarrow \sigma } ... \mathit{d}_H(\mathit{p},\mathit{q})
- M_\mathrm{tot} ... z = 1/2\,
- A = \begin{pmatrix}1&1&2\\
3& 1& -1\\
\end{pmatrix} ... \tilde{\mathbf n} = - \hat{\mathbf n}
-
\sum_{n=1}^\infty \frac1n
... \text{X}
- \omega_{cyc} = \omega_{rad}/2\pi\, ... \begin{matrix}\omega_{ce} > 1/\tau \\
\hbar \omega_{ce} > k_B T \\
\end{matrix}
- x,y_1,\ldots,y_n ... (X,\mathcal{F},\mu)
- \mathrm{C} = \tfrac{1}{n_p-1}\sum_{i=1}^T \mathbf{x_i}\mathbf{x_i^T}, ... F^1 \subset F^2\subset \cdots \subset F^m \,
- \bold j = \frac{1}{2m}\left[\left(\Psi^* \bold{\hat{p}} \Psi - \Psi \bold{\hat{p}} \Psi^*\right) - \frac{2q}{c} \bold{A} |\Psi|^2 \right]\,\! ... \mathbb{C}\mathbf{P}^1
- \text{Var}\left(\hat{\alpha} + \hat{\beta}x_d\right) = \text{Var}\left(\hat{\alpha}\right) + \left(\text{Var} \hat{\beta}\right)x_d^2 + 2 x_d\text{Cov}\left(\hat{\alpha},\hat{\beta}\right) . ...
\begin{align}
X &=\sum_{i=1}^N \langle \phi_i,X\rangle \phi_i\\
&=\sum_{i=1}^N \phi_i^T X \phi_i
\end{align}
- S\ = \gamma_{SG}-(\gamma_{SL}+\gamma_{LG}) ... \mathbb{N}_{0}
- P^{\prime }=(w,\vec{0}), ... \mathbf{A} = \begin{pmatrix}
a & b
\end{pmatrix}\,, \quad \mathbf{B} = \begin{pmatrix}
p & q \\
r & s
\end{pmatrix}\,, \quad \mathbf{C} = \begin{pmatrix}
x \\
y \\
\end{pmatrix}\,,
-
\Phi(z,s,a)=\sum_{k=0}^n \frac{z^k}{(a+k)^s}
+z^n\sum_{m=0}^\infty (1-m-s)_{m}\operatorname{Li}_{s+m}(z)\frac{(a+n)^m}{m!};\ a\rightarrow-n
... B_{max} \approx R
- \displaystyle{e^{tM}(0,0,b)=Je^{tN}J(0,0,b)=Je^{tN}(b,0,0)=(0,0,e^{tN}b).} ... f(x) = \lim_{r\to 0^+} M^rf(x). \,
- 2 (2^{13-1}-1)/13 = 630 ... o_{ck} = \sum_{u=1}^N \frac{the~number~of~c-k~pairs~in~u}{m_u - 1} = o_{kc}
- (0,0)\, ... \sigma_\varphi(R) = \{ \ t : t \in R, \ \varphi(t) \ \}
- t_i \cdot \pi \cdot \frac{K_{i}}{K} ... (A \rightarrow (A \rightarrow B)) \rightarrow (A \rightarrow B)
- \hat{K} ... \lambda_p \leq \lambda_s \leq \lambda_i
- \Omega\simeq 500\rm Hz ... C_{\alpha \beta}=\langle \psi_\alpha |\psi_\beta\rangle
- S(a,q,x) ... L_1(\beta)=L_2(\beta) = 1
- K_e= \{ x \in S\;|\; \exists n>0:\; x^n \in G_e \} ...
P(\sup_x|F(x)-F_n(x)|>\varepsilon)\le2e^{-2n\varepsilon^2}.
- D>0 ... f = \frac{f_0}{\gamma}
- l,m,l',m' ... \Gamma_L = 0 \,
- K =k_1 + \cdots + k_n ... B = \frac{4}{a-d}
- \mathbf{F} = \frac{q_1 q_2}{r^2} \mathbf{\hat r} ... \bold{v} = (v_1, \ldots, v_n)
- \{\{1, 2, 3,\ldots\}, \{2, 3, 4,\ldots\}, \{3, 4, 5,\ldots\},\ldots\} ... \tilde K_0(A)=\operatorname{Pic} A.
- U = - U_\text{Kin}, \, ... \max E \left[ \int_0^T e^{-\rho s}u(c_s) \, ds + e^{-\rho T}u(W_T) \right]
- \theta=\frac{t-\pi}{2} ... T(A, R) = 1 + A\cdot R^2
-
\begin{matrix}
x^2\\
\qquad\qquad\quad x-3\overline{) x^3 - 2x^2 + 0x - 4}\\
\qquad\;\; x^3 - 3x^2
\end{matrix}
... k = R/(f_1, \dots, f_n)
- \bar\psi(x_i) ... VHC = \rho c_p
- \scriptstyle \eta(x)=\zeta(x)=1 ... A \rightarrow B: A
- Q_{CA} \, ... F
- \scriptstyle f(x_1,x_2,x_3)=0. ... \bold{\bar{3}}
- \int_{-\frac{a}{2}}^{\frac{a}{2}} x^2\cos^2 {\frac{n\pi x}{a}}\;\mathrm{d}x = \frac{a^3(n^2\pi^2-6)}{24n^2\pi^2} \qquad\mbox{(for }n=1,3,5...\mbox{)}\,\! ... G=\Delta_x
- a ^ b = a \cdot (a ^ {(b - 1)}),\,\! ... \tilde{\Gamma}
- 2^{2^{6}} + 1 = 2^{64} + 1 = 274177 \times 67280421310721 ... x_{max}
- y_t = \frac{ r_n(\rho - R)}{\rho - r_n} ... f(x)=\sum_{n=1}^\infty {a_n \over n!} x^n \qquad
\mathrm{and} \qquad g(x)=\sum_{n=1}^\infty {b_n \over n!} x^n.
- h_k=\operatorname{dim}_{\mathbb{Q}}\operatorname{IH}^{2k}(X,\mathbb{Q}) ... T(w) = 2^{|w|}
- r_n = r_{n-1} - \frac{f(r_{n-1})}{ (r_{n-1}-p_n)(r_{n-1}-q_n)(r_{n-1}-s_{n-1}) }; ... (\forall u)(\exists v)(P)
- \alpha \, ... \tau=1\;
- p V\; ... \nabla f({\mathbf x}_0) \cdot {\mathbf \gamma}'(0)=0.
- M_{\mathrm{left}}^{\mathrm{fixed}} = \int_{0}^{L} \left \{ - q_0 \frac{x}{L} dx \frac{x (L-x)^2}{L^2} \right \} = - \frac{q_0 L^2}{30} ... (a + P\cdot b)/(a+b) .
- \eta = 2 \rarr \delta = \frac{\gamma +1}{2} ... \sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots.
- e^2/kT=1.44\times10^{-7}\,T^{-1}\,\mbox{cm} ... D(l,m,n)=\langle x,y \mid x^l,y^m,(xy)^n\rangle.
- \tau = - m g L \sin\theta\, ... 1 = \chi(1)
- [Rf_!\mathcal{F},\mathcal{G}] \cong [\mathcal{F},f^!\mathcal{G}] . \,\! ... \hbar = \frac{1}{\alpha} \approx 137.035999679
- F(x,u,u',\ \cdots,\ u^{(n)})=0 \quad x \in I. ... NaN
- f(x_1)+f(x_2) = f(x_1+x_2) ... t=t'-(q_{hash}+q_{sig}+1) \cdot \mathcal{O}(k^3)
- \frac{f_{\theta_1}(x_1)}{f_{\theta_0}(x_1)} \geq \frac{f_{\theta_1}(x_0)}{f_{\theta_0}(x_0)}, ... \phi:M\to \prod_{i\in F}R\,
- (a \and b) \rightarrow c ... \tau_b\propto \exp[\Delta U/(k_B T_f)]
- X_j = \alpha^{i_j} ... a^{(N-1)/2} \equiv -1\pmod{N}\!
- \left( a - \lambda \right) \left( b-\lambda\right) -c^2 = 0 ... u(0,x)= 0
- \left( \mathcal{P} (M), \pi \right) ... |E_g|\approx\frac{GM}{R} = E_k\approx\frac{M^{2/3} N^{5/3} \hbar^2}{2m R^2}.
- N=\frac{ln (1-0.99)}{ln [1-\frac{2.0\times10^4 basepairs}{3.0\times10^9 basepairs}]} ... \frac{-1+\frac{2a e^{\tfrac{a}{b}} {\rm E}({1-\tfrac{1}{b}},\tfrac{a}{b}) }{b}}{a^2}
- \displaystyle A^\top Ax=A^\top b ... y = mx + b \,
- (\nabla\cdot\nabla) \mathbf{A} = (\nabla_i \nabla_i) \mathbf{A} ... p \approx 2^{-20}
- M \le n < M + R. ... \frac{P(x)}{(1-x)(1-x^2)\cdots(1-x)^n} = \prod_{(i,j)\in \lambda} (1-x^{h_{(i,j)}})^{-1}
- c=1+3.535\omega+0.533\omega^2 ... \begin{matrix} {2 \choose 1}{2 \choose 1}{11 \choose 4}{4 \choose 1}^4 \end{matrix}
- \int f_n \geq \int \limits_{E_n} f_n \geq \alpha \int \limits_{E_n} \phi ... \mathrm{[OH^-]} = \frac{K_{\mathrm w}}{\mathrm{[H^+]}}
- D_0(f)=\int_{-\infty}^\infty x^2|f(x)|^2\,dx. ... z \mapsto z^n
- \exists p\,\phi ... {\pi\over 5}\ {\pi\over 5}\ {2\pi\over 3}
- x_{n+1} - x_n = b_n(\alpha - N(x_n)), \qquad \bar{x}_n = \frac{1}{n} \sum^{n-1}_{i=0} x_i ... u = 0.999999
- {P_{Rx}} ... L_t = (L^x_t)_{x \in E}
- n = \frac{\lambda}{\Delta x}\,\! ... G_r^\pm
- U(x) = \sum_{i\in \mathbb{Z}} L(x-i) ... \{p_3, r_3\}
-
\begin{align}
a_{11}x_1 + \cdots + a_{1n}x_n &= a_{1,n+1}\\
&\vdots&\\
a_{n-k,1}x_1 + \cdots + a_{n-k,n}x_n &= a_{n-k,n+1}.
\end{align}
... wp(S, R)
- J-1 ... (x-a)(x-b)(x-c)=0
-
m , m-2 , m-4 , \dots . \,
... \Lambda(A_1:A_2|B) = \frac{P(B|A_1)}{P(B|A_2)} ,
- \widehat{\mu}(x) = \int_{\widehat{G}} \overline{X(x)} \, d \mu(X), \quad x \in G ... P\left[ \bigcap_{i = 1 }^n \frac{ | X_i - \mu_i | }{ \sigma_i } \le k_i \right] \ge \prod{ ( 1 - \frac{ 1 }{ k_i^2 } ) }
- \textstyle I(P) ... (\mathbf{AB})^\mathrm{T} = \mathbf{B}^\mathrm{T}\mathbf{A}^\mathrm{T}
- \mathrm{^{238}_{\ 92}U + \,^{1}_{0}n \;\rightarrow\; ^{239}_{\ 92}U \;\rightarrow\; ^{239}_{\ 93}Np + \beta \;\rightarrow\; ^{239}_{\ 94}Pu + \beta} ... x^4+px^2+q=0
- \lambda (n) = (-1)^{\Omega(n)}.\; ... \frac{dz(t)}{dt}=-\beta*y(t)
- |\mathcal{F}| > \sum_{i=0}^{k-1} {\binom{n}{i}} ... \scriptstyle r\searrow 1
- j = \left\lfloor {k \cdot r} \right\rfloor = \left\lfloor {m \cdot s} \right\rfloor \,. ...
\sum_r {x_{ij}^r = T_{ij} }
- \mathrm{laea}_y ... {\bar{R}}_3
- \mathbf{e}^i\cdot\mathbf{e}_k=e^{ij}\mathbf{e}_j\cdot\mathbf{e}_k=e^{ij}e_{jk} = \delta^i_k. ... p(y|\theta,\xi)\,
- \bold{j}_\perp ... p_O
- [x_1, \; x_2, \; x_3] ... \alpha
- N(L/K) ... F_N \in H(N,N),
- \int\frac{x^k \, dx}{\sqrt{Q(x)}} ... \lim_{n \to \infty} \varphi(t_n, x) = y
- \langle a \rangle\,\! ... \mu_1,\ldots,\mu_c
- \vec{A} ... \Delta w''=w''(x+)-w''(x-)
- \textstyle T = \left( \begin{array}{cc} 3 & 4 \\ 2 & 3 \end{array} \right) ... \scriptstyle S^3
-
Q_n^{(c)}(t) < \sum_{b=1}^N\mu_{nb}^{(c)}(t)
... m \ge \sqrt{\frac{(n+1)d}{2}} - \sqrt{\frac {(n+1)d}{2}} + \frac{d}{2} - 1 = \frac{d}{2} -1
- d_\mathrm{i} ... \sigma^2_W/\mu_W
- 0! = 1, \ ... \frac{a_{2}}{a_{1}}={(\frac{T_{2}}{T_{1}})}^{0.5}
- \ \beta = 180 ... dV = r^{n-1}\sin^{n-2}(\phi_1)\sin^{n-3}(\phi_2) \cdots \sin(\phi_{n-2})\,
dr\,d\phi_1\,d\phi_2 \cdots d\phi_{n-1},
- Z_{11} = {((1 + S_{11}) (1 - S_{22}) + S_{12} S_{21}) \over \Delta_S} Z_0 \, ... ZZ_3 = E
- y_i = \begin{cases}
y_i^* & \textrm{if} \; y_L<y_i^* <y_U \\
y_L & \textrm{if} \; y_i^* \leq y_L \\
y_U & \textrm{if} \; y_i^* \geq y_U.
\end{cases} ... {(1+z)^2}
- \frac{4}{3} \log(g(\Sigma)), ... \varphi = \varphi \,
- F_W = 6\cdot\pi\cdot\eta\cdot\text{r}_{H}\cdot\nu ... \widetilde{f} \left( \sum_{i=1}^n l_i e_i\right) := f \left( \sum_{i=1}^n l_i^\theta e_i \right)
- \log_{\sqrt{2}}3 ... \omega
- \Delta k=k_3-k_1-k_2 ... \mathcal E^\bullet=\bigoplus_i \Gamma(E_i)
-
V(t) = V_o e^{-t / \tau}
... \textbf{P}_{k\mid k-1}^{a} = \begin{bmatrix} & \textbf{P}_{k\mid k-1} & & 0 & \\ & 0 & &\textbf{R}_{k} & \end{bmatrix}
- \kappa = 0 \, ... M_r=\frac{2}{\pi}\int_{0}^{\frac{\pi}{2}}\!M(\varphi)\,d\varphi\!
- p(x|m) = \exp (V(x)) ... u(0,x,y,z) = 0, \quad u_t(0,x,y,z) = \phi(x,y,z). \,
- s * (hi + ho + 1) * 2 - s ... \gamma_i(t)=P(X_t=i|Y,\theta) = \frac{\alpha_i(t)\beta_i(t)}{\sum_{j=1}^N \alpha_j(t)\beta_j(t)}
- \forall x . R(x,f(x)) ... K\to R
- S^{n-1} \to S^n ... f:X\to\mathbb R^k, \ f(x)= (f_1(x),\ldots,f_k(x))^T
- Y\left( \begin{bmatrix} 1 \\ 0 \end{bmatrix},z\right) = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} ... r\in\C
- \varnothing\vdash A ... f^\downarrow( q_l, q_r ) = f( q_l )
- \Gamma_\phi ... \hat{\rho}(t)=\hat{U}^{\dagger}(t)\hat{\rho}(0)\hat{U}(t)
- k^2 = \frac{1}{\hbar^2}2mE_n ... f_{y}
- 1/x = 1 - (x-1) + (x-1)^2 - (x-1)^3 + (x-1)^4 - ... ... \sqrt{S} = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3+\,\ddots}}}
- \kappa = 8/3 ... \nabla:\Omega^pM\rightarrow T^*M\otimes\Omega^pM
- \scriptstyle |U| ... C = -\sum_j d_j \log(p_j)
- P < Q/2 ... 0 \to A\times 0
- 220_5 = 214.\overline4_5 ... f(n)\geq\log_2(n!).
- ckl@ckl ... \sum_{k \geq 3} (k-2) (f_k-g_k) = 0.
- c_k=\frac{1}{2\pi}\int_{-\pi}^\pi f(t)e^{-ikt}dt, ... \Delta H_{fus} \, = \, -0.88 + \sum H_{fus,i}
- z_1 z_2 = r_1 r_2 (\cos(\varphi_1 + \varphi_2) + i \sin(\varphi_1 + \varphi_2)).\, ... \scriptstyle f \;=\; t_A / (t_A \,+\, t_B) \;=\; 0.75
- f(x^*) ...
W = T \cos \theta ,\quad F = T \sin \theta
- 1\otimes v_\lambda ... -1 + \sum_{k=0}^n \binom{n}{k} \frac{2^{n-k+1}}{n-k+1}B_{k}(0) = [n=0]
-
F=\frac{X/\nu_1}{Y/\nu_2}
... = \omega^2 v t \left(\cos\alpha, \sin\alpha\right )=\omega^2 \mathbf{r_B}(t) \ .
- \| u_j \| \leq 1 . ...
E =
\begin{cases} \displaystyle
x + \frac{1}{60} x^3 + \frac{1}{1400}x^5 + \frac{1}{25200}x^7 + \frac{43}{17248000}x^9 + \frac{ 1213}{7207200000 }x^{11} +
\frac{151439}{12713500800000 }x^{13}+ \cdots \ | \ x = ( 6 M )^\frac{1}{3}
, & \varepsilon = 1 \\
\\
\displaystyle
\frac{1}{1-\varepsilon} M
- \frac{\varepsilon}{( 1-\varepsilon)^4 } \frac{M^3}{3!}
+ \frac{(9 \varepsilon^2 + \varepsilon)}{(1-\varepsilon)^7 } \frac{M^5}{5!}
- \frac{(225 \varepsilon^3 + 54 \varepsilon^2 + \varepsilon ) }{(1-\varepsilon)^{10} } \frac{M^7}{7!}
+ \frac{ (11025\varepsilon^4 + 4131 \varepsilon^3 + 243 \varepsilon^2 + \varepsilon ) }{(1-\varepsilon)^{13} } \frac{M^9}{9!}+ \cdots
, & \varepsilon \ne 1
\end{cases}
- F(a,t) = a\, ... W^{\mathbb C} \cong W\oplus \overline{W}.
- \pi / 4 ... \tilde{h}^{ab} \frac{\partial}{\partial \tilde{\sigma}^a} X^\mu \frac{\partial}{\partial \tilde{\sigma}^b} X^\nu = h^{cd} \frac{\partial \tilde{\sigma}^a}{\partial \sigma^c} \frac{\partial \tilde{\sigma}^b}{\partial \sigma^d} \frac{\partial}{\partial \tilde{\sigma}^a} X^\mu \frac{\partial}{\partial \tilde{\sigma}^b} X^\nu = h^{ab} \partial_a X^\mu \partial_b X^\nu
- \int_{-\infty}^\infty \delta(\tau)\, g(t - \tau)\, d\tau = g(t) ... \Delta\;h = u\cdot \Delta\;v_w
- \chi_\text{e}^\text{SI} = \chi_\text{e}^\text{LH} = 4\pi \chi_\text{e}^\text{G} ... 2\ell+1
- \log(f(z)/z)=2 \sum^\infty_{n=1}\gamma_nz^n. ... \frac{3}{2}k_{\rm B} T = \frac{m}{2} v_{\rm rms}^2
- \rho > 2b/2D ... \!X[F/x] = \{ s[F(s)/x] : s \in X\}
- Rb = 1 ... \operatorname{nassoc}(A, B) = \frac{w(A, A)}{w(A, V)} + \frac{w(B, B)}{w(B, V)}
- \Delta_{ti} ... 2\,
- p\mathrm{[H_2]} ... -\frac{1}{\theta} \log\!\left( 1+\frac{(\exp(-\theta u)-1)(\exp(-\theta v)-1)}{\exp(-\theta)-1} \right)
- %\text{ ohms reactance on kva base}_2=\frac{\text{kva base}_2}{\text{kva base}_1} * %\text{ ohms reactance on base}_1 ... P(\text{well}\cap\text{positive})=P(\text{well})\times P(\text{positive}|\text{well})=99%\times1%=0.99%.
-
\begin{align}
(1) ~~~e > e_s > e_i \\
(2) ~~~e_s > e > e_i \\
(3) ~~~e_s > e_i > e \\
\end{align}
... \mathbf{x}_i^{t+1}=\mathbf{x}_i^t + \beta \exp[-\gamma r_{ij}^2] (\mathbf{x}_j^t - \mathbf{x}_i^t) +\alpha_t \boldsymbol{\epsilon}_t
- \scriptstyle n\geq 1 ... m(t) = \mathbb{E}[N(t)]
- Z_N(K,L) = 2 e^{N(K+L)} \sum_{ P \subset \Lambda_D} e^{-2Lr-2Ks} ... b(x) = x-a
- \sum_i T_{\mathrm{actual}}(o_i) ... \binom{n}{l}
- (X_{2}=\cos\Omega t,Y_{2}=-\sin\Omega t,Z_{2}=0)^{T} ... \alpha = x/\sqrt{2} - \pi/8
- G\in \mathcal{P} ... \mathrm{Sh} = 2 + 0.6\, \mathrm{Re}^{\frac{1}{2}} \, \mathrm{Sc}^{\frac{1}{3}}, ~ 0 \le ~ \mathrm{Re} < 200, ~ 0 \le \mathrm{Sc} < 250
- \frac{dTR}{dP} = Q\left(f'(P) \cdot \frac{P}{Q} + 1\right) ... A_\text{pfd} =
- S\in\tbinom{[n]}m ... m_i \equiv m \mod p_i
- f : E \to E'. ... \omega\in\Lambda
- A(\eta) = -\log(\theta) = -\log(-\eta) ... L_{0}=Tv
- X:=(x^2-y^3=0) \subset W:= \mathbf{R}^2. ... D_3(z)=2+Kz -22 z^2 +24 z^3
- \mathbb R^3 ... \psi(\bar{x})
- \theta_2=62.25^\circ ... F_i^{-1}
- x_{r,s}\geq 0 ... S_i[p..n_i]
- \displaystyle{ f_s(z)=f_t(\varphi_{s,t}(z)).} ... d = \frac{(b+d)-(b-d)}{2}\, ,
- \cos(20^\circ) \cdot \cos(40^\circ) \cdot \cos(80^\circ)=\frac{1}{8}. ... z = -(Dx + Ey + F).
- c_\beta = \sum_{n\ge 1} {\operatorname{mult}(\beta/n)\over n}. ... F^V
- Q_{s3} = q_{1} - q_{2} + q_{3} - q_{4}\! ...
\Pr(X = k) = \left(\frac{r}{r+m}\right)^r \frac{\Gamma(r+k)}{k! \, \Gamma(r)} \left(\frac{m}{r+m}\right)^k \quad\text{for }k = 0, 1, 2, \dots.
- \eta \colon \mathcal{S}(X) \to \mathcal{N} (X) ... V_{i}
- x_{n+1}=g(x_n) ... \big(f(p),g(l)\big) \in I'
- [0,1,0,0,0] ... \gamma/r^2
- f(x)=\sum_{n=0}^\infty a_n x^n ... N=2k(a\phi(front)-b\phi(rear))=2k(a-b)(\theta-\psi)-2k\frac{(a^2+b^2)}{V}\frac{d\theta}{dt}+2ka\eta
- \begin{matrix}\frac{1}{2}\end{matrix} (m_\textrm{b}+m_\textrm{p})\cdot v^2 = (m_\textrm{b}+m_\textrm{p})\cdot g\cdot h ... \sigma_{ij}=
\begin{bmatrix}
\sigma_1 & 0 & 0\\
0 & \sigma_2 & 0\\
0 & 0 & \sigma_3
\end{bmatrix}
\,\!
- E_F = \frac{\hbar^2}{2m_e} \left( 3 \pi^2 \ 10^{28 \ \div \ 29} \ \mathrm{m}^{-3} \right)^{2/3} \approx 2 \ \div \ 10 \ \mathrm{eV} ... \Rightarrow_{S \to A}\ ASSS \ \Rightarrow_{S \to A}\ AASS \ \Rightarrow_{S \to A}\ AAAS \ \Rightarrow_{S \to A}\ AAAA
- \boldsymbol{c}_g=c_g\,\boldsymbol{e}_k ... i \in G
- d_{i,j}=f \Big ( \Big| x_i - x_j \Big | \Big ) ... \mathbf{x}'_i\boldsymbol\beta
- \Delta t > \Delta \tau\, ... \displaystyle K=\sqrt{(e+f+g+h)(efg+fgh+ghe+hef)}.
- \|f\|_r = \max_{|z| \le r} |f(z)| = \max_{|z| = r} |f(z)| ... X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk }
\qquad
k = 0,\dots,N-1.
- \{ H_n(\theta) \} ... \operatorname{build-param-lists}[\lambda q.\lambda x.x\ (q\ q\ x)), D, V, \_]
- W_o ... y^* \,
- \phi \wedge \chi \vdash \phi ... \deg(P - Q) \leq \max(\deg(P),\deg(Q))
-
F = A \sigma
... \Phi_\Lambda
- \max(3,d)^{\min(n,s)}. ... \sum_{n=1}^{2^k} \,\frac{1}{n} \;\geq\; 1 + \frac{k}{2}
- a_{i,j} = -\overline{a_{j,i}}, ... 2\sin\left(54^\circ\right) = \phi
- Q - X_1 - X_2 - P(M_3,3) - P(M_4,4) - P(M_5, 5) ... \left[E_k(\mathbf{R})+\mathcal{T}_\mathrm{k}(\mathbf{R})\right]
- n\times\log_2(n) ... 3^i5^j7^k
- \mu_2=\mu_2^+-\mu_2^- ...
\mathbf{M} = \chi_v \mathbf{H}
- \frac{1}{x}R ... (2)\quad B_{ab}=h^c_{\;\;a}\, h^d_{\;\;b}\, \nabla_d Z_c = \nabla_b Z_a +A_a Z_b\;,
- F = \frac{\Delta p}{\Delta t} = \frac{m v_x^2}{L}. ... 10\uparrow\uparrow\uparrow 8=(10 \uparrow \uparrow)^8 1
- PGL(2,5) \cong S_5, ... \left|\sum_{k=0}^n u_k \right|^p \le \sum_{k=0}^n |u_k|^p \text{ when } p<1
- T^2 = \frac{n_1 n_2}{n_1+n_2}(\overline{\mathbf x}_1-\overline{\mathbf x}_2)'{\mathbf S_\text{pooled}}^{-1}(\overline{\mathbf x}_1-\overline{\mathbf x}_2). ... c_\eta(a,b)=\frac{\mathrm{sinh}\beta b}{2b(\mathrm{cosh}\beta a-\eta\,\mathrm{cosh}\beta b)}
- \mathbb{N}, x_{1} ... x_{n} ... \varnothing = \{u \in w \mid (u \in u) \land \lnot (u \in u) \}
- f(t)=(t-1)^2+(t^3-1)^2-10 ...
\Beta(x,y) \cdot \Beta(x+y,1-y) =
\dfrac{\pi}{x \sin(\pi y)},
\!
- L \subseteq X \times Y ... \begin{align}
r(t) &= s(t) \cos (2 \pi f_0 t) \\
&= I(t) \cos (2 \pi f_0 t)\cos (2 \pi f_0 t) - Q(t) \sin (2 \pi f_0 t)\cos (2 \pi f_0 t)
\end{align}
- \{ f_n \} ... \tilde{P_n}(x) = \frac{1}{n!} {d^n \over dx^n } \left[ (x^2 -x)^n \right].\,
- \hat{\Pi}\equiv I-\Pi ... \ |k_a|+|k_b|+|k_c| = 3
- \scriptstyle\pi/2 ... p_{\tfrac{1}{2}1} \leftarrow 64x^3+192x^2+80x+8
-
\mathbb{E}_{X^{n}}\left\{ \frac{1}{M}\sum_{m}\text{Tr}\left\{ \Pi
_{\rho,\delta}^{n}\rho_{X^{n}\left( m\right) }\Pi_{\rho,\delta}^{n}\right\}
\right\} ... N\left( \mathcal{S}\right)
- \langle B, \in\rangle ... -|1\rangle
- \log_{10}(P) = 10{.}3291 - \frac{1642{.}89}{351{.}47 - 42{.}85} = 5{.}005727378 = \log_{10}(101328\ \mathrm{Pa}). ... P_x=
-
A = \cfrac{C_0^2 - T_0^2}{T_0} ~;~~ B = C_0 ~.
... E \{ (\hat{x}_{\mathrm{MMSE}}-x)\hat{x}^T \} = 0.
- \alpha = ai\, ... \{ [M(OH)]^{(z-1)+} \} = K_{1,1}\{ M^{z+}\} \{OH^-\}
- g(z) = z + b_1 z^{-1} + b_2 z^{-2} + \cdots. ... c_m=\frac{e^{-m\gamma}}{m}\qquad \mathrm{for}\,m>0
- f(z) = \frac{P(z)}{Q(z)} ... n = 1,2,\cdots ,m
- a \in \mathcal{A} ... n_c
- \forall f_1, \forall f_2, \forall i \in \{1,2\},\ \pi_i \circ \langle f_1, f_2\rangle = f_i ... f^{-1}\left( \, f(x) \, \right) = x
- V_m = \left( v_1, v_2, \cdots, v_m \right) ... \gcd(x,y) = \gcd(y, x % y)
- \textrm{Var}\left(X\right)=p\left(1-p\right).\, ... [Divs\ received\ from\ 3rd\ parties] -
[Divs\ paid\ to\ 3rd\ parties] -
\{ Divs\ paid\ to\ NCI\ but\ not\ intracompany\ div\ payments\ \}\,
- \tbinom{2m-2}{m-1} ... \sigma \left (\mathbf{P}^{2i_1}(\mathbf{C}) \times \dots \times \mathbf{P}^{2i_k}(\mathbf{C}) \right) = 1.
- p_s ... \tau = \frac{Gb}{L-2r} \,\!
- C^q(\mathcal U, \mathcal F) ... \scriptstyle H\,=\,2\,a\,
- yx = (-1)^{|x||y|}xy\, ... I_i = \frac{V_i - V_o}{Z} = \frac{V_i (1 + A_v)}{Z}
- y^m = kx^n ... \sigma_{\theta\theta}\,
- u'_2 ... E_0 = 1 \mathrm{\frac{MV}{m}}
- y = \left(y_1,y_2,\ldots,y_n\right)^\mathsf{T} ... z \simeq \beta = \frac{v}{c},
- \; (fg)^* = f^*g^* ... C_1;C_2
- \alpha = \frac{R_{100} - R_0}{100R_0} ... d >> \sigma
- \sqrt {-g} ... \scriptstyle\langle B^2\rangle = \langle B_{\theta}^2 + B_{\rho}^2\rangle
- X\backslash \{p\} ... \ \sum_{w \in V} f_i(u,w) = 0.
- W_{PPT}=|C_{n^{*}l^{*}}|^{2}\sqrt{\frac{6}{\pi}}f_{lm}E_{i}(2(2E_i)^{\frac{3}{2}}/F)^{n^{*2}-|m|-3/2}(1+\gamma)^{2})^{|m/2|+3/4}A_{m}(\omega, \gamma)e^{-(2(2E_i)^{\frac{3}{2}}/F)g(\gamma)} ... ) \land
- (a \oplus b) \otimes c = a \otimes c \oplus b \otimes c ... colgroups
- \mathrm{ker}(A) = (\mathrm{im}(A^\mathrm{T}))^\perp ... L^{p_0}(\mathbf{R}) \cap L^{p_1}(\mathbf{R}) \subset L^p(\mathbf{R}) \subset L^{p_0}(\mathbf{R}) + L^{p_1}(\mathbf{R}), \ \ \text{when} \ \ 1 \le p_0 \le p \le p_1 \le \infty,
- g(r) ... \frac{\det \left(-\frac{d^2}{dx^2} + A\right)}{\det \left(-\frac{d^2}{dx^2}\right)} = \frac{\sinh L\sqrt A}{L\sqrt A}.
- \scriptstyle a \;\mapsto\; -a ... \alpha_m ~ = ~ k_0 ~ \sin \theta_0 ~ \cos \phi_0 ~ + ~ \frac{2m\pi}{l_x} ~~~~~~~~~~~(2.2a)
- F(x_1,x_2,\dots,x_n) = \prod_{i=1}^n \left ( \sum_{j=1}^n a_{ij} x_j \right ) = \left ( \sum_{j=1}^n a_{1j} x_j \right ) \left ( \sum_{j=1}^n a_{2j} x_j \right ) \cdots \left ( \sum_{j=1}^n a_{nj} x_j \right ). ... \mu_r = 1
- \nu_3 ... u^{+i}u^-_i = 1
- g_2(\tau) = {2\pi^4 \over 3} \left[\vartheta(0; \tau)^8+\vartheta_{01}(0;\tau)^8 + \vartheta_{10}(0; \tau)^8\right] ... {x_N \choose \theta_N} = \lambda^N {x_1 \choose \theta_1}
- u(x,t)=v(x \pm ct)\equiv v(z),\, ... f_1(c) = \|x-c\|_1
- \frac{\Delta K}{K} ... \mathbf X'\tilde{\mathbf W}_\delta\mathbf X
- H=1/2\sum (p_i)^2 ... z=ix
Run test for all mathjax-texvc commands:
✓ 1 $\thetasym$
✓ 2 $\koppa$
✓ 3 $\stigma$
✓ 4 $\coppa$
✓ 5 $\C$
✓ 6 $\cnums$
✓ 7 $\Complex$
✓ 8 $\H$
✓ 9 $\N$
✓ 10 $\natnums$
✓ 11 $\Q$
✓ 12 $\R$
✓ 13 $\reals$
✓ 14 $\Reals$
✓ 15 $\Z$
✓ 16 $\sect$
✓ 17 $\P$
✓ 18 $\AA$
✓ 19 $\alef$
✓ 20 $\alefsym$
✓ 21 $\weierp$
✓ 22 $\real$
✓ 23 $\part$
✓ 24 $\infin$
✓ 25 $\empty$
✓ 26 $\O$
✓ 27 $\ang$
✓ 28 $\exist$
✓ 29 $\clubs$
✓ 30 $\diamonds$
✓ 31 $\hearts$
✓ 32 $\spades$
✓ 33 $\textvisiblespace$
✓ 34 $\and$
✓ 35 $\or$
✓ 36 $\bull$
✓ 37 $\plusmn$
✓ 38 $\sdot$
✓ 39 $\sup$
✓ 40 $\sub$
✓ 41 $\supe$
✓ 42 $\sube$
✓ 43 $\isin$
✓ 44 $\hArr$
✓ 45 $\harr$
✓ 46 $\Harr$
✓ 47 $\Lrarr$
✓ 48 $\lrArr$
✓ 49 $\lArr$
✓ 50 $\Larr$
✓ 51 $\rArr$
✓ 52 $\Rarr$
✓ 53 $\harr$
✓ 54 $\lrarr$
✓ 55 $\larr$
✓ 56 $\gets$
✓ 57 $\rarr$
✓ 58 $\oiint$
✓ 59 $\oiiint$
✓ 60 $\Alpha$
✓ 61 $\Beta$
✓ 62 $\Epsilon$
✓ 63 $\Zeta$
✓ 64 $\Eta$
✓ 65 $\Iota$
✓ 66 $\Kappa$
✓ 67 $\Mu$
✓ 68 $\Nu$
✓ 69 $\Omicron$
✓ 70 $\Rho$
✓ 71 $\Tau$
✓ 72 $\Chi$
✓ 73 $\Koppa$
✓ 74 $\Stigma$
✓ 75 $\Coppa$
✓ 76 $\uarr$
✓ 77 $\darr$
✓ 78 $\Uarr$
✓ 79 $\uArr$
✓ 80 $\Darr$
✓ 81 $\dArr$
✓ 82 $\rang$
✓ 83 $\lang$
✓ 84 $\arccot$
✓ 85 $\arcsec$
✓ 86 $\arccsc$
✓ 87 $\bold{x}$
✓ 90 $\pagecolor{red}x$
✓ 91 $\vline$
✓ 92 $\image$
✓ 93 $\ointctrclockwise$
✓ 94 $\varointclockwise$
✓ 95 $\text{[h]}$
✓ 96 $\ce{H2O2}$
✓ 97 $\ce{H H H}$
✓ 98 $\ce{H H H}$
✓ 99 $\ce{H_2HHHHH\bond{...}H}$
✓ 100 $\ce{^}$
✓ 101 $\ce{CO2 + C -> 2 CO}$
✓ 102 $\ce{CO_2 + C -> 2 CO}$
✓ 103 $\ce{\underbrace{O2}_{oxygen molecule} -> 2O}$
✓ 104 $\ce{^{227}_{90}Th+}$
✓ 105 $\ce{CO2 + C -> 2 CO}$
✓ 106 $\ce{Hg^2+ ->[I-] HgI2}$
✓ 107 $\ce{H2O}$
✓ 108 $\ce{Sb2O3}$
✓ 109 $\ce{N2}$
✓ 110 $\ce{O2}$
✓ 111 $\ce{CO2}$
✓ 112 $\ce{A <--> B}$
✓ 113 $\ce{H2O\\ CO2}$
✓ 114 $\ce{\frac{1}{2}H\bond{-}H \ce{H2O}}$
✓ 115 $\ce{\color{red}{H2O}}$
✓ 116 $\ce{CrO4^2-}$
✓ 117 $\ce{CrO4^2-}$
✓ 118 $\ce{\underbrace{a}_{b}}$
✓ 119 $\ce{H+}$
✓ 121 $\ce{[AgCl2]-}$
✓ 122 $\ce{Y^99+}$
✓ 123 $\ce{Y^{99+}}$
✓ 124 $\ce{Fe^{II}Fe^{III}2O4}$
✓ 125 $\ce{2H2O}$
✓ 126 $\ce{2 H2O}$
✓ 127 $\ce{0.5H2O}$
✓ 128 $\ce{1/2H2O}$
✓ 129 $\ce{(1/2)H2O}$
✓ 130 $\ce{\begin{math}n\end{math}H2O}$
✓ 131 $\ce{^{227}_{90}Th+}$
✓ 132 $\ce{^227_90Th+}$
✓ 133 $\ce{^{0}_{-1}n^{-}}$
✓ 134 $\ce{^0_-1n-}$
✓ 135 $\ce{H{}^3HO}$
✓ 136 $\ce{H^3HO}$
✓ 137 $\ce{(NH4)2S}$
✓ 138 $\ce{[\{(X2)3\}2]^3+}$
✓ 139 $\ce{H2(aq)}$
✓ 140 $\ce{CO3^2-{}_{(aq)}}$
✓ 141 $\ce{NaOH(aq,\begin{math}\infty\end{math})}$
✓ 142 $\ce{OCO^{.-}}$
✓ 143 $\ce{NO^{(2.)-}}$
✓ 144 $\ce{\mu-Cl}$
✓ 145 $\ce{[Pt(\eta^2-C2H4)Cl3]-}$
✓ 146 $\ce{NaOH(aq,\begin{math}\infty\end{math})}$
✓ 147 $\ce{Fe(CN)_{\begin{math}\frac{6}{2}\end{math}}}$
✓ 148 $\ce{\begin{math}cis\end{math}{-}[PtCl2(NH3)2]}$
✓ 149 $\ce{{(+)}_589{-}[Co(en)3]Cl3}$
✓ 150 $\ce{{(+)}_589{-}[Co(en)3]Cl3}$
✓ 151 $\ce{KCr(SO4)2*12H2O}$
✓ 152 $\ce{KCr(SO4)2.12H2O}$
✓ 153 $\ce{KCr(SO4)2 * 12 H2O}$
✓ 154 $\ce{C6H5-CHO}$
✓ 155 $\ce{A-B=C#D}$
✓ 156 $\ce{A-B=C#D}$
✓ 157 $\ce{A\bond{-}B\bond{=}C\bond{#}D}$
✓ 158 $\ce{A\bond{1}B\bond{2}C\bond{3}D}$
✓ 159 $\ce{A\bond{~}B\bond{~-}C}$
✓ 160 $\ce{A\bond{~--}B\bond{~=}C\bond{-~-}D}$
✓ 161 $\ce{A\bond{...}B\bond{....}C}$
✓ 162 $\ce{A\bond{->}B\bond{<-}C}$
✓ 163 $\underset{\mathrm{red}}{\ce{[Hg^{II}I4]^2-}}$
✓ 164 $\ce{Hg^2+ ->[I-] \begin{math}\underset{\mathrm{red}}{\ce{HgI2}}\end{math}} $
✓ 169 $\ce{A ->[H2O] B}$
✓ 170 $\ce{A ->[H2O] B}$
✓ 171 $\ce{A ->[{text above}][{text below}] B}$
✓ 172 $\ce{A ->[{text above}][{text below}] B}$
✓ 173 $\ce{A ->[\begin{math}x\end{math}][\begin{math}x_i\end{math}] B}$
✓ 175 $\ce{A ->[\begin{math}{x}\end{math}] B}$
✓ 177 $\ce{A + B}$
✓ 178 $\ce{A - B}$
✓ 179 $\ce{A = B}$
✓ 180 $\ce{A \pm B}$
✓ 181 $\ce{SO4^2- + Ba^2+ -> BaSO4 v}$
✓ 182 $\ce{A v B (v) -> B ^ B (^)}$
✓ 183 $\ce{Zn^2+}$
✓ 184 $\ce{RNO2 &<=>[+e] RNO2^{-.}}$
✓ 185 $\ce{NaOH(aq,\begin{math}\infty\end{math})}$
✓ 186 $\ce{H2O}$
✓ 187 $\ce{Fe(CN)_{\begin{math}\frac{6}{2}\end{math}}}$
✓ 188 $\ce{NO_x}$
✓ 189 $\ce{Fe^n+}$
✓ 190 $\ce{x Na(NH4)HPO4 ->[\Delta] (NaPO3)_x + x NH3 ^ + x H2O}$
✓ 191 $\ce{NO_\begin{math}x\end{math}}$
✓ 192 $\ce{NO_\begin{math}{x}\end{math}}$
✓ 193 $\ce{NO_{\begin{math}x\end{math}}}$
✓ 194 $$\ce{\begin{math}cis\end{math}{-}[PtCl2(NH3)2]}$$
✓ 195 $\underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}}$
✓ 196 $\underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}$
✓ 197 $K = \frac{[\ce{Hg^2+}][\ce{Hg}]}{[\ce{Hg2^2+}]}$
✓ 198 $K = \ce{\frac{[Hg^2+][Hg]}{[Hg2^2+]}}$
✓ 199 $^1$
✓ 200 $_1$
✓ 201 $1^1$
✓ 202 $1_1$
✓ 203 $\strokeint$
✓ 204 $\intbar$
✓ 205 $\ $
✓ 206 $\ce {\ }$
✓ 207 $\ce {A\;+\;B\;->\;C}$
✓ 208 $\ce {pH=-\log _{10}[H+]}$
✓ 209 $\ce {pH = -\begin{math}\log_10\end{math}[H+]}$
✓ 210 $\ce {pH = -$\log_10$[H+]}$
✓ 211 $\$$
✓ 212 $$$
Parse
✓ should parse: ""
✓ should parse: "a"
✓ should parse: "a^2"
✓ should parse: "a^2+b^{2}"
✓ should parse: "l_a^2+l_b^2=l_c^2"
✓ should parse texvc example
✓ should parse texvc specific functions
Render
✓ should correctly render ""
✓ should correctly render "a"
✓ should correctly render "a^2"
✓ should correctly render "a^2+b^{2}"
✓ should correctly render "a^{2}+b^{2}"
✓ should correctly render "l_a^2+l_b^2=l_c^2"
✓ should correctly render "\\sin(x)+{}{}\\cos(x)^2 newcommand"
480 passing (26s)
313 pending
$ package-lock-lint package-lock.json
Checking package-lock.json
$ git add .
$ git commit -F /tmp/tmpukf2fql0
On branch master
Your branch is up to date with 'origin/master'.
nothing to commit, working tree clean