This run took 468 seconds.
$ date
--- stdout ---
Fri Mar 24 22:06:42 UTC 2023
--- end ---
$ git clone file:///srv/git/mediawiki-services-texvcjs.git repo --depth=1 -b master
--- stderr ---
Cloning into 'repo'...
--- stdout ---
--- end ---
$ git config user.name libraryupgrader
--- stdout ---
--- end ---
$ git config user.email tools.libraryupgrader@tools.wmflabs.org
--- stdout ---
--- end ---
$ git submodule update --init
--- stdout ---
--- end ---
$ grr init
--- stdout ---
Installed commit-msg hook.
--- end ---
$ git show-ref refs/heads/master
--- stdout ---
4ac4238c1c60e23941ce937560babc2967d4dd4c refs/heads/master
--- end ---
$ /usr/bin/npm audit --json --legacy-peer-deps
--- stdout ---
{
"auditReportVersion": 2,
"vulnerabilities": {},
"metadata": {
"vulnerabilities": {
"info": 0,
"low": 0,
"moderate": 0,
"high": 0,
"critical": 0,
"total": 0
},
"dependencies": {
"prod": 2,
"dev": 376,
"optional": 1,
"peer": 0,
"peerOptional": 0,
"total": 377
}
}
}
--- end ---
Upgrading n:eslint-config-wikimedia from 0.23.0 -> 0.24.0
$ /usr/bin/npm install
--- stdout ---
added 379 packages, and audited 380 packages in 4s
63 packages are looking for funding
run `npm fund` for details
found 0 vulnerabilities
--- end ---
$ package-lock-lint package-lock.json
--- stdout ---
Checking package-lock.json
--- end ---
$ package-lock-lint package-lock.json
--- stdout ---
Checking package-lock.json
--- end ---
$ ./node_modules/.bin/eslint . --fix
--- stdout ---
--- end ---
$ ./node_modules/.bin/eslint . -f json
--- stdout ---
[{"filePath":"/src/repo/.eslintrc.yml","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/arrayTree.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/build-parser.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/check.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/d3json.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/feedback.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/flatList.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/index.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/big.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/box.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/chemFun2u.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/chemWord.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/curly.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/declh.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/dollar.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/dq.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/fq.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/fun1.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/fun1nb.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/fun2.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/fun2nb.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/fun2sq.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/infix.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/literal.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/lr.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/matrix.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/mhchem.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/nodeutil.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/texArray.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/texnode.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/nodes/uq.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/render.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/texutil.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/texutil.json","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/texvcinfo.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/lib/tokenTypes.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/package-lock.json","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/package.json","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/utils/createDoc.js","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]},{"filePath":"/src/repo/vis/data.json","messages":[],"suppressedMessages":[],"errorCount":0,"fatalErrorCount":0,"warningCount":0,"fixableErrorCount":0,"fixableWarningCount":0,"usedDeprecatedRules":[{"ruleId":"no-new-require","replacedBy":[]},{"ruleId":"no-process-exit","replacedBy":[]}]}]
--- end ---
$ /usr/bin/npm ci --legacy-peer-deps
--- stdout ---
added 379 packages, and audited 380 packages in 4s
63 packages are looking for funding
run `npm fund` for details
found 0 vulnerabilities
--- end ---
$ /usr/bin/npm test
--- stdout ---
> mathoid-texvcjs@0.5.1 test
> npm run build && npm run lint && npm run cover && npm run check-coverage
> mathoid-texvcjs@0.5.1 build
> node -e 'require("./lib/build-parser")'
> mathoid-texvcjs@0.5.1 lint
> eslint --max-warnings 0 --ext .js . bin/texvcjs
> mathoid-texvcjs@0.5.1 cover
> nyc --reporter=lcov _mocha --recursive
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 (45ms)
✔ should parse its own output (62ms)
✔ 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 (46ms)
✔ should parse its own output
✔ should match ocaml output
Big
✔ output should be correct (75ms)
✔ should parse its own output (449ms)
✔ 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 (40ms)
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 (67ms)
✔ 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 show a deprecation warning for \and
✔ should not show a deprecation warning for \land
✔ should not retry parsing if oldmhchem is set
All formulae from chem regression dataset:
✔ {\displaystyle {\ce {H2SO4\;->[P_{2}O5]\;H2O\;+\;SO3}}} ... {\displaystyle {\ce {AgNO3\;+\;H2S\;->\;Ag2S\;+\;}}} (3110ms)
✔ {\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}}} (2264ms)
✔ {\displaystyle {\ce {1/8SO3\;+\;H2O\;->\;H2SO4\quad \quad \Delta H=-73,69\;kJ/mol}}} ... {\displaystyle {\ce {6Al\;+\;3CO\;->\;Al4C3\;+\;6CO}}} (1856ms)
✔ {\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 }\ =}}} (1820ms)
✔ {\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}}} (1929ms)
✔ {\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)}}} (1859ms)
✔ {\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}}} (1788ms)
✔ {\displaystyle {\ce {2Na{+}Cl2={\Delta }}}} ... {\displaystyle {\ce {{2MgO_{(s)}}+{Si_{(s)}}+{2CaO_{(s)}}->{2Mg_{(}g)}+Ca2SiO4(s)}}} (1848ms)
✔ {\displaystyle {\ce {H-{\overset {\displaystyle {H2-CH3-T5} \atop |}{\underset {| \atop \displaystyle H}{C}}}}}} ... {\displaystyle {\ce {[A]_{\mathit {t}}=[A]_{0}-[B]_{\mathit {t}}}}} (1961ms)
✔ {\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}^{-}}}}} (1966ms)
✔ {\displaystyle {\ce {2NO3^{-}\;+\;2CH2O\;+\;H3O^{+}\;+\;->\;N2O\;+\;2CO2\;+\;5}}} ... {\displaystyle {\ce {S\;+\;1/2O2\;->\;SO\quad \quad \Delta H_{f}=+7\;kJ/mol}}} (1850ms)
✔ {\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}}}} (1697ms)
✔ {\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}}} (1909ms)
✔ {\displaystyle {\ce {N_{2}O\;+\;O_{2}\;->\;2NO}}} ... {\displaystyle {\ce {HSo3^{-}\;->\;H2O2\;+\;O2}}} (1794ms)
✔ {\displaystyle {\ce {NaCl\;+\;NaSO4\;->[200\;{}^{\circ }C]\;HCl\;+\;NaHSO4}}} ... {\displaystyle {\ce {S^{IV}O2\;+\;H2O2\;->\;H2SO4}}} (481ms)
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 mathrm
✔ should process partial trees
✔ should process parsed search input
Some broken formulae from en-wiki:
✔ \begin{alignat}2
\ 0270c7af664da7afddcac31d7ac3ad0f
✔ ρ\colon P \to N 0448c022977e58b500445d3c92a6579a
✔ a>b"="\<< 0e7c8b2fe70a6310bb546f3506e8c2ae
✔ \begin{alignat}2
15212ec94e20fb0a97994cdee3b47dd8
✔ U(0)=−1 17a71941f66112018c433832caa51851
✔ \ln N! ≈ N \ln N - N 267b6df35d46a8a5ef4b910298d1bb16
✔ P_{\text{new link to 34cd4915dc9878e6a836e546a1725c86
✔ |\pm\rangle=\frac{1} 6007c325e853ca12cfb61f00f9d36109
✔ CCAI=D-140.7 \
(\lo 629979cd7de132f3d6884d3c48064c76
✔ \left<|v|\right> 665cf2ffe7708e3cae870b92deddfb6d
✔ \begin{alignat}2
e_ 6a844321d746ca110ed895f82c622684
✔
\begin{align}
[K_c] 6e2ea999c31f52054218db930bd4803d
✔
\begin{array}{|l|l| 740162aa0b844cc286c4a59c0c81fdfe
✔ p_\pi(\boldsymbol\e 866f63344780c4751fe344d954023fc9
✔ \begin{alignat}2
h_ 960cf2f7a6a5b4a03beba84473829eb3
✔ \left[\begin{array}{ 9cd7310f8613eeebb28046da004bc237
✔ A_iR_j \subseteq A_{ bf76a4641adb9a399d70feec04d37660
✔ P_{\text{new link to c159c37865e286fab2b505de11ad4ce9
✔ { P_{rad} } = d3152d83fd1079191e4cbd3995470ddf
✔
S = \left[ N\ln V\r e0199f5a37a0ab1813cfd0628f826f80
✔ \left[\begin{array}{ e3cc368e634d90cee0694fa0834b39b2
✔ \mathcal{G} × \mathc e9f6be4c2ba14f4866fe4263bf5c6a0f
✔ Z^{X × Y} f338c7dea84103c7be9626def39d1c7f
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 (1727ms)
✔ S_\ell=e^{2i\delta_\ell} ... \scriptstyle W[k] = (-1)^k\cdot W_0[k]. (1392ms)
✔
\psi(x)=\sum_{n\le x}\Lambda(n). \;
... \quad k(\phi)\;=\;\frac{P'M'}{PM}\;=\;\frac{\delta x}{R\cos\phi\,\delta\lambda}, (1255ms)
✔ B = { I_0 \over 2 } e^{ -j \phi } ... \ \mathcal{L}_\mathrm{gf} = - \frac{1}{2} \operatorname{Tr}(F^{\mu \nu} F_{\mu \nu}) (1139ms)
✔ \displaystyle p_n(x;a|q) = {}_2\phi_1(q^{-n},0;aq;q,qx) = \frac{1}{(a^{-1}q^{-n};q)_n}{}_2\phi_0(q^{-n},x^{-1};;q,x/a) ... \scriptstyle Z=A (1300ms)
✔
[\mathrm{J}_k,\mathrm{J}_l] = i\hbar\epsilon_{klm}\mathrm{J}_m, \quad \mathrm{where}\quad k,l,m \in (x,y,z),
... \sigma_{Z_1}^2. (1364ms)
✔
IMD_i = \left( e_i^t - h_i^t \right) \times \left( G_i - G \right)
...
P = p + \frac{1}{2} \rho r^2 \Omega^2.
(1234ms)
✔ S_-|s,m\rangle=\hbar \sqrt{s(s+1)-m(m-1)}|s,m-1\rangle ... f(\phi)\, (1221ms)
✔ P^s (S) = \inf \left\{ \left. \sum_{j \in J} P_0^s (S_j) \right| S \subseteq \bigcup_{j \in J} S_j, J \text{ countable} \right\}, ... \mu \ = \mu_r \,\mu_0 \,\! (1239ms)
✔ = \int_{0}^{\infty}C\, \operatorname{d}t ... \bar{\mathsf{S}} (1301ms)
✔ \begin{cases} u_{t}=ku_{xx} & (x, t) \in [0, \infty) \times (0, \infty) \\
u(x,0)=g(x) & IC \\ u(0,t)=0 & BC \end{cases} ... \varphi=2\cos(\pi/5)=2\cos 36^\circ\, (1379ms)
✔ \textstyle N^x ... s_n\uparrow t (1277ms)
✔ \{a_1, \dots, a_n\}\ ... \sqrt p (1255ms)
✔ \phi\wedge\phi'=(-1)^{|\phi||\phi'|
+[\phi][\phi']}\phi'\wedge\phi ... \begin{align}
e_1(x_1,\ldots,x_n) &= p_1(x_1,\ldots,x_n),\\
2e_2(x_1,\ldots,x_n) &= e_1(x_1,\ldots,x_n)p_1(x_1,\ldots,x_n)-p_2(x_1,\ldots,x_n),\\
3e_3(x_1,\ldots,x_n) &= e_2(x_1,\ldots,x_n)p_1(x_1,\ldots,x_n) - e_1(x_1,\ldots,x_n)p_2(x_1,\ldots,x_n) + p_3(x_1,\ldots,x_n).\\
\end{align} (1293ms)
✔ M=S^3 ... \{U_i\}_{i=1}^k (1252ms)
✔ F_{Y}(y)=P(Y\leq y) ... \delta t=-6.5\pm7\ (\mathrm{stat.}) \pm6\ (\mathrm{sys.}) (1405ms)
✔ \left\Vert \mathbf{x} - \mathbf{c} \right\Vert^2=r^2 ... \mu_n = \{1,\zeta_n,\zeta_n^2,\dots,\zeta_n^{n-1}\} (1396ms)
✔ \hat{H}(\mathbf{k}) ... Ob (1254ms)
✔ \int xdy = xy - \int y dx ... e_n \sim \mathcal{N}(0,1), (1292ms)
✔ \frac{dP_{\text{Magnetic dipole}}(\mathbf{x})}{d\Omega}=\frac{Z_0}{32 \pi^2}k^4\|\mathbf{m}\|_2^2\sin^2\theta ... \textstyle Z_{3} (1256ms)
✔ 1-\frac{\ln(1-(1-p) e^{-\beta x})}{\ln p} ... F_\lambda (1217ms)
✔ f(x) = f_n H_n(x) ... \mathrm{Ad}: G\to\mathrm{Aut}(\mathfrak g)\sub\mathrm{GL}(\mathfrak g) (1173ms)
✔ \textstyle c ... 94906265.625x^2 - 189812534x + 94906268.375 (1277ms)
✔ h(X) = -\int_X f(x) \log f(x) \,d\mu(x), ... b_i = a_i - 2e_i (1199ms)
✔ V_{CB} = V_{CE} - V_{BE} ... R_\lambda f = \int_0^\infty e^{-\lambda t}T_t f\,dt. (1148ms)
✔ {1}/\sqrt{\omega} ... \text{inquire}(j) (1333ms)
✔ \ I(r,d)=\delta I_bR\exp(\alpha d) ... (\mathbf{b_{1}}, \mathbf{b_{2}}, \mathbf{b_{3}}) (1258ms)
✔ \varphi\star \varphi^\prime ... \beta_\rho(\pi(x_1,x_n)) = \min \{ \alpha_{\rho}(x_i,x_{i+1}) | i=1,\ldots,n-1 \} (1139ms)
✔
\mathrm{var}(T)
\geq
\frac{[\psi'(\theta)]^2}{I(\theta)}
... \tan\theta = \frac{S_1/\sqrt{n_1}}{S_2/\sqrt{n_2}} (1205ms)
✔ \chi\, ... e_s(T) (1313ms)
✔ \|f\|_p= \sum_{n}|a_n|^p \qquad (0 < p < 1) ... \partial^2 u/\partial z^2 (1213ms)
✔ x = \frac{i}{f} = \frac{S}{f}\sqrt{t}. ... m_1 = m_2 = m_3 = \cdots = m_n\, (1276ms)
✔ A(z) = 0.5[P(z)+ Q(z)] ... 2g (1343ms)
✔ e = \sum_{k=0}^\infty \frac{1}{k!} ... \sigma_\mathrm n (1244ms)
✔ \begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\end{pmatrix} ... f^{1}(\theta) (1296ms)
✔ p_1, \cdots, p_n ... ~|x\rangle~ (1229ms)
✔ \frac{V_1^2}{2} ... \;_j\psi_k \left[\begin{matrix}
a_1 & a_2 & \ldots & a_j \\
b_1 & b_2 & \ldots & b_k \end{matrix}
; q,z \right] = \sum_{n=-\infty}^\infty
\frac {(a_1, a_2, \ldots, a_j;q)_n} {(b_1, b_2, \ldots, b_k;q)_n} \left((-1)^nq^{n\choose 2}\right)^{k-j}z^n. (1239ms)
✔ x=r_k,y=s ... \gamma_{\mathrm{rad},0} (1280ms)
✔ \operatorname{E} [X] = \int_\Omega X \, \mathrm{d}P = \int_\Omega X(\omega) P(\mathrm{d}\omega) ... X=\mathbb{R}^n, (1269ms)
✔ \textstyle m \in \mathcal{M} ... a \in \mathbb{A} (1205ms)
✔ {\rm tr}\left( \left(\frac{\partial g(\mathbf{U})}{\partial \mathbf{U}}\right)^{\rm T} \frac{\partial \mathbf{U}}{\partial X_{ij}}\right) ... J^k_p(M,N) (1250ms)
✔ \displaystyle z(\alpha_1,\beta_1,\gamma_1,\delta_1)+(1-z)(\alpha_2,\beta_2,\gamma_2,\delta_2) ... f(t)=\sin(\ln(t)),\; t>0 (1283ms)
✔ g_1,\,g_2\ldots\,g_n ... \mathbf{A}^{-1} = \begin{bmatrix}
a & b \\ c & d \\
\end{bmatrix}^{-1} =
\frac{1}{\det(\mathbf{A})} \begin{bmatrix}
\,\,\,d & \!\!-b \\ -c & \,a \\
\end{bmatrix} =
\frac{1}{ad - bc} \begin{bmatrix}
\,\,\,d & \!\!-b \\ -c & \,a \\
\end{bmatrix}. (1272ms)
✔ P_A = A (A^\mathrm{T} A)^+ A^\mathrm{T} ... h(\gamma) = \int_0^1 \log\,(Q'(p; \gamma))\,\mathrm dp = \log(\gamma)\,+\,\log(4\,\pi).\! (1212ms)
✔ C_V = 3Nk\left({\epsilon\over k T}\right)^2{e^{\epsilon/kT}\over \left(e^{\epsilon/kT}-1\right)^2} ... d_n = 2\lambda Kp_nq_n + Kq_n^2 = Kq_n[2\lambda + (1 - 2\lambda)q_n] (1226ms)
✔ \frac{\partial^2 \psi}{\partial x \partial y} - \frac{\partial^2 \psi}{\partial y \partial x} = 0. ... j=1,\ldots, n (1257ms)
✔ {q}={F(k)} ... R^2-r^2 (1178ms)
✔ x(u)=a \mathrm{sn(u,k)}+(a/k)((1-k^2)u - E(u,k)) ... D=\frac{1}{\ell \nu} (1224ms)
✔ \frac{\rm d}{{\rm d}z}\,\mathrm{erf}(z)=\frac{2}{\sqrt{\pi}}\,e^{-z^2}. ... \left [ 1 - {\left ( \frac{\partial z}{\partial x} \right )}_y {\left ( \frac{\partial x}{\partial z} \right )}_y \right ] dz = \left [ {\left ( \frac{\partial z}{\partial x} \right )}_y {\left ( \frac{\partial x}{\partial y} \right )}_z + {\left ( \frac{\partial z}{\partial y} \right )}_x \right ] d y. (1251ms)
✔ r=C_S^2 K_1K_2C_AC_B ... \mathbf{B}'(t) = 3(1-t)^2(\mathbf{P}_1 - \mathbf{P}_0) + 6(1-t)t(\mathbf{P}_2 - \mathbf{P}_1) + 3t^2(\mathbf{P}_3 - \mathbf{P}_2) \,. (1266ms)
✔ \frac{m \left | \mathbf{v} \right | }{\left | \mathbf{r} \right |} = q \left | \mathbf{B} \right | \sin \theta, \,\! ... \langle \phi | \psi \rangle = 0 (1180ms)
✔ \{a_1^n \dotso a_{2^{k+1}}^n|n\geq0\} ... n\leq \frac{f(b)-f(a)}{\alpha}\ (1225ms)
✔ b \notin\{-2,-1/2,0,\pm1\}, a^2=-(b^2+2b) ... \frac{1}{2}+is (1227ms)
✔ (i,j)\in\kappa ... \operatorname{de-lambda}[F\ P = E] (1354ms)
✔
F_z =\ -J_3\ \frac{1}{r^5}\ \frac{3}{2}\ \left(5\ \sin^2 i \ \sin^2 u\ -1\right)\ \cos i
... 0\le c\le 1 (1469ms)
✔ \Theta_p:T_p\mathbf{R}^3\to\mathbf{R} ... \tau =\xi^{\,z} (1268ms)
✔ PR=\frac{P_2}{P_1} ... 10^6 ~ S/m (1242ms)
✔ F(6) ... f(\mathfrak{a}) (1285ms)
✔ \cfrac{r_{xy}}{\sqrt{r_{xx} \cdot r_{yy}}} ... y^2+a_1xy+a_3=x^3+a_2x^2_2+a_4x+a_6 (1591ms)
✔ (20)\quad L+M=r\,,\quad l_+ + l_- =2\sqrt{M^2-Q^2}\,\cos\theta\,,\quad z=(r-M)\cos\theta\,, ... \int_a^b f(x)\, dx \approx \sum_{i=1}^{n-1} w_i\, f(x_i). (1203ms)
✔ \sqrt 4 ...
R\ln x_i = - \frac{H_i ^\circ }{T} + \frac{H_i^\circ }{T_i^\circ }
(1326ms)
✔ \scriptstyle \Gamma(1/2) = \sqrt{\pi} ... t(C_n^{1,2}) = nF_n^2 (1198ms)
✔ H_0\psi^{(0)}(\vec{r}_1, \vec{r}_2) = E^{(0)} \psi^{(0)}(\vec{r}_1, \vec{r}_2) ... C + D \cdot K = P + S. \, (1199ms)
✔ R_\mathrm{internal} ... C = 2 \sum_{i}^{\rm core} h_{ii} + \sum_{ij}^{\rm core} \left( 2 \left\langle ij \left.\right| ij\right\rangle - \left \langle ij \left.\right| ji\right\rangle \right) - 2 \sum_{i}^{\rm core} \epsilon_i (1401ms)
✔ a_{ij} = \langle\psi_i | {a} | \psi_j\rangle ... \mathbf{u}' (1540ms)
✔ v_{t} = \sqrt{ gd \frac{ \rho_{obj} }{\rho} }. \, ... \mathcal{L}^* = \{ \mathbf{v} \in V \quad | \quad \langle \mathbf{v},\mathbf{x} \rangle \in R, \forall \mathbf{x} \in \mathcal{L} \} (1375ms)
✔ \textstyle N(C) > 0 ... \langle \hat{L} \rangle (1262ms)
✔ 1.3 \cdot 10^{5} ... \pm 1 \pm 3\cdots \pm (n-1) = 0 (1360ms)
✔ (x)_n ... p_{\mathrm{i}} = x_{\mathrm{i}} \cdot p (1461ms)
✔ X_1,\ldots,X_N ... \left( \frac{1+|x|^2}{1+|y|^2} \right)^t \le 2^{|t|} (1+|x-y|^2)^{|t|}. (1291ms)
✔ b(t;u) = H(u-t)\cdot e^{-(u-t)r} = \begin{cases} e^{-(u-t) r} & t < u\\ 0 & t > u,\end{cases} ...
A' = U^{\dagger} A U
\, , (1451ms)
✔ \bigoplus_{d=0}^\infty H^0(V, L^d) ... P(X \geq x) \leq \frac{e^{-\lambda} (e \lambda)^x}{x^x}, \text{ for } x > \lambda , (1249ms)
✔ \nu\,\! ... \rho^{T_B} = \frac{1}{4}\begin{pmatrix}
1-p & 0 & 0 & -2p\\
0 & p+1 & 0 & 0\\
0 & 0 & p+1 & 0 \\
-2p & 0 & 0 & 1-p\end{pmatrix} (1279ms)
✔ p(\lambda) = \mathrm{Gamma}(\lambda; \alpha + n, \beta + n \overline{x}). ... d_j S(t) = E[d_j S(t)] + d J_S(t) = h(S(t^-)) (\int_z z \eta(S(t^-),z) \, dz) dt + d J_S(t). (1200ms)
✔ n=\sum_{i=0}^{l-1}n_ib^i \text{ with } |n_i|<b ... y = \frac{h}{b^2} x^2 (1427ms)
✔ \{q_j\} ... x^2 \cdot 2^{-1} = \frac{\sqrt{5}}{2} (1166ms)
✔ \Psi_0=\Psi_1=\Psi_3=\Psi_4=0\,,\quad \Psi_2=-\frac{M(u)}{r^3}\,, ... cov(w_i, z_i) = az(1 - z) - (a + b)z^2(1 - z) = z[1 - z][a - (a + b)z] (1207ms)
✔ p_3=\frac{100}{5}\left(3-\frac{1}{2}\right)=50. ... \vec{y} (1261ms)
✔ \gamma(x,y)=\gamma_s(y-x). ... X = -2\sum_{i=1}^k \log_e(p_i) \sim \chi^2(2k) . (1200ms)
✔ \frac{13+10}{2} - 10=1.5 ... ||A|| = \inf\{C: ||A\mathbf{x}||_V \leq C||\mathbf{x}||_U\} (1333ms)
✔ \eta(f) \mapsto \sum_{s \in \bigcup_{S \in \mathfrak{P}(V)}\sum{v_i \in S} \left( \{v_i\} \times D_i \right)} f(s) ... d\Omega=\sin(\theta)\,d\theta\,d\phi. (1215ms)
✔ o(f(n)) ... \scriptstyle \sqrt[4]{g\sigma/\rho} (1183ms)
✔ \Omega_{\mu \nu} ^{ab} = R_{\mu \nu} ^{ab} ... A-E[A]\in T_p^{(e)} (1218ms)
✔ cos({\alpha})=1 ...
u_r(r) = -z\phi(r) \quad \text{and} \quad u_\theta(r) = 0 \,.
(1219ms)
✔ M = M_0 \supset M_1 \supset M_2 \supset \cdots ... c_2=\sqrt[3]{3\sqrt{33}-17} (1259ms)
✔ \sum_{\mathbb{S}}{f} ... \oint\frac{\delta Q}{T}=0 (1374ms)
✔ S = -\left(\frac{\partial A}{\partial T}\right)_V
=Nk\left[ \ln\left(\frac{(V-Nb')T^{3/2}}{N\Phi}\right)+\frac{5}{2} \right] ... \succ_W (1240ms)
✔ \frac{d}{dt}\hat{\mathbf{x}}(t) = \mathbf{F}(t)\hat{\mathbf{x}}(t) + \mathbf{B}(t)\mathbf{u}(t) + \mathbf{K}(t) (\mathbf{z}(t)-\mathbf{H}(t)\hat{\mathbf{x}}(t)) ... \,\!\phi^* (1198ms)
✔ \textstyle z_\mathrm {mn} ... R_{\mu \nu} = K \left(T_{\mu \nu} - {1 \over 2} T g_{\mu \nu}\right) (1250ms)
✔ \operatorname{Var}\left(\sum_{i}^n a_iX_i\right) = \sum_{i=1}^na_i^2 \operatorname{Var}(X_i) + 2\sum_{1\le i}\sum_{<j\le n}a_ia_j\operatorname{Cov}(X_i,X_j) ... {\varphi}_{{\lambda}_{1}}\circ\delta_{[1,{j}_{1},{c}_{1}]}[I] =
{\varphi}_{{\lambda}_{2}}\circ\delta_{[1,{j}_{2},{c}_{2}]}[I] (1239ms)
✔ b = \sum_i \sum_j x_i \; x_j \; b_{ij} ... \rho (z+z') - \rho (z) = \frac{\partial \rho (z)}{\partial z} z' (1232ms)
✔ \langle E_1(t) E_2^*(t - \tau) \rangle = \langle E_{a1}(t) E_{a2}^*(t - \tau) \rangle + \langle E_{a1}(t) E_{b2}^*(t - \tau) \rangle + \langle E_{b1}(t) E_{a2}^*(t - \tau) \rangle + \langle E_{b1}(t) E_{b2}^*(t - \tau) \rangle ... dU =\frac{1}{\beta}d\left(\log Z+\beta U\right) - X\,dx \, (1255ms)
✔ S^+ = E^T \mbox{Diag} (e^+) E ... b(v_1) \cdot v_1 = \frac{v_1^2}{2} \Rightarrow b(v_1) = \frac{v_1}{2} (1355ms)
✔ f=\frac{1}{2 i k}(e^{2 i \delta_s}-1)\approx \delta_s/k \approx - a_s ... \{\alpha_i\}_{i=1}^G (1204ms)
✔ m^{p-1}\equiv 1\pmod p \! ... x^3+px^2+qx=N (1335ms)
✔
\operatorname{E}(Y | X) = \int y f(y|x) dy = \int y \frac{f(x,y)}{f(x)} dy
...
\frac{\partial}{\partial A} \ln p(\mathbf{x}; A)
=
\frac{1}{\sigma^2} \left[ \sum_{n=0}^{N-1}x[n] - N A \right]
(1381ms)
✔ H = -\mu\boldsymbol{\sigma}\cdot\mathbf{B} ... \gamma=\mu-\alpha_ja (1234ms)
✔ W ... \mathfrak{P}^{20} (1294ms)
✔ x = -3 ... t_1<t_2 (1298ms)
✔ \displaystyle u_t=u_{xxx}/2 +3uu_x-6ww_x ... P(k,\rho,V) = \frac{(V\rho)^k e^{-(V\rho) }}{k!} . \,\! (1272ms)
✔ a \ge 0 ... \oplus_{n \in \mathbf Z}Hom_n(A,B) (1223ms)
✔ -0.493091109\ldots ... \theta_m = m \circ T_\pi (1169ms)
✔ t_0 = T\,e^{ik\ell/\cos\theta} ... \hat{H}'_0= \beta p_0 (1200ms)
✔ U_2 ... \psi(\mathbf{r})=j_l(kr)Y_{lm}(\theta,\phi) (1177ms)
✔ \int_0^{\infty}x^\alpha e^{-x} L_n^{(\alpha)}(x)L_m^{(\alpha)}(x)dx=\frac{\Gamma(n+\alpha+1)}{n!}\delta_{n,m}~, ... \bar{\delta} l^a=(\alpha+\bar{\beta})l^a-\bar{\sigma}m^a-\rho\bar{m}^a\,; (1199ms)
✔
F_{ax} \ \stackrel{\mathrm{def}}{=}\ \left( \frac{4}{3} \right) \frac{\xi^{2}}{2 - (S/p^{2})}
... a=1+i. (1185ms)
✔ U\,\left[
\begin{array}{l}
\frac{d_1}{b_{1,1}}\\
\cdots\\
\frac{d_k}{b_{k,k}}\\
h_{k+1}\\
\cdots\\
h_n
\end{array}
\right]\,, ... \Delta : \{\bold{x}\} \times M \to \mathbb{R} (1280ms)
✔ \nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \qquad \quad \ (4) ... \frac{-y_1}{f} = \frac{x_1}{x_3} (1311ms)
✔ \color{Thistle}\text{Thistle} ... {\rm JSD}(P_1, P_2, \ldots, P_n) = H\left(\sum_{i=1}^n \pi_i P_i\right) - \sum_{i=1}^n \pi_i H(P_i) (1175ms)
✔ = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x(t) w(t-\tau) \, e^{-j \omega t} \, d\tau \, dt. ... f( E( x ) ) \le E( f( x ) ) (1185ms)
✔ h(v_i, v_g) \leq d^\star(v_i,v_g) ... \mathbf{\hat{e}}_{\parallel}\,\! (1225ms)
✔ (V_t \cup V_n) ... \mathfrak I_{\Phi} := (\mathfrak T_{\Phi},\beta_{\Phi}) (1269ms)
✔ r^N D = \frac{W}{2}. ... O(\Delta t^4) (1340ms)
✔ \textbf{c}=U\textbf{b} ... =\mathbf{I}_1 (1358ms)
✔ \partial_t^2 + 2\gamma\partial_t + \omega_0^2 ... h_{n+1} (1249ms)
✔ x^2 + y^2 = L^2 ... {{D \over Dt} = {({\partial \over \partial t})_p} + {({\overrightarrow{V} \cdot \nabla})_p} + {\omega {\partial \over \partial p}}} (1377ms)
✔ \rho = \frac{M_s + M_w}{V_s + V_w + V_a}= \frac{M_t}{V_t} ... \zeta(-n,x) = - \frac{B_{n+1}(x)}{n+1} \ . (1275ms)
✔ \varphi' = \varphi - \frac{\partial \lambda}{\partial t}, \quad \mathbf A' = \mathbf A + \mathbf \nabla \lambda ... (aX+bY)^{'n} = \sum_{i=0}^n {n\choose i}a^ib^{n-i} X^{'i} Y^{'{n-i}} (1276ms)
✔ \ u ... p \to [a]q\,\! (1229ms)
✔ B = \int_0^1 L(X) dX. ... \displaystyle\chi_\lambda(1) \equiv {\rm dim}\, V = {\prod_{\alpha>0} (\lambda + \rho,\alpha)\over \prod_{\alpha>0} (\rho,\alpha)}. (1347ms)
✔ B=\frac{V_t}{V_d}\ \ln(A_x)+\ln\left(y'(0)+\sqrt{{y'(0)}^2+1}\right) ... 4:m\ (1217ms)
✔ \textstyle E_{+}=E_{-} ... \textstyle q (1240ms)
✔ f(\alpha {\mathbf v}) = \alpha f({\mathbf v}) ... \rho: G \to \mathrm{Aut}(X) (1252ms)
✔ T_eP=sl(2,\mathbb{R}) ... \begin{align}
\mathbf{v}_1 & = [ (v_1)^1, (v_1)^2, \cdots (v_1)^n ] \\
\mathbf{v}_2 & = [ (v_2)^1, (v_2)^2, \cdots (v_2)^n ] \\
\vdots \\
\mathbf{v}_n & = [ (v_n)^1, (v_n)^2, \cdots (v_n)^n ] \\
\end{align} (1163ms)
✔ e=0\,\! ...
AF = \frac{9.73}{\lambda \sqrt{G} }
(1267ms)
✔ {} 3.141024 < \pi < 3.142704. ... \mathbb{W}^{k} (1287ms)
✔ H_0(\mathbb{Z}S) = \frac{\ker \partial_0}{\mathrm{im} \partial_1} = \mathbb{Z} \langle v \rangle \cong \Z, ... k,\, \theta\! (1222ms)
✔ k_{t+1} ... f_{st} = \frac{ m_{ox, 0}}{sm_{fu, 1} + m_{ox ,0}} (1196ms)
✔ \{\hat{\pi}_i\} ... \text{transient inertial forces + convective inertial forces}=\text{gravitational force + Pressure force + viscous forces}\,\! (1352ms)
✔ -\Delta u_i^{(k)} = f_i, \qquad u_i^{(k)}|_{\partial\Omega} = 0, \quad u^{(k)}_i|_\Gamma = \lambda^{(k)} ... f(f(\dots f(z^*))) = z^* (1203ms)
✔ (-,-) ... \psi_I(x) = A_I e^{i \rho y} + A_{II} e^{-i\rho y}\quad y<-1 (1183ms)
✔ M+2L \rightleftharpoons ML_2: [ML_2]=\beta_{12}[M][L]^2 ...
\begin{pmatrix}\rm Li &\rm Be \\\rm Na &\rm Mg \end{pmatrix}
\otimes
\begin{pmatrix}\rm Li &\rm Be \\\rm Na &\rm Mg \end{pmatrix}
=
\begin{pmatrix}
\rm Li_2 &\rm LiBe &\rm BeLi &\rm Be_2 \\
\rm LiNa &\rm LiMg &\rm BeNa &\rm BeMg \\
\rm NaLi &\rm NaBe &\rm MgLi &\rm MgBe \\
\rm Na_2 &\rm NaMg &\rm MgNa &\rm Mg_2 \\
\end{pmatrix}
(1229ms)
✔ \delta W = (\sum_{i=1}^n \mathbf{F}_i)\cdot\mathbf{d}\times \vec{\omega}\delta t+ (\sum_{i=1}^n \mathbf{F}_i)\cdot\mathbf{v}\delta t + (\sum_{i=1}^n \mathbf{X}_i \times\mathbf{F}_i)\cdot\vec{\omega}\delta t = (\sum_{i=1}^n \mathbf{F}_i)\cdot(\mathbf{v}+\mathbf{d}\times \vec{\omega}) \delta t + (\sum_{i=1}^n \mathbf{X}_i \times\mathbf{F}_i)\cdot\vec{\omega}\delta t . ... \mu_\mathrm{k}\, (1463ms)
✔ F(h(X_1, X_2)) ... \bar{v_i} (1413ms)
✔
\left(
1 - \sum_{i=1}^p \phi_i B^i
\right)
\left(
1-B
\right)^d
X_t
=
\left(
1 + \sum_{i=1}^q \theta_i B^i
\right) \varepsilon_t \, .
... P(k^{}_j=i)=w(n,i)\big/{\sum}_\ell w(n,\ell) (1593ms)
✔ \scriptstyle{(r_{1},\theta_{1})} ... x(w)= -y(w)-y(w^{-1}) (1481ms)
✔ \omega_0 = \frac{1}{\sqrt{L C}}. ... \mathbf{\gamma}(t_0) = \mathbf{p}_0 (1403ms)
✔ \scriptstyle \vec S = \vec J - \vec L ... a^4+b^4+(a+b)^4+c^4+d^4+(c+d)^4 = (a+b)^4+(c+d)^4+(a+b+c+d)^4 (1396ms)
✔ n_s=2 f_s/p ... f(iy)=-ay^2+iby+c=P_0(y)+iP_1(y)=-ay^2+c+i(by). (1225ms)
✔
\Pr \left\{ \lambda_{\text{min}}\left( \sum_k \mathbf{X}_k \right) \leq (1-\delta)\mu_{\text{min}} \right\} \leq d \cdot \left[ \frac{e^{-\delta}}{(1-\delta)^{1-\delta}} \right]^{\mu_{\text{min}}/R} \quad \text{for } \delta\in [0,1]\text{, and}
... \text{A} \mapsto 1, \text{B} \mapsto 2, \text{C} \mapsto 3, (1275ms)
✔ 5x^2+8xy+5y^2=1. ... \kappa=\frac{\sqrt{(z''y'-y''z')^2+(x''z'-z''x')^2+(y''x'-x''y')^2}}{(x'^2+y'^2+z'^2)^{3/2}} (1410ms)
✔ a'_{\ell\ell} = a_{\ell\ell} + t a_{k \ell} \,\! ... \lim_{n\to\infty} x_n \frac{\log n}n = 1, (1301ms)
✔ k+jd \le m+ld ... R = (1310ms)
✔ (x, y, z) = \left(\frac{2 \mathrm{Re}(\zeta)}{1 + \bar \zeta \zeta}, \frac{2 \mathrm{Im}(\zeta)}{1 + \bar \zeta \zeta}, \frac{-1 + \bar \zeta \zeta}{1 + \bar \zeta \zeta}\right). ... \mathcal F, \mathcal G (1150ms)
✔ \mbox{high} - \mbox{low} ... \begin{align}
A_x & = - \frac{1}{\sqrt{2}} A_+ + \frac{1}{\sqrt{2}} A_{-} \\
A_y & = + \frac{i}{\sqrt{2}} A_+ + \frac{i}{\sqrt{2}} A_{-} \\
A_z & = A_0
\end{align} (1308ms)
✔ \left\langle\mathtt{halt},\ v\right\rangle ... X(Y,Z)=(\nabla_X Y,Z) + (Y,\nabla_X Z) (1262ms)
✔ CE(1,1,x) ... p \in pred_b (1273ms)
✔ \frac{\mbox{Cash Flow}}{\mbox{Market Recapitalisation}} ... R_{\alpha}^{\beta}=-\left ( \frac{1}{2}\sqrt{-g} \right ) \frac{\partial}{\partial t} \left (\sqrt{-g} \varkappa_{\alpha}^{\beta} \right )-P_{\alpha}^{\beta}=0, (1363ms)
✔ K_{1/2}(z)=\sqrt{\frac{\pi}{2z}} e^{-z} ... \boldsymbol{w} (1357ms)
✔ F_{preload} ... \| \mathbf{L}_k \|^2 \le \| \mathbf{L}_k \mathbf{L}_k ^* \| = \| \mathbf{A}_k \|. (1305ms)
✔ \beta = \frac{p_1 c}{E_1 + m_2 c^2} ... G(z)=S(z+\mu(z))\ (1669ms)
✔ \displaystyle{\int_{C} -U_y \,dx + U_x \, dy = 2\pi} ... f(0,\dots,0)=0 (1548ms)
✔ 2^{n} a_{2^{n}} ... \cos\delta=\frac{x_1}{-c\,t_1} (1502ms)
✔ x \mapsto \mu_{x} ... \phi_F=Y_D\circ F (1360ms)
✔
\operatorname{Li}_s(z) = \tfrac{1}{2}z + z \int_0^\infty \frac{\sin[s \arctan t \,- \,t \ln(-z)]} {(1+t^2)^{s/2} \,\sinh(\pi t)} \,\mathrm{d}t \,,
... \pi^{kl} (1209ms)
✔ \hat{h}(\xi) = \hat{f}(\xi)\cdot \hat{g}(\xi). ... V_f(x,t) = A \sin (\omega t - kx),\, (1355ms)
✔ \{X_1,\dots,X_N\} ... \ (w' - w)\cos w (1309ms)
✔ \textstyle F(B) = f^{-1}(B) ... (\Delta = \omega - \omega_0) (1376ms)
✔ A=\left(\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & \frac{1}{\epsilon} \\ 0 & \frac{1}{\mu} & 0 \end{matrix}\right), ... \lambda = - \beta(x) (1459ms)
✔ es \in E \Longrightarrow s \in E. ... \textbf{y}(t) = \begin{bmatrix} n_{1}& n_{2}& n_{3}& n_{4} \end{bmatrix}\textbf{x}(t). \, (1391ms)
✔ V_Z ... \begin{matrix} {13 \choose 1}{12 \choose 2} \end{matrix} (1405ms)
✔ D_{i_1, ... i_m} ... \scriptstyle \hat z' \;=\; R_{\beta'} \hat z R_{\beta'}^\dagger (1396ms)
✔ x(yz) = (xy)z. ... \zeta(\bar{a},b)+\zeta(b,\bar{a})=\zeta(b)\phi(a)-\phi(a+b) (1307ms)
✔ \mathbf{H} = \sum_k \sum_{s = 1}^3 \hbar \, \omega_{k,s}
\left( b_{k,s}^{\dagger}b_{k,s} + 1/2 \right). ... \chi_i(t) = \frac{\langle \mathbf{e}_i'(t), \mathbf{e}_{i+1}(t) \rangle}{\| \mathbf{\gamma}^'(t) \|} (1258ms)
✔ \ \begin{array}{rrcl} & \sigma^* &=& h(b^*) \\
\Rightarrow & Q \sigma Q^T &=& h(F^*(F^*)^T) \\
\Rightarrow & Q h(b) Q^T &=& h(QFF^TQ^T) \\
\Rightarrow & Q h(b) Q^T &=& h(QbQ^T). \end{array} ... \mathbb{R}^d. (1378ms)
✔ \operatorname{Ass}_R(M) ... F[t_1, t_2, \dots, t_n] (1313ms)
✔ \textstyle a a = a \, , \quad b b = 0 \, , \quad a b = b a = 0 ... \frac{\Delta G^\ominus}{T} = -R \ln K (1392ms)
✔ r_n = a ... \mathbf{S}_{1i} (1239ms)
✔ \frac{1}{1-2^{k+1}}\sum_{i=0}^k \frac{1}{2^{i+1}} \sum_{j=0}^i {i \choose j} (-1)^j (j+1)^k ... \Delta S = n R \ln \frac{V}{V_0} = - n R \ln \frac{P}{P_0} . (1236ms)
✔ \sum_{(x,y) \in C^2, x\neq y} d(x,y) ... i=1,2,3\ldots,N (1255ms)
✔ x \to (y \to (x \and y)) = 1 , ... I_{\pm} (1216ms)
✔ \theta = \arctan \left( \frac{\text{opposite side}}{\text{adjacent side}} \right) ... d_{\bar k} (1243ms)
✔ \operatorname{E}(w_i\,\Delta z_i) = \operatorname{E}(w_i z'_i) - \operatorname{E}(w_i z_i) ... S(r) = kdr^{d-1}. (1408ms)
✔
\begin{align}
\omega^1 & = \cos\theta \, \mathrm{d}s,\quad \omega^2 = -\sin\theta \, \mathrm{d}s\\
\omega_i^j & = -\omega_j^i\\
\omega_1^2 & = \kappa_g \, \mathrm{d}s + \mathrm{d}\theta\\
\omega_1^3 & = (\kappa_n\cos\theta + \tau_r\sin\theta) \, \mathrm{d}s\\
\omega_2^3 & = -(\kappa_n\sin\theta + \tau_r\cos\theta) \, \mathrm{d}s
\end{align}
... x-y (1387ms)
✔ \alpha = v_d/v_p ...
{\rm Pr}\Big(\hat{f}(x)-w(x) \le f(x) \le \hat{f}(x)+w(x) \;\;\;\; \text{ for all } x\Big) = 1-\alpha.
(1203ms)
✔ C_{PL} ... f_{in} =
43994140.625Hz (1238ms)
✔
\boldsymbol{\sigma} = \cfrac{2}{J}\left[\cfrac{1}{J^{2/3}}\left(C_1 + \bar{I}_1~C_2\right)\boldsymbol{B} -
\cfrac{1}{J^{4/3}}~C_2~\boldsymbol{B} \cdot\boldsymbol{B} \right] + \left[2D_1(J-1)-
\cfrac{2}{3J}\left(C_1\bar{I}_1 + 2C_2\bar{I}_2~\right)\right]\boldsymbol{\mathit{1}}
... m\ddot{x} + c\dot{x} + kx = F(t) (1287ms)
✔ p(\eta|y)\; ... i\hbar\partial_t\psi=-\mu\vec{\sigma}\cdot\vec{B}\psi (1270ms)
✔ \mathrm{succ}(u,v)=\begin{cases}
\mathrm{next}(v,u) & \mathrm{next}(v,u)\neq \mathrm{nil} \\
\mathrm{first}(v)&\text{otherwise}.
\end{cases}
... X_1=0 (1195ms)
✔ \alpha = \arccos \left( \frac{A\cos \beta-V}{W} \right) = \arccos \left( \frac{A\cos \beta-V}{\sqrt{A^2 + V^2 -2AV\cos{\beta}}} \right) ... -2\xi \frac{\mathrm{d} c}{\mathrm{d} \xi} = \frac{\mathrm{d}}{\mathrm{d} \xi} \left[ D(c) \frac{\mathrm{d} c}{\mathrm{d} \xi} \right] (1349ms)
✔ \boldsymbol\omega_p = \frac{(\boldsymbol I_s - \boldsymbol I_p) \boldsymbol\omega_s} {\boldsymbol I_p} ... \pi_1 \pi_2 \ldots (1257ms)
✔ p_n(x(x+\gamma+\delta+1)) = {}_4F_3\left[\begin{matrix} -n &n+\alpha+\beta+1&-x&x+\gamma+\delta+1\\
\alpha+1&\gamma+1&\beta+\delta+1\\ \end{matrix};1\right]. ...
\begin{align}
\mathbf{u}_1 &= \mathbf{a}_1,
& \mathbf{e}_1 &= {\mathbf{u}_1 \over \|\mathbf{u}_1\|} \\
\mathbf{u}_2 &= \mathbf{a}_2-\mathrm{proj}_{\mathbf{e}_1}\,\mathbf{a}_2,
& \mathbf{e}_2 &= {\mathbf{u}_2 \over \|\mathbf{u}_2\|} \\
\mathbf{u}_3 &= \mathbf{a}_3-\mathrm{proj}_{\mathbf{e}_1}\,\mathbf{a}_3-\mathrm{proj}_{\mathbf{e}_2}\,\mathbf{a}_3,
& \mathbf{e}_3 &= {\mathbf{u}_3 \over \|\mathbf{u}_3\|} \\
& \vdots &&\vdots \\
\mathbf{u}_k &= \mathbf{a}_k-\sum_{j=1}^{k-1}\mathrm{proj}_{\mathbf{e}_j}\,\mathbf{a}_k,
&\mathbf{e}_k &= {\mathbf{u}_k\over\|\mathbf{u}_k\|}
\end{align}
(1286ms)
✔ \mathbb{F}_q = \left\{ 0,1, \gamma, \gamma^2, \ldots ,\gamma^{n-1}\right\} ... \gamma'p (1375ms)
✔ \scriptstyle \frac{\partial M}{\partial x} = \,0 ... \xi\in (-\infty,+\infty) \, (1355ms)
✔ S_i=-n_tR[x\ln x+(1-x)\ln(1-x)]. ... k2^{n+1}+1 (1249ms)
✔ T>0 ... (a+b)^n (1353ms)
✔ (u,v) ... B=(a,0) (1224ms)
✔ oid(O_{j}) ... \int e^{-(x^2+y^2)}\,d(x,y), (1226ms)
✔ \psi_{1,m} ... ''3x^3+4=28'' (1362ms)
✔ v(n)=0 ... U(t) (1255ms)
✔ Powe{{r}_{cpu}}={{\propto }_{1}}\left( IFetc{{h}_{miss}} \right)+{{\propto }_{2}}\left( DataDep \right)+{{\propto }_{3}}\left( DataTL{{B}_{miss}} \right)+{{\propto }_{4}}\left( InsTL{{B}_{miss}} \right)+{{\propto }_{5}}\left( InstExec \right)+{{K}_{cpu}} ... a_{1,2,\ldots,n}x_1x_2\ldots x_n \! (1216ms)
✔ y=3x ... y \ll h (1285ms)
✔ \ A {cos(\phi)}^n ... C_{\alpha \beta} =\begin{bmatrix}
K+4 \mu\ /3 & K-2 \mu\ /3 & K-2 \mu\ /3 & 0 & 0 & 0 \\
K-2 \mu\ /3 & K+4 \mu\ /3 & K-2 \mu\ /3 & 0 & 0 & 0 \\
K-2 \mu\ /3 & K-2 \mu\ /3 & K+4 \mu\ /3 & 0 & 0 & 0 \\
0 & 0 & 0 & \mu\ & 0 & 0 \\
0 & 0 & 0 & 0 & \mu\ & 0 \\
0 & 0 & 0 & 0 & 0 & \mu\
\end{bmatrix}.
\,\! (1397ms)
✔ S^3 = \left\{q\in\mathbb{H} : ||q|| = 1\right\}. ... \scriptstyle{ TS = T \circ S} (1324ms)
✔ r = r^{*} ... \psi(0) = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 \\ 1 \end{pmatrix} (1273ms)
✔ A + \operatorname{core}B \subset \operatorname{core}(A + B) ... \left(-\log(t)\right)^\theta (1254ms)
✔
\begin{align}
a + \infty = +\infty + a & = +\infty, & a & \neq -\infty \\
a - \infty = -\infty + a & = -\infty, & a & \neq +\infty \\
a \cdot (\pm\infty) = \pm\infty \cdot a & = \pm\infty, & a & \in (0, +\infty] \\
a \cdot (\pm\infty) = \pm\infty \cdot a & = \mp\infty, & a & \in [-\infty, 0) \\
\frac{a}{\pm\infty} & = 0, & a & \in \mathbb{R} \\
\frac{\pm\infty}{a} & = \pm\infty, & a & \in (0, +\infty) \\
\frac{\pm\infty}{a} & = \mp\infty, & a & \in (-\infty, 0)
\end{align}
... C_n < \operatorname{SO}(3) (1325ms)
✔ I'[u_k]\rightarrow 0 ... \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega \! (1317ms)
✔
P(J_{i_1\cdots i_r}) = \sqrt{\dfrac{N^{r-1}}{J^2 \pi r!}} \exp\left\{-\dfrac{N^{r-1}}{J^2 r!}\left(J_{i_1\cdots i_r} - \dfrac{J_0 r!}{2N^{r-1}}\right)\right\}
... \mbox{eGFR} = \mbox{186}\ \times \ \mbox{Serum Creatinine}^{-1.154} \ \times \ \mbox{Age}^{-0.203} \ \times \ {[1.210\ if\ Black]} \ \times \ {[0.742\ if\ Female]} (1388ms)
✔ \phi \land \chi \to \phi ... \scriptstyle{RR} (1385ms)
✔ \Delta V = \sqrt{ V_{t,a}^{2} + V_{GEO}^{2} - 2 V_{t,a} V_{GEO} \cos \Delta i} ... F_j=f(\alpha^j)=\sum_{i=0}^lL_i(\alpha^{jk_i}) (1638ms)
✔ z\rightarrow -z^5 + z_0 ... \nabla_\mu \psi = (\partial_\mu - {i \over 4} \omega_\mu^{IJ} \sigma_{IJ}) \psi (1428ms)
✔ X = \{x_1, x_2,..., x_p\} ... \frac{1}{2} + \sgn(x-\mu)\frac{\gamma\left[1/\beta, \left( \frac{|x-\mu|}{\alpha} \right)^\beta\right]}{2\Gamma(1/\beta)} (1442ms)
✔ f(x+1)=xf(x) \text{ for } x>0, \, ... f'={\frac{1}{1- {\frac{2M}{r}}}}\sqrt{\frac{2M}{r}} (1255ms)
✔ h(x)=[0;a_2,a_3,\dots].\, ... c_{i\,j\,k\,\ell} (1435ms)
✔ u'(t) = \Delta_Du(t) ... \rho( \bold T ) < 1 (1655ms)
✔ A(C;x,y) = \sum_{i=0}^n A_i x^i y^{n-i} ... \mathfrak C (1415ms)
✔ - \left\lfloor \frac{m}{2} \right\rfloor \le r < m-\left\lfloor \frac{m}{2} \right\rfloor ... P(\alpha_i,\beta_i) (1404ms)
✔ \Omega BQC \simeq B(S^{-1} S) ... \mathbb{S}^c(x) = c - \sum_{i=1}^n x_i \cdot \log(x_i) (1281ms)
✔ x^9 + x^4 + x^2 ... \mathcal P:= \overline{K}^2,\qquad
\mathcal Z:= \{\{(a_1,b_1),(a_2,b_2),(a_3,b_3)\} \ | \ \{a_1,a_2,a_3\}=\{b_1,b_2,b_3\}=\overline{K}\} (1382ms)
✔ \delta_{\sigma \sigma'} ...
Z' = \int D \mathbf{R} \exp \left[ - \beta U_0 (\mathbf{R}) \right] \qquad (7)
(1368ms)
✔ \ln(x) = -\lim_{\epsilon \to 0} \int_\epsilon^\infty \frac{dt}{t}\left( e^{-xt} - e^{-t} \right) ... C= B \log_2(1+\mathrm{SINR}) (1292ms)
✔ \Delta \rho ... \frac{f'(x)}{f(x)} = h'(x) \ln(g(x)) + h(x)\frac{g'(x)}{g(x)} (1359ms)
✔ x =\left(\begin{matrix}\frac{a+b}{2}\end{matrix}\right)\cos(\omega t) + \left(\begin{matrix}\frac{a-b}{2}\end{matrix}\right)\cos(\omega t) ... F_e(\phi_E + \phi_P)/2 + F_w(\phi_W + \phi_P)/2 = D_e(\phi_E - \phi_P) + D_w(\phi_P - \phi_W) (1336ms)
✔ 10^{pH_i} ... x_e (1289ms)
✔ [-1,1]\times [-1,1] ... X_{\text{poly}}=\frac{m_{\text{Pol}}}{\sum_i\int_0^t\dot{m}_{i,\text{in}}(\tau)d\tau} (1347ms)
✔ \mathbb{E}^g[X \mid \mathcal{F}_t] := Y_t ... Z=0.9152 (1274ms)
✔ W_n, K_n,
N_n, ... f'(x^*)(y-x^*) \geq 0\qquad\forall y \in I (1330ms)
✔ x = b (X - v T) \, ... g(x,y) = x^2+y^5 (1377ms)
✔ B = {\left ( \frac{4}{5} \right )}^{3/2} \frac{\mu_0 n I}{R} ... \frac{ \left\Vert A^{-1} e \right\Vert / \left\Vert A^{-1} b \right\Vert }{ \left\Vert e \right\Vert / \left\Vert b \right\Vert } . (1301ms)
✔ X_k =
\sum_{n=0}^{N-1} x_n \cos \left[\frac{\pi}{N} \left(n+\frac{1}{2}\right) \left(k+\frac{1}{2}\right) \right] \quad \quad k = 0, \dots, N-1. ... R_{ext} (1312ms)
✔ \pi(x)P(x\rightarrow x') = \pi(x')P(x'\rightarrow x) ... \widehat{R}(\Delta\theta,\hat{\mathbf{e}}_z) = I - \frac{i}{\hbar}\Delta\theta \widehat{L}_z (1415ms)
✔
\begin{align}
\overline{X_t} &\leq \sum_{i=1}^{[at]} \mathrm{Geometric}(p) \\
\mathbb{E}\left[\,\overline{X_t}\,\right]^2 &\leq C_1 t + C_2 t^2 \\
P\left(\frac{X_t}{t} > x\right) &\leq \frac{E\left[X_t^2\right]}{t^2x^2} \leq \frac{E\left[\overline{X_t}^2\right]}{t^2x^2} \leq \frac{C}{x^2}.
\end{align}
... \lambda_{100} = \lambda_{111} = \lambda (1479ms)
✔ E_p = \frac{K_1 E_a+K_2 E_b+K_3 E_c}{K_1+K_2+K_3} ... \tfrac{f'_{x}}{f'_{y}}=\tan\alpha' (1255ms)
✔ \begin{Bmatrix} 2 , p \end{Bmatrix} ... 0 \rightarrow H_{2}(X) \rightarrow\, \mathbb{Z}\ \xrightarrow{\alpha} \ \mathbb{Z} \oplus \mathbb{Z} \rightarrow \, H_1(X) \rightarrow 0 \! (1512ms)
✔ R(M,x) = \frac{x' A' A x}{x' x} ... \rho_{\mathrm{bound}} = \nabla\cdot (-\mathbf{P}) (1422ms)
✔ R \subseteq R^{+} ... \mathbf{a}^{\rm T} (1281ms)
✔ \mathrm{Hom}_{\mathbf{X}}(F(-), G(-)) : \mathbf{C}^{op} \times \mathbf{C} \to \mathbf{Set} ... 0 \;\rightarrow\; A\;\rightarrow\; B\;\rightarrow\; C \;\rightarrow\; 0 (1359ms)
✔ \kappa_0(\mathcal B)\,\! ...
\dot{p}_x = -\frac{1}{2}\frac{\partial V}{\partial x}
(1352ms)
✔ H_\text{KL}(k_\text{x},k_\text{y},k_\text{z})=-\frac{\hbar^2}{2m}\left[(\gamma_1+{\textstyle\frac52 \gamma_2}) k^2 -
2\gamma_2(J_\text{x}^2k_\text{x}^2+J_\text{y}^2k_\text{y}^2
+J_\text{z}^2k_\text{z}^2) -2\gamma_3 \sum_{m \ne n}J_mJ_nk_mk_n\right] ... dN_E= \frac{dg_E}{\Phi(E)} (1189ms)
✔ \mathfrak{M} = \frac{u_\mathrm{o}}{(k_\mathrm{B}T_\mathrm{e}/m_\mathrm{i})^{1/2}} ... q_d (1355ms)
✔ O(M) ... S_\mathbf{r} = \bigcup_{j \in T} S_{M_j} (1519ms)
✔ L_1/L_2 ... P'_D (1318ms)
✔ R_{0} < \frac{N}{S(0)} , ... \frac{\partial \rho}{\partial t} + \nabla\cdot\left(\rho\mathbf{v}\right)=\frac{D\rho}{D t} + \rho\nabla\cdot\mathbf{v}= 0, (1498ms)
✔ A_{n}^{x}+B_{n}^{y}=C_{n}^{z}; ... q \in C_{i} (1236ms)
✔ 107 = 53 ... Y_n\ \xrightarrow{L^r}\ Y (1322ms)
✔ \dot{n}_i=\sum_j w_{ij}n_j-n_i\, ... G(r) = {C \over r^{d-2} } (1299ms)
✔
\gamma_n^2B_2^2T_{1n}T_{2n} \geq {1}
... \eta^{\mu \nu} (1248ms)
✔
\dfrac{
\dfrac{
\dfrac{
\dfrac{
\dfrac{the}{NP/N}
\dfrac{dog}{N}
\qquad
}{NP}>
}{S/(S\backslash NP)}T_>
\qquad
\dfrac{bit}{(S\backslash NP)/NP}
}{S/NP}B_>
\qquad
\dfrac{John}{NP}
}{S}>
... p\left( \mathbf{\hat{x}}\right) \propto\exp\left( -\frac{1}{2}(\mathbf{\hat{x}}-\mathbf{\hat{\mu}})^{\mathrm{T}}\hat{Q}^{-1}(\mathbf{\hat{x}}-\mathbf{\hat{\mu}})\right) , (1298ms)
✔ \Psi(x) = \tfrac{1}{2} \kappa |x - m|^2, ...
\begin{align}
\frac{\partial \zeta}{\partial t}
&+ \frac{1}{a \cos( \varphi )} \left[
\frac{\partial}{\partial \lambda} (uD)
+ \frac{\partial}{\partial \varphi} \left(vD \cos( \varphi )\right)
\right]
= 0,
\\[2ex]
\frac{\partial u}{\partial t}
&- v \left( 2 \Omega \sin( \varphi ) \right)
+ \frac{1}{a \cos( \varphi )} \frac{\partial}{\partial \lambda} \left( g \zeta + U \right)
=0
\qquad \text{and} \\[2ex]
\frac{\partial v}{\partial t}
&+ u \left( 2 \Omega \sin( \varphi ) \right)
+ \frac{1}{a} \frac{\partial}{\partial \varphi} \left( g \zeta + U \right)
=0,
\end{align}
(1325ms)
✔ P_0 = ( x_0, y_0 ) ...
(\ddot{q}_d-\frac{u-K_0q-K_1q^3-b\dot{q}}{m(1+q^2)}+\alpha \dot{e}) = -\frac{\kappa}{2}(\dot{e}+\alpha e)
(1311ms)
✔ S=\frac{2\pi R}{n}\sqrt{E_c(2E-E_c)}, ... F_{\alpha \beta} = \partial_{\alpha} A_{\beta} - \partial_{\beta} A_{\gamma} \, (1370ms)
✔ {t_{far}} - {t_{near}} ... (a_i)_{i\in I} (1369ms)
✔ \left(r,\theta,\zeta\right) ... M = \sum_{i=1}^j\ f_i - 6 (1381ms)
✔ \frac{2(\boldsymbol\Sigma \otimes \boldsymbol\Omega)}{\beta(2\alpha-n-1)} ... E_\gamma + E_e = E_{\gamma'} + E_{e'}.\! (1367ms)
✔ 0 = (\mathbf{\bar y}')^{T} \, ((\mathbf{T}')^{T})^{-1} \, \mathbf{F} \, \mathbf{T}^{-1}\, \mathbf{\bar y} = (\mathbf{\bar y}')^{T} \, \mathbf{\bar F} \, \mathbf{\bar y} ... Q = xi + yj + zk\, (1376ms)
✔ \varphi(p^k) = p^k -p^{k-1} =p^{k-1}(p-1) = p^k \left( 1 - \frac{1}{p} \right). ... x_n = \sqrt {S} \cdot (1 + \varepsilon_n). (1310ms)
✔ \frac{4}{3}m^{3} ... F(e^\lambda g) = F(g) - d\lambda (1471ms)
✔ \begin{pmatrix}0&0&\cdots&0&-a_0\\1&0&\cdots&0&-a_1\\0&1&\cdots&0&-a_2\\\vdots&\vdots&\ddots&\vdots&\vdots\\0&0&\cdots&1&-a_{n-1}\end{pmatrix}. ... 145 = 1! + 4! + 5! (1368ms)
✔ 0 = \frac{1}{2\pi i}\oint_{\partial K} {F'(z) \over F(z)}\,dz = N_F(K)-P_F(K) ... /x (1531ms)
✔ x_{m+1}(z) = x_{m-1}(z) + a_m\cdot((2\cdot m+1)\cdot z + (2\cdot m-1)\cdot z^{-1}) \cdot z^{(-1)^m} \cdot x_{m}(z) ... f:Y \to \prod_{i \in I} X_i \mathrm{ , } \quad f(y) := (f_i(y))_{i \in I} (1632ms)
✔ y = c t^k + \cdots ... [3.25] = 3 (1520ms)
✔ F'(R,Q:AL < P < AU)=\sum_{T\!A=1}^{U\!A=\infty}
\frac{F'(R,Q:P_{(ta)})}{U\!A};\,\! ... G(s)= \exp \left [\lambda \frac {\alpha-1}{\alpha} \left( \frac{\theta} {\alpha-1} \right)^\alpha \left\{ \left(1- \frac{1} {\theta}+ \frac {s} {\theta}\right)^\alpha-1 \right\}\right] (1614ms)
✔ \begin{pmatrix}0 & -1 \\ 1 & a\\\end{pmatrix} ... P_s\; (1304ms)
✔ \gamma_n=1 ... \mathrm{error}\bigl(x(t_0 + 5\Delta t)\bigl) = 15\,O(\Delta t^4) (1245ms)
✔ R(z;A)= (A-zI)^{-1}. ... \gamma \frac{n}{2} (1286ms)
✔ 6) \ x=-1\pm\sqrt{3} ...
D(p||q)=\psi(p)+\phi(q)-\theta^i(p)\eta_i(q)
(1273ms)
✔ i\frac{\partial f}{\partial x}(z_0)=\frac{\partial f}{\partial y}(z_0), ...
e_I^{[\alpha} e^{\beta]}_K C_{\beta J}^{\;\;\;\; K} + e^{K [\beta} e^{\alpha]}_J C_{\beta KI} = 0
(1310ms)
✔
\left. \left[ -2k_{c}\frac{\partial H}{\partial\mathbf{e}_2}+\gamma k_n+\bar{k}\frac{d\tau_g}{ds}\right]\right\vert _{C}=0
... f: A \to B (1296ms)
✔ X(t)= V_0 * t + A*t^2\, ... {\rm ATIME}(t(n)) (1403ms)
✔ \frac{d U_\text{eff}}{dr} = 0 ... HU = 1000\times\frac{\mu_X - \mu_{water}}{\mu_{water}} (1255ms)
✔ \sum_{m=0}^n P(3m+2)=P(3n+4)-1 ... \{ f_\theta (x)\}_{\theta\in \Theta} (1247ms)
✔ z_1(x,y)=F(y-\frac{1}{2}x^2) ... P \cup \Delta (1248ms)
✔
f(\boldsymbol{x}) = f(T_{\theta}\boldsymbol{x}), \quad \forall \boldsymbol{x}, \theta . ... 0.2 \times std (1203ms)
✔ \Delta_x \gamma(z,x)=0 ... r^2 = x^2+y^2 (1240ms)
✔ d_p \rightarrow \infty ... \,c_{pd} (1283ms)
✔ \textstyle{M=log_2(R/G)=log_2(R)-log_2(G)} ... \scriptstyle{r_1 > r_0} (1203ms)
✔ v = \frac{L^2}{8r} ... H = H\left(q_1,\cdots,q_N;\frac{\partial S}{\partial q_1},\cdots,\frac{\partial S}{\partial q_N};t\right)\,\! (1207ms)
✔ \alpha\!+\!\ln(\beta\Gamma(\alpha))\!-\!(1\!+\!\alpha)\Psi(\alpha) ... X_{t-1} = \lbrace x_{t-1}^{[1]}, x_{t-1}^{[2]}, \ldots, x_{t-1}^{[M]} \rbrace (1262ms)
✔ \boldsymbol{\mu}_d ... \frac{y_2}{y_1}=\frac{1}{2}\left(\sqrt{1+8 F r_1^2} - 1\right) (1296ms)
✔ \overline{\Gamma}_{\alpha \beta}^\gamma ... S(P) = P - \alpha(P-1) \qquad = \alpha + P(1-\alpha). \, (1471ms)
✔ A = \sum_\lambda \lambda \operatorname{E}_A(\lambda) ... \phi ( I ) = I. \, (1228ms)
✔ \textbf{A}_P = \frac{d}{dt}(R\dot{\theta}\textbf{e}_t) = - R\dot{\theta}^2\textbf{e}_r + R\ddot{\theta}\textbf{e}_t. ... \sup_{x\in\mathbb R}\left|F_n(x) - \Phi(x)\right| \le C_0\cdot\psi_0, \ \ \ \ (3) (1289ms)
✔ Q(x,p(x)) ... \Phi : L(H_A) \rightarrow L(H_B) (1229ms)
✔ WF_A(Pf) \subseteq WF_A(f) ... {1\over 970864271032320000} + {1\over 685597979049984000} = {691\over 277667181515243520000 }. (1299ms)
✔ \frac{1}{A} d_2(f(x),f(y))-B\leq d_1(x,y)\leq A d_2(f(x),f(y))+B \text{ for all } x,y\in M_1 ... 2+\phi=3.618 (1247ms)
✔ \frac{x}{y}=a ... \{p,\ \bot\rightarrow \bot,\ p \land \neg\bot \rightarrow s\}. (1314ms)
✔ = \operatorname{E}_X\left[\operatorname{E}[Y^2\mid X]\right] - \operatorname[{E}_X\left[\operatorname{E}[Y\mid X]\right]]^2 ... k = k_1 N_2^{-1} N_2 + k_2 N_1^{-1} N_1 \mod N, (1407ms)
✔ \frac{a_{n+1}}{a_n} \le \frac{b_{n+1}}{b_n} ... f(x)=1+x^{32}+x^{47}+x^{58}+x^{90}+x^{121}+x^{128} (1233ms)
✔ \left|\mathbf{x}\right|^2 = x_1^2 - x^2_2 + x_3^2 ... K_B = k_B G (1271ms)
✔ g_i + g_j = g_{i+j} ... |\mathbf{F}_\mathrm{c}| = m |\mathbf{a}_\mathrm{c}| = \frac{m|\mathbf{v}|^2}{r} \ . (1312ms)
✔ a=\begin{bmatrix}-1\\ 1 \\ 1\end{bmatrix}. ... p(t) = \det(t\delta_{ij}-a_{ij}). (1258ms)
✔ \sqrt{x^2 + bn} ... Z_2 = \sqrt{-2 \ln(U_1)} \sin(2 \pi U_2) (1294ms)
✔
H(\mathbf{Y})=-\frac{1}{N}\sum_{t=1}^N \ln\frac{p_\mathbf{x}(\mathbf{x}^t)}{|\mathbf{W}|p_\mathbf{s}(\mathbf{y}^t)}
... \begin{bmatrix}
c_3 c_2 c_1 - s_3 s_1 & - c_3 s_2 & c_2 c_3 s_1 + c_1 s_3 \\
c_1 s_2 & c_2 & s_1 s_2 \\
-c_3 s_1 - c_1 c_2 s_3 & s_2 s_3 & c_3 c_1 - c_2 s_3 s_1
\end{bmatrix} (1261ms)
✔ f(z) = (z - z_0)e^{g(z)} ... \tfrac{\lambda(1-\nu)}{\nu} (1256ms)
✔ (a_1 b_2 + a_2 b_1 + a_3 b_4 - a_4 b_3)^2 +\, ... \mu_r = 1 + 2.5 \cdot \phi (1390ms)
✔ x_N[n]\ \stackrel{\text{def}}{=} \sum_{m=-\infty}^{\infty} x[n-mN]. ... \log |f(z)| (1383ms)
✔ T dS= (n+1)P dV + n V dP\, ... 0 \not\in \operatorname{core}(\operatorname{core}(A)) (1295ms)
✔ \sum_{n=0}^\infty (-1)^n {n+p\choose n} a_n = \sum_{n=0}^\infty (-1)^n
{n+p\choose n}\frac {\Delta^n a_0} {2^{n+p+1}} ... \mathbb E( e^{-\theta F} )= \frac{1}{2 \lambda}(\lambda + \mu + \theta - \sqrt{(\lambda + \mu + \theta)^2 - 4 \lambda \mu}) (1269ms)
✔
\lim_{t\rightarrow\infty} \frac{Q_n^{(c)}(t)}{t} = 0 \text{ with probability 1}
... C_{\beta KI} = - C_{\beta IK} (1110ms)
✔ (\overline{y}_{11} - \overline{y}_{12}) - (\overline{y}_{21} - \overline{y}_{22}) ... \Psi \equiv \Phi' \equiv \Phi \wedge \Phi \rightarrow \phi (1566ms)
✔ v_c ... \,\{e+ig\} = e^{i\theta}\{e+ig\} (1452ms)
✔ \epsilon >0 ... \int_{0}^{\infty}\delta (t-a)e^{-st} \, dt=e^{-sa}. (1391ms)
✔ A_{t+1}=R_{t+1}(A_{t}+y_{t}-c_{t}) ... \int \langle x, (O-\lambda I)y \rangle \langle y, \psi \rangle dy = h(x). (1343ms)
✔ F(x) = (x^m)(10^b), ... \rho_{max} (1209ms)
✔ N = (a_1\cdot100 +a_2\cdot10+a_3)^2 ... \begin{matrix} \frac{1}{2} \end{matrix} (z+1) (1200ms)
✔ {a \over b} ... \gamma_y(t)=i\,y+w\,t (1356ms)
✔ \mathcal{L}_X f ... x \leftarrow x + l (1239ms)
✔ \{s_1,\ldots,s_k\} ... \mathbf{v}= \left( \frac{-y}{x^2+y^2}, \frac{x}{x^2+y^2}, 0 \right). (1370ms)
✔ a_1, a_2, a_3, \ldots ... \int\frac{\cos^2 ax\;\mathrm{d}x}{\sin ax} = \frac{1}{a}\left(\cos ax+\ln\left|\tan\frac{ax}{2}\right|\right) +C (1176ms)
✔ \,\phi(A) ...
H(P, Q) = \frac{1}{\sqrt{2}} \; \|\sqrt{P} - \sqrt{Q} \|_2 .
(1299ms)
✔ {} = 1 \cdot (-3) - 2 \cdot (-6) + 3 \cdot (-3) = 0. ... (\Phi(0) \land \forall i (\Phi(i) \to \Phi(i+1))) \to \forall i \Phi(i)\,\! (1285ms)
✔ Q_p \psi = -i\hbar \partial_x \psi ... \hat{\mathbf{x}}_{i+1}=A_i\hat{\mathbf{x}}_i+B_i{\mathbf{u}}_i+K_i \left({\mathbf{y}}_i-C_i{\hat{\mathbf{x}}}_i \right), \hat{\mathbf{x}}_0=E({\mathbf{x}}_0) (1323ms)
✔ 1 + 2 \times 3 = 9, \; ... 7+ 58+ 39+ 23+ 10+ 55+ 42+ 26 = 260 (1224ms)
✔ R(x,y) ... \left[\frac{F}{m}\right] (1289ms)
✔ n = 0, 1, 2, 3 ... \mathbf x = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix} (1213ms)
✔ 2.0000 ... y_i = y_j (1390ms)
✔ v_i=\exp \left( \frac {R_0-R_i} {b} \right) ... \mathbf{r}=0 (1324ms)
✔ \int_{\Delta V} \frac{d}{dx}\left (\Gamma \frac{d \phi}{dx}\right ) dV + \int_{\Delta V} S dV = \left (\Gamma A \frac{d \phi}{dx}\right )_e - \left (\Gamma A \frac{d \phi}{dx}\right )_w + \overrightarrow{S} \Delta V= 0 ... -0.980\pm0.053 (1375ms)
✔ \sqrt[x]{a}\, ... \ c_L = c_{L_0} + 2\pi\alpha (1386ms)
✔ x_\mathrm{a}(t) = e^{-j \omega_0 t} + j^2\cdot e^{-j \omega_0 t} = 0\, ... wp(\alpha,\psi) (1314ms)
✔ \widehat s(t) ... (xp_r,p_s)=(p_r,xp_s)=0 (1244ms)
✔ R = k[x_1, \ldots, x_n] ... z=ix (272ms)
Feedback
✔ should give adequate feedback ""
✔ should give adequate feedback "{\\cos(x).}"
✔ should give adequate feedback "{\\cos\\left(x.\\right)}"
✔ should give adequate feedback "\\mathbb{x}"
✔ should give adequate feedback "a+\\badfunc-b"
✔ should give adequate feedback "\\sin\\left(x)"
✔ should give adequate feedback "\\ce{H2O}"
✔ should give adequate feedback "\\ce{H2O}"
✔ should give adequate feedback "\\ce {\\log}"
Gold Identifiers
✔ in qID1 should be discovered "W(2, k) > 2^k/k^\\varepsilon"
✔ in qID2 should be discovered "(X,\\Sigma)"
✔ in qID3 should be discovered "(p-1)!^n"
✔ in qID4 should be discovered "f_c(z) = z^2 + c"
✔ in qID5 should be discovered "\\forall x \\, \\forall y \\, P(x,y) \\Leftrightarrow \\forall y \\, \\forall x \\, P(x,y)"
✔ in qID6 should be discovered "\\alpha(x)"
✔ in qID7 should be discovered "\\alpha(x)"
✔ in qID8 should be discovered "\\alpha(x)"
✔ in qID9 should be discovered "|{\\Psi}\\rangle=\\sum_{i_1,i_2,\\alpha_1,\\alpha_2}\\Gamma^{[1]i_1}_{\\alpha_1}\\lambda^{[1]}_{\\alpha_1}\\Gamma^{[2]i_2}_{\\alpha_1\\alpha_2}\\lambda^{[2]}_{{\\alpha}_2}|{i_1i_2}\\rangle|{\\Phi^{[3..N]}_{\\alpha_2}}\\rangle"
✔ in qID10 should be discovered "z*x\\le y"
✔ in qID11 should be discovered " \\frac{d}{dx}\\left( \\log_c x\\right) = {1 \\over x \\ln c} , \\qquad c > 0, c \\ne 1"
✔ in qID12 should be discovered "\\theta = n \\times 137.508^\\circ,"
✔ in qID13 should be discovered "s_V(\\mathcal{R})"
✔ in qID14 should be discovered "\\ell(m)"
✔ in qID15 should be discovered "bx-x^2"
✔ in qID16 should be discovered "\\omega_{k}"
✔ in qID17 should be discovered "\\mathbf{m}_1"
✔ in qID18 should be discovered "r_{ij}"
✔ in qID19 should be discovered " Z = \\sum_{j} g_j \\cdot \\mathrm{e}^{- \\beta E_j}"
✔ in qID20 should be discovered "S'"
✔ in qID21 should be discovered "S'"
✔ in qID22 should be discovered "\\text{Ker} (k_* - l_*) \\cong \\text{Im} (i_*, j_*)."
✔ in qID23 should be discovered "D(G,H) = \\sum_{i=1}^{29} | F_i(G) - F_i(H) |"
✔ in qID24 should be discovered " E_\\text{k} = E_t + E_\\text{r} \\, "
✔ in qID25 should be discovered "\\lambda(L(B)) \\leq d"
✔ in qID26 should be discovered "L\\left(C\\right) \\leq L\\left(T\\right)"
✔ in qID27 should be discovered "v = \\frac{c}{n}"
✔ in qID28 should be discovered "\\sigma_y^2(\\tau) = \\frac{2\\pi^2\\tau}{3}h_{-2}"
✔ in qID29 should be discovered " R_{s\\ normal} = \\sqrt{ \\frac{\\omega \\mu_0} {2 \\sigma} }"
✔ in qID30 should be discovered " \\phi_1 = -30^\\circ...+30^\\circ"
✔ in qID31 should be discovered "T_c"
✔ in qID32 should be discovered "T_c"
✔ in qID33 should be discovered "T_c"
✔ in qID34 should be discovered "P_1(X)=P(X)/(X-\\alpha_1)"
✔ in qID35 should be discovered "= \\frac{k}{n}."
✔ in qID36 should be discovered "n = \\prod_{i=1}^r p_i^{a_i}"
✔ in qID37 should be discovered "H(j \\omega) = \\mathcal{F}\\{h(t)\\}"
✔ in qID38 should be discovered "\\pi/4"
✔ in qID39 should be discovered "(x+y)^n = \\sum_{k=0}^n {n \\choose k}x^{n-k}y^k = \\sum_{k=0}^n {n \\choose k}x^{k}y^{n-k}.\n"
✔ in qID40 should be discovered "\\ [A]_t = -kt + [A]_0"
✔ in qID41 should be discovered "q^{42}"
✔ in qID42 should be discovered "\\alpha(d) \\le \\left(\\sqrt{3/2} + \\varepsilon\\right)^d"
✔ in qID43 should be discovered " f^{\\mu} = - 8\\pi { G \\over { 3 c^4 } } \\left ( {A \\over 2} T_{\\alpha \\beta} + {B \\over 2} T \\eta_{\\alpha \\beta} \\right ) \\left ( \\delta^{\\mu}_{\\nu} + u^{\\mu} u_{\\nu} \\right ) u^{\\alpha} x^{\\nu} u^{\\beta} "
✔ in qID44 should be discovered " \\frac{D_g u_g}{Dt} - f_{0}v_a - \\beta y v_g = 0 "
✔ in qID45 should be discovered "I_c"
✔ in qID46 should be discovered "\\, A \\mapsto M\\alpha(A)M^{-1} ,"
✔ in qID47 should be discovered "\\Gamma_{\\infty}"
✔ in qID48 should be discovered "Y = \\beta T_8 + I X"
✔ in qID49 should be discovered " \\mu (A)= \\begin{cases} 1 & \\mbox{ if } 0 \\in A \\\\ \n 0 & \\mbox{ if } 0 \\notin A.\n\\end{cases}"
✔ in qID50 should be discovered "\\lambda_{in}"
✔ in qID51 should be discovered "rpm_{motor}"
✔ in qID52 should be discovered "\\underbrace{u_1(\\mathbf{x},z_1)=v_1+\\dot{u}_x}_{\\text{By definition of }v_1}=\\overbrace{-\\frac{\\partial V_x}{\\partial \\mathbf{x}}g_x(\\mathbf{x})-k_1(\\underbrace{z_1-u_x(\\mathbf{x})}_{e_1})}^{v_1} \\, + \\, \\overbrace{\\frac{\\partial u_x}{\\partial \\mathbf{x}}(\\underbrace{f_x(\\mathbf{x})+g_x(\\mathbf{x})z_1}_{\\dot{\\mathbf{x}} \\text{ (i.e., } \\frac{\\operatorname{d}\\mathbf{x}}{\\operatorname{d}t} \\text{)}})}^{\\dot{u}_x \\text{ (i.e., } \\frac{ \\operatorname{d}u_x }{\\operatorname{d}t} \\text{)}}"
✔ in qID53 should be discovered "E \\left[ \\hat{\\sigma}^2\\right]= \\frac{n-1}{n} \\sigma^2"
✔ in qID54 should be discovered "\\mathsf{fv}"
✔ in qID55 should be discovered "\\sum_x \\sum_y I(x,y) \\,\\!"
✔ in qID56 should be discovered "\\boldsymbol{F}_r"
✔ in qID57 should be discovered "0\\rightarrow B\\rightarrow A\\oplus B\\rightarrow A\\rightarrow0."
✔ in qID58 should be discovered "(\\nabla_Y T)(\\alpha_1, \\alpha_2, \\ldots, X_1, X_2, \\ldots) =Y(T(\\alpha_1,\\alpha_2,\\ldots,X_1,X_2,\\ldots))"
✔ in qID59 should be discovered " \\sum_{n \\in \\mathbb{Z}^d} |\\psi(t,n)|^2 |n| \\leq C "
✔ in qID60 should be discovered " p = {\\frac{-x\\pm\\sqrt{x^2-4(\\frac{-gx^2}{2v^2})(\\frac{-gx^2}{2v^2}-y)}}{2(\\frac{-gx^2}{2v^2}) }}"
✔ in qID61 should be discovered "\\left\\{ z \\in H: \\left| z \\right| > 1,\\, \\left| \\,\\mbox{Re}(z) \\,\\right| < \\frac{1}{2} \\right\\}"
✔ in qID62 should be discovered "T-\\lambda I"
✔ in qID63 should be discovered "\n y\\left( x \\right) = {\\mathop{\\rm sgn}} \\left( {{\\rho }} \\right)\\frac{{{\\sigma _y}}}{{{\\sigma _x}}}\\left( {x - {\\mu _x}} \\right) + {\\mu _y}.\n "
✔ in qID64 should be discovered "x=b \\ "
✔ in qID65 should be discovered "H^1(K)=\\sqrt{2}"
✔ in qID66 should be discovered "P_i = \\mbox{head}(E_K (S_{i-1}), x) \\oplus C_i"
✔ in qID67 should be discovered "\\frac{ \\partial f}{ \\partial x} = f_x = \\partial_x f."
✔ in qID68 should be discovered " P_x = P - \\{ a\\mid a \\geq x\\} "
✔ in qID69 should be discovered "\\eta = \\frac{ work\\ done } {heat\\ absorbed} = \\frac{ Q1-Q2 }{ Q1}"
✔ in qID70 should be discovered "df = {\\partial f \\over \\partial x}dx + {\\partial f \\over \\partial y}dy = pdx + vdy"
✔ in qID71 should be discovered "h_{r,s}"
✔ in qID72 should be discovered " K^M_*(k) := T^*(k^\\times)/(a\\otimes (1-a)) "
✔ in qID73 should be discovered "\\{C : K_X \\cdot C = 0\\}"
✔ in qID74 should be discovered "\\Theta \\wedge\n(d\\Theta)^n \\neq 0"
✔ in qID75 should be discovered "D\\left(\\rho u_i\\right)/Dt\\approx0"
✔ in qID76 should be discovered " z_{t} = \\lambda_{1}z_{t-1} + \\varepsilon_{t} "
✔ in qID77 should be discovered "b_3"
✔ in qID78 should be discovered "b_3"
✔ in qID79 should be discovered " \\Delta W = \\int_{V_1}^{V_2} p \\mathrm{d}V \\,\\!"
✔ in qID80 should be discovered "\\dim f(Z) > n"
✔ in qID81 should be discovered "\\frac{d}{dt} \\log_e t = \\frac{1}{t}."
✔ in qID82 should be discovered "h_i : X \\to \\{-1,+1\\}"
✔ in qID83 should be discovered "2\\le seqs \\le6"
✔ in qID84 should be discovered " F = \\{ (x,y) : x \\in \\mathcal{R}^b,\\, y \\in \\mathcal{R}^n,\\; x=y \\}."
✔ in qID85 should be discovered "X_i(\\omega)=\\omega_i"
✔ in qID86 should be discovered "\n{\\partial{L}\\over \\partial q_i} = {\\mathrm{d} \\over \\mathrm{d}t}{\\partial{L}\\over \\partial{\\dot{q_i}}}.\n"
✔ in qID87 should be discovered "x_7"
✔ in qID88 should be discovered "\\Pi_n"
✔ in qID89 should be discovered "\\sigma^2 = X^TVX,"
✔ in qID90 should be discovered "\\int_{\\mathbb{R}^n}f\\,dx = \\int_0^\\infty\\left\\{\\int_{\\partial B(x_0;r)} f\\,dS\\right\\}\\,dr."
✔ in qID91 should be discovered "\n\\{x, p_x\\}_{DB} = \\{y, p_y\\}_{DB} = \\frac{1}{2}\n"
✔ in qID92 should be discovered "G_{k, \\sigma} (y)= 1-(1+ky/\\sigma)^{-1/k} "
✔ in qID93 should be discovered "L(H_B) \\otimes C(X)"
✔ in qID94 should be discovered "\\pi_i = 2^{-N} \\tbinom Ni"
✔ in qID95 should be discovered "(\\sqrt{p_1}, \\cdots ,\\sqrt{p_n})"
✔ in qID96 should be discovered "\\boldsymbol{s}"
✔ in qID97 should be discovered "\\mathbf{J^TW\\ \\Delta y}"
✔ in qID98 should be discovered "\\bar V^*"
✔ in qID99 should be discovered "\\;\\frac{(n+\\delta-1)(n+\\delta-2)\\cdots n}{(\\delta-1)!}\\;"
✔ in qID100 should be discovered "y_k[n]"
Gold Identifiers (Node test)
✔ in qID1 should be discovered "W(2, k) > 2^k/k^\\varepsilon"
✔ in qID2 should be discovered "(X,\\Sigma)"
✔ in qID3 should be discovered "(p-1)!^n"
✔ in qID4 should be discovered "f_c(z) = z^2 + c"
✔ in qID5 should be discovered "\\forall x \\, \\forall y \\, P(x,y) \\Leftrightarrow \\forall y \\, \\forall x \\, P(x,y)"
✔ in qID6 should be discovered "\\alpha(x)"
✔ in qID7 should be discovered "\\alpha(x)"
✔ in qID8 should be discovered "\\alpha(x)"
✔ in qID9 should be discovered "|{\\Psi}\\rangle=\\sum_{i_1,i_2,\\alpha_1,\\alpha_2}\\Gamma^{[1]i_1}_{\\alpha_1}\\lambda^{[1]}_{\\alpha_1}\\Gamma^{[2]i_2}_{\\alpha_1\\alpha_2}\\lambda^{[2]}_{{\\alpha}_2}|{i_1i_2}\\rangle|{\\Phi^{[3..N]}_{\\alpha_2}}\\rangle"
✔ in qID10 should be discovered "z*x\\le y"
✔ in qID11 should be discovered " \\frac{d}{dx}\\left( \\log_c x\\right) = {1 \\over x \\ln c} , \\qquad c > 0, c \\ne 1"
✔ in qID12 should be discovered "\\theta = n \\times 137.508^\\circ,"
✔ in qID13 should be discovered "s_V(\\mathcal{R})"
✔ in qID14 should be discovered "\\ell(m)"
✔ in qID15 should be discovered "bx-x^2"
✔ in qID16 should be discovered "\\omega_{k}"
✔ in qID17 should be discovered "\\mathbf{m}_1"
✔ in qID18 should be discovered "r_{ij}"
✔ in qID19 should be discovered " Z = \\sum_{j} g_j \\cdot \\mathrm{e}^{- \\beta E_j}"
✔ in qID20 should be discovered "S'"
✔ in qID21 should be discovered "S'"
✔ in qID22 should be discovered "\\text{Ker} (k_* - l_*) \\cong \\text{Im} (i_*, j_*)."
✔ in qID23 should be discovered "D(G,H) = \\sum_{i=1}^{29} | F_i(G) - F_i(H) |"
✔ in qID24 should be discovered " E_\\text{k} = E_t + E_\\text{r} \\, "
✔ in qID25 should be discovered "\\lambda(L(B)) \\leq d"
✔ in qID26 should be discovered "L\\left(C\\right) \\leq L\\left(T\\right)"
✔ in qID27 should be discovered "v = \\frac{c}{n}"
✔ in qID28 should be discovered "\\sigma_y^2(\\tau) = \\frac{2\\pi^2\\tau}{3}h_{-2}"
✔ in qID29 should be discovered " R_{s\\ normal} = \\sqrt{ \\frac{\\omega \\mu_0} {2 \\sigma} }"
✔ in qID30 should be discovered " \\phi_1 = -30^\\circ...+30^\\circ"
✔ in qID31 should be discovered "T_c"
✔ in qID32 should be discovered "T_c"
✔ in qID33 should be discovered "T_c"
✔ in qID34 should be discovered "P_1(X)=P(X)/(X-\\alpha_1)"
✔ in qID35 should be discovered "= \\frac{k}{n}."
✔ in qID36 should be discovered "n = \\prod_{i=1}^r p_i^{a_i}"
✔ in qID37 should be discovered "H(j \\omega) = \\mathcal{F}\\{h(t)\\}"
✔ in qID38 should be discovered "\\pi/4"
✔ in qID39 should be discovered "(x+y)^n = \\sum_{k=0}^n {n \\choose k}x^{n-k}y^k = \\sum_{k=0}^n {n \\choose k}x^{k}y^{n-k}.\n"
✔ in qID40 should be discovered "\\ [A]_t = -kt + [A]_0"
✔ in qID41 should be discovered "q^{42}"
✔ in qID42 should be discovered "\\alpha(d) \\le \\left(\\sqrt{3/2} + \\varepsilon\\right)^d"
✔ in qID43 should be discovered " f^{\\mu} = - 8\\pi { G \\over { 3 c^4 } } \\left ( {A \\over 2} T_{\\alpha \\beta} + {B \\over 2} T \\eta_{\\alpha \\beta} \\right ) \\left ( \\delta^{\\mu}_{\\nu} + u^{\\mu} u_{\\nu} \\right ) u^{\\alpha} x^{\\nu} u^{\\beta} "
✔ in qID44 should be discovered " \\frac{D_g u_g}{Dt} - f_{0}v_a - \\beta y v_g = 0 "
✔ in qID45 should be discovered "I_c"
✔ in qID46 should be discovered "\\, A \\mapsto M\\alpha(A)M^{-1} ,"
✔ in qID47 should be discovered "\\Gamma_{\\infty}"
✔ in qID48 should be discovered "Y = \\beta T_8 + I X"
✔ in qID49 should be discovered " \\mu (A)= \\begin{cases} 1 & \\mbox{ if } 0 \\in A \\\\ \n 0 & \\mbox{ if } 0 \\notin A.\n\\end{cases}"
✔ in qID50 should be discovered "\\lambda_{in}"
✔ in qID51 should be discovered "rpm_{motor}"
✔ in qID52 should be discovered "\\underbrace{u_1(\\mathbf{x},z_1)=v_1+\\dot{u}_x}_{\\text{By definition of }v_1}=\\overbrace{-\\frac{\\partial V_x}{\\partial \\mathbf{x}}g_x(\\mathbf{x})-k_1(\\underbrace{z_1-u_x(\\mathbf{x})}_{e_1})}^{v_1} \\, + \\, \\overbrace{\\frac{\\partial u_x}{\\partial \\mathbf{x}}(\\underbrace{f_x(\\mathbf{x})+g_x(\\mathbf{x})z_1}_{\\dot{\\mathbf{x}} \\text{ (i.e., } \\frac{\\operatorname{d}\\mathbf{x}}{\\operatorname{d}t} \\text{)}})}^{\\dot{u}_x \\text{ (i.e., } \\frac{ \\operatorname{d}u_x }{\\operatorname{d}t} \\text{)}}"
✔ in qID53 should be discovered "E \\left[ \\hat{\\sigma}^2\\right]= \\frac{n-1}{n} \\sigma^2"
✔ in qID54 should be discovered "\\mathsf{fv}"
✔ in qID55 should be discovered "\\sum_x \\sum_y I(x,y) \\,\\!"
✔ in qID56 should be discovered "\\boldsymbol{F}_r"
✔ in qID57 should be discovered "0\\rightarrow B\\rightarrow A\\oplus B\\rightarrow A\\rightarrow0."
✔ in qID58 should be discovered "(\\nabla_Y T)(\\alpha_1, \\alpha_2, \\ldots, X_1, X_2, \\ldots) =Y(T(\\alpha_1,\\alpha_2,\\ldots,X_1,X_2,\\ldots))"
✔ in qID59 should be discovered " \\sum_{n \\in \\mathbb{Z}^d} |\\psi(t,n)|^2 |n| \\leq C "
✔ in qID60 should be discovered " p = {\\frac{-x\\pm\\sqrt{x^2-4(\\frac{-gx^2}{2v^2})(\\frac{-gx^2}{2v^2}-y)}}{2(\\frac{-gx^2}{2v^2}) }}"
✔ in qID61 should be discovered "\\left\\{ z \\in H: \\left| z \\right| > 1,\\, \\left| \\,\\mbox{Re}(z) \\,\\right| < \\frac{1}{2} \\right\\}"
✔ in qID62 should be discovered "T-\\lambda I"
✔ in qID63 should be discovered "\n y\\left( x \\right) = {\\mathop{\\rm sgn}} \\left( {{\\rho }} \\right)\\frac{{{\\sigma _y}}}{{{\\sigma _x}}}\\left( {x - {\\mu _x}} \\right) + {\\mu _y}.\n "
✔ in qID64 should be discovered "x=b \\ "
✔ in qID65 should be discovered "H^1(K)=\\sqrt{2}"
✔ in qID66 should be discovered "P_i = \\mbox{head}(E_K (S_{i-1}), x) \\oplus C_i"
✔ in qID67 should be discovered "\\frac{ \\partial f}{ \\partial x} = f_x = \\partial_x f."
✔ in qID68 should be discovered " P_x = P - \\{ a\\mid a \\geq x\\} "
✔ in qID69 should be discovered "\\eta = \\frac{ work\\ done } {heat\\ absorbed} = \\frac{ Q1-Q2 }{ Q1}"
✔ in qID70 should be discovered "df = {\\partial f \\over \\partial x}dx + {\\partial f \\over \\partial y}dy = pdx + vdy"
✔ in qID71 should be discovered "h_{r,s}"
✔ in qID72 should be discovered " K^M_*(k) := T^*(k^\\times)/(a\\otimes (1-a)) "
✔ in qID73 should be discovered "\\{C : K_X \\cdot C = 0\\}"
✔ in qID74 should be discovered "\\Theta \\wedge\n(d\\Theta)^n \\neq 0"
✔ in qID75 should be discovered "D\\left(\\rho u_i\\right)/Dt\\approx0"
✔ in qID76 should be discovered " z_{t} = \\lambda_{1}z_{t-1} + \\varepsilon_{t} "
✔ in qID77 should be discovered "b_3"
✔ in qID78 should be discovered "b_3"
✔ in qID79 should be discovered " \\Delta W = \\int_{V_1}^{V_2} p \\mathrm{d}V \\,\\!"
✔ in qID80 should be discovered "\\dim f(Z) > n"
✔ in qID81 should be discovered "\\frac{d}{dt} \\log_e t = \\frac{1}{t}."
✔ in qID82 should be discovered "h_i : X \\to \\{-1,+1\\}"
✔ in qID83 should be discovered "2\\le seqs \\le6"
✔ in qID84 should be discovered " F = \\{ (x,y) : x \\in \\mathcal{R}^b,\\, y \\in \\mathcal{R}^n,\\; x=y \\}."
✔ in qID85 should be discovered "X_i(\\omega)=\\omega_i"
✔ in qID86 should be discovered "\n{\\partial{L}\\over \\partial q_i} = {\\mathrm{d} \\over \\mathrm{d}t}{\\partial{L}\\over \\partial{\\dot{q_i}}}.\n"
✔ in qID87 should be discovered "x_7"
✔ in qID88 should be discovered "\\Pi_n"
✔ in qID89 should be discovered "\\sigma^2 = X^TVX,"
✔ in qID90 should be discovered "\\int_{\\mathbb{R}^n}f\\,dx = \\int_0^\\infty\\left\\{\\int_{\\partial B(x_0;r)} f\\,dS\\right\\}\\,dr."
✔ in qID91 should be discovered "\n\\{x, p_x\\}_{DB} = \\{y, p_y\\}_{DB} = \\frac{1}{2}\n"
✔ in qID92 should be discovered "G_{k, \\sigma} (y)= 1-(1+ky/\\sigma)^{-1/k} "
✔ in qID93 should be discovered "L(H_B) \\otimes C(X)"
✔ in qID94 should be discovered "\\pi_i = 2^{-N} \\tbinom Ni"
✔ in qID95 should be discovered "(\\sqrt{p_1}, \\cdots ,\\sqrt{p_n})"
✔ in qID96 should be discovered "\\boldsymbol{s}"
✔ in qID97 should be discovered "\\mathbf{J^TW\\ \\Delta y}"
✔ in qID98 should be discovered "\\bar V^*"
✔ in qID99 should be discovered "\\;\\frac{(n+\\delta-1)(n+\\delta-2)\\cdots n}{(\\delta-1)!}\\;"
✔ in qID100 should be discovered "y_k[n]"
Identifiers
✔ should be discovered ""
✔ should be discovered "."
✔ should be discovered "a"
✔ should be discovered "a."
✔ should be discovered "a_\\text{x}"
✔ should be discovered "a_{bc}"
✔ should be discovered "a_{b,c}"
✔ should be discovered "a_{+}"
✔ should be discovered "a_{\\emptyset}"
✔ should be discovered "a_{-\\infty}"
✔ should be discovered "a_b^c"
✔ should be discovered "\\int_0^\\infty"
✔ should be discovered "a_{b\\pm c}"
✔ should be discovered "\\mathrm{def}"
✔ should be discovered "k_{\\mathbf{B}}"
✔ should be discovered "\\boldsymbol{\\sigma}"
✔ should be discovered "\\mathbf{\\hat{n}}"
✔ should be discovered "a^2"
✔ should be discovered "a^2+b^2"
✔ should be discovered "a^{2}+b^{2}"
✔ should be discovered "\\frac2b"
✔ should be discovered "t_a"
✔ should be discovered "\\mathrm{kg}"
✔ should be discovered "\\sqrt[3]{81}"
✔ should be discovered "a'_{k}"
✔ should be discovered "x_n*x_{n-1}"
✔ should be discovered "a_{i_{j}}"
✔ should be discovered "\\operatorname{arg min}"
✔ should be discovered "\\underbrace{x+y}_2"
✔ should be discovered "\\hat{U}(t,t_0)=\\exp{\\left(-\\frac{i}\\hbar \\int_{t_0}^t \\hat{H}(t')dt'\\right)}"
✔ should be discovered "\\begin{align}\n &[\\mathrm j_k, \\mathrm j_l]\n \\equiv \\mathrm j_k \\mathrm j_l - \\mathrm j_l \\mathrm j_k\n = i \\hbar \\sum_m \\varepsilon_{k, l, m} \\mathrm j_m\n & k, l, m &\\in \\{\\mathrm x, \\mathrm y, \\mathrm z\\}\n\\end{align}"
✔ should be discovered "x = \\int_1^y {\\mathrm{d}t \\over t}"
✔ should be discovered "f'(x) = \\lim_{h \\to 0}{f(x+h) - f(x)\\over{h}}"
✔ should be discovered "\\dot m = C_d A \\sqrt{k \\rho_0 P_0 \\left(\\frac{2}{k + 1}\\right)^{\\frac{k + 1}{k - 1}}}"
✔ should be discovered "\\forall x \\Big(\\forall y (y \\in x \\rightarrow P[y]) \\rightarrow P[x]\\Big) \\rightarrow \\forall x \\, P[x]"
✔ should be discovered "\\text{Magnetic Reynolds number }"
✔ should be discovered "\\int_{R_n} \\cdots \\int_{R_2} \\int_{R_1} f(x_1, x_2, \\ldots, x_n) \\, dx_1 dx_2\\cdots dx_n \\equiv \\int_R f(\\boldsymbol{x}) \\, d^n\\boldsymbol{x}"
✔ should be discovered "\\mathbf{M}_{\\rm orb}"
✔ should be discovered "F=\\overline{(A \\wedge B) \\vee (C \\wedge D)}"
✔ should be discovered "\\mathrm{2\\ Squares\\ of\\ Land}"
✔ should be discovered "\\mathrm{d_k,d^k,d_{klo},\\left(d_{\\begin{matrix}a\\end{matrix}}\\right),\\frac12}"
✔ should be discovered "\\mathrm{\\begin{matrix}a\\end{matrix},\\big(,\\mbox{A},{\\rm b},1_2_3,1^2,1^2^3,1_2^3,_1^2}"
✔ should be discovered "\\mathrm{a \\choose b, \\sqrt{4}}"
✔ should be discovered "\\sideset{c}{d}e+\\sideset{_\\dagger^*}{_\\dagger^*}\\prod"
✔ should be discovered "\\mathrm{_a^b}"
✔ should be discovered "\\mathrm{\\sqrt[3]{81}}"
✔ should be discovered "\\mathrm{\\sideset{c}{d}e}"
✔ should be discovered "\\mathrm{{}_c}"
✔ should be discovered "\\mathrm{'_c}"
✔ should be discovered "0_{d_k,d^k,d_{klo},\\left(d_{\\begin{matrix}a\\end{matrix}}\\right),\\frac12}"
✔ should be discovered "0_{\\begin{matrix}a\\end{matrix},\\big(,\\mbox{A},{\\rm b},1_2_3,1^2,1^2^3,1_2^3,_1^2}"
✔ should be discovered "0_{a \\choose b, \\sqrt{4}}"
✔ should be discovered "0_{_a^b}"
✔ should be discovered "0_{\\sqrt[3]{81}}"
✔ should be discovered "0_{\\sideset{c}{d}e}"
✔ should be discovered "0_{{}_c}"
✔ should be discovered "0_{\\it a}"
✔ should be discovered "0_{\\cal a}"
✔ should be discovered "0_{\\bf a}"
✔ should be discovered "0_{\\bf }"
✔ should be discovered "{\\frac {\\operatorname {d} u_{x}}{\\operatorname {d} t}}"
✔ should be discovered "\\ce{H2O}"
✔ should be discovered "a_{\\ce{H2O}}"
✔ should be discovered "\\mathbb{\\ce{H2O}}"
✔ should be discovered "\\ce{\\underbrace{a}_{b}}"
✔ should be discovered "\\phantom{a}"
✔ should be discovered "\\hphantom{a}"
✔ should be discovered "\\vphantom{a}"
✔ should be discovered "{{ab}}"
✔ should be discovered "{{ab}}"
✔ should be discovered "\\rm sgn"
✔ should be discovered "\\dot{q_{i}}"
Index
✔ should correctly handle ""with option""
✔ should correctly handle "\\mathbb{x}"with option{"format":"tree"}
✔ should correctly handle "\\mathbb{x}"with option{"format":"identifier"}
✔ should correctly handle "\\mathbb{x}"with option{"format":"list"}
✔ should correctly handle "\\mathbb{x}"with option{"format":"json"}
✔ should correctly handle "\\mathbb{x}"with option{"format":"all"}
✔ should correctly handle "\\invalid"with optionundefined
✔ should correctly handle "\\left("with optionundefined
✔ should throw an exception in debug mode
✔ should handle type-errors
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 $$$
Big Node test
✔ Should not create an empty Big
✔ Should not create a Big with one argument
✔ Should not create a Big with incorrect type
✔ Should create an basic function
✔ Should extract identifiers
✔ Should create exactly on set of curlies
Box Node test
✔ Should not create an empty Box
✔ Should not create a Box with one argument
✔ Should not create a Box with incorrect type
✔ Should create an basic function
✔ Should create exactly on set of curlies
✔ Should extract identifiers
ChemFun2u Node test
✔ Should not create an empty ChemFun2u
✔ Should not create a ChemFun2u with one argument
✔ Should not create a ChemFun2u with incorrect type
✔ Should create an basic ChemFun2u
✔ Should extract identifiers
ChemWord Node test
✔ Should not create an empty ChemWord
✔ Should not create a ChemWord with one argument
✔ Should not create a ChemWord with incorrect type
✔ Should create an basic ChemWord
✔ Should extract identifiers
Test 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 mathrm
Curly node test
✔ Should not create an empty curly
✔ Should not create a curly with more than one argument
✔ Should not create a curly with incorrect type
✔ Should render a curly with empty array
✔ Should render a list
✔ Should not create extra curlies
✔ Should not create extra curlies
✔ Should extract identifier modifications
✔ Should extract subscripts
Declh Node test
✔ Should not create an empty Declh
✔ Should not create a Declh with one argument
✔ Should not create a Declh with incorrect type
✔ Should create a basic function
✔ Should create a function with two arguments
✔ Should create exactly one set of curlies
✔ Should extract identifiers
✔ Should extract multiple identifiers
✔ Should extract subscripts for rm font modification
✔ Should extract subscripts for it font modification
✔ Should extract subscripts for cal font modification
✔ Should extract subscripts for bf font modification
✔ Should not extract empty font modifier subscripts
Dollar node test
✔ Should not create an empty dollar
✔ Should not create a dollar with more than one argument
✔ Should not create a dollar with incorrect type
✔ Should render a dollar with empty tex array
✔ Should render a list
✔ Should extract identifiers
DQ Node test
✔ Should not create an empty Dq
✔ Should not create a Dq with one argument
✔ Should not create a Dq with incorrect type
✔ Should create an basic Dq
✔ Should create an empty base Dq
✔ Should extract identifiers
✔ Should extract identifiers for uncertain base
✔ Should extract identifiers of derivatives
✔ Should extract identifiers with empty base
✔ Should extract identifiers in integral
✔ Should extract subscripts
✔ Should not extract subscripts for unknown constructs
Fq Node test
✔ Should not create an empty Fq
✔ Should not create a Fq with one argument
✔ Should not create a Fq with incorrect type
✔ Should create an basic Fq
✔ Should apply contains_func on children
Fun1 Node test
✔ Should not create an empty Fun1
✔ Should not create a Fun1 with one argument
✔ Should not create a Fun1 with incorrect type
✔ Should create an basic function
✔ Should create exactly on set of curlies
✔ Should extract identifiers
✔ Should not extract extended literals as identifiers
✔ Should not extract phantom identifiers
✔ Should ignore unknown functions
✔ Should extract identifier modifications
✔ Should extract subscripts
✔ Should extract subscripts for extended literals
✔ Should not extract subscripts for empty mods
Fun1nb Node test
✔ Should not create an empty Fun1nb
✔ Should not create a Fun1nb with one argument
✔ Should not create a Fun1nb with incorrect type
✔ Should create a basic function
✔ Should create exactly one set of curlies
Fun2 Node test
✔ Should not create an empty Fun2
✔ Should not create a Fun2 with one argument
✔ Should not create a Fun2 with incorrect type
✔ Should create an basic function
✔ Should create exactly on set of curlies
✔ Should extract identifiers
Fun2nb Node test
✔ Should not create an empty Fun2nb
✔ Should not create a Fun2nb with one argument
✔ Should not create a Fun2nb with incorrect type
✔ Should create an basic function
✔ Should create exactly on set of curlies
Fun2sq Node test
✔ Should not create an empty Fun2sq
✔ Should not create a Fun2sq with one argument
✔ Should not create a Fun2sq with incorrect type
✔ Should create an basic function
✔ Should create exactly on set of curlies
Identifiers
✔ should be discovered ""
✔ should be discovered "."
✔ should be discovered "a"
✔ should be discovered "a."
✔ should be discovered "a_\\text{x}"
✔ should be discovered "a_{bc}"
✔ should be discovered "a_{b,c}"
✔ should be discovered "a_{+}"
✔ should be discovered "a_{\\emptyset}"
✔ should be discovered "a_{-\\infty}"
✔ should be discovered "a_b^c"
✔ should be discovered "\\int_0^\\infty"
✔ should be discovered "a_{b\\pm c}"
✔ should be discovered "\\mathrm{def}"
✔ should be discovered "k_{\\mathbf{B}}"
✔ should be discovered "\\boldsymbol{\\sigma}"
✔ should be discovered "\\mathbf{\\hat{n}}"
✔ should be discovered "a^2"
✔ should be discovered "a^2+b^2"
✔ should be discovered "a^{2}+b^{2}"
✔ should be discovered "\\frac2b"
✔ should be discovered "t_a"
✔ should be discovered "\\mathrm{kg}"
✔ should be discovered "\\sqrt[3]{81}"
✔ should be discovered "a'_{k}"
✔ should be discovered "x_n*x_{n-1}"
✔ should be discovered "a_{i_{j}}"
✔ should be discovered "\\operatorname{arg min}"
✔ should be discovered "\\underbrace{x+y}_2"
✔ should be discovered "\\hat{U}(t,t_0)=\\exp{\\left(-\\frac{i}\\hbar \\int_{t_0}^t \\hat{H}(t')dt'\\right)}"
✔ should be discovered "\\begin{align}\n &[\\mathrm j_k, \\mathrm j_l]\n \\equiv \\mathrm j_k \\mathrm j_l - \\mathrm j_l \\mathrm j_k\n = i \\hbar \\sum_m \\varepsilon_{k, l, m} \\mathrm j_m\n & k, l, m &\\in \\{\\mathrm x, \\mathrm y, \\mathrm z\\}\n\\end{align}"
✔ should be discovered "x = \\int_1^y {\\mathrm{d}t \\over t}"
✔ should be discovered "f'(x) = \\lim_{h \\to 0}{f(x+h) - f(x)\\over{h}}"
✔ should be discovered "\\dot m = C_d A \\sqrt{k \\rho_0 P_0 \\left(\\frac{2}{k + 1}\\right)^{\\frac{k + 1}{k - 1}}}"
✔ should be discovered "\\forall x \\Big(\\forall y (y \\in x \\rightarrow P[y]) \\rightarrow P[x]\\Big) \\rightarrow \\forall x \\, P[x]"
✔ should be discovered "\\text{Magnetic Reynolds number }"
✔ should be discovered "\\int_{R_n} \\cdots \\int_{R_2} \\int_{R_1} f(x_1, x_2, \\ldots, x_n) \\, dx_1 dx_2\\cdots dx_n \\equiv \\int_R f(\\boldsymbol{x}) \\, d^n\\boldsymbol{x}"
✔ should be discovered "\\mathbf{M}_{\\rm orb}"
✔ should be discovered "F=\\overline{(A \\wedge B) \\vee (C \\wedge D)}"
✔ should be discovered "\\mathrm{2\\ Squares\\ of\\ Land}"
✔ should be discovered "\\mathrm{d_k,d^k,d_{klo},\\left(d_{\\begin{matrix}a\\end{matrix}}\\right),\\frac12}"
✔ should be discovered "\\mathrm{\\begin{matrix}a\\end{matrix},\\big(,\\mbox{A},{\\rm b},1_2_3,1^2,1^2^3,1_2^3,_1^2}"
✔ should be discovered "\\mathrm{a \\choose b, \\sqrt{4}}"
✔ should be discovered "\\sideset{c}{d}e+\\sideset{_\\dagger^*}{_\\dagger^*}\\prod"
✔ should be discovered "\\mathrm{_a^b}"
✔ should be discovered "\\mathrm{\\sqrt[3]{81}}"
✔ should be discovered "\\mathrm{\\sideset{c}{d}e}"
✔ should be discovered "\\mathrm{{}_c}"
✔ should be discovered "\\mathrm{'_c}"
✔ should be discovered "0_{d_k,d^k,d_{klo},\\left(d_{\\begin{matrix}a\\end{matrix}}\\right),\\frac12}"
✔ should be discovered "0_{\\begin{matrix}a\\end{matrix},\\big(,\\mbox{A},{\\rm b},1_2_3,1^2,1^2^3,1_2^3,_1^2}"
✔ should be discovered "0_{a \\choose b, \\sqrt{4}}"
✔ should be discovered "0_{_a^b}"
✔ should be discovered "0_{\\sqrt[3]{81}}"
✔ should be discovered "0_{\\sideset{c}{d}e}"
✔ should be discovered "0_{{}_c}"
✔ should be discovered "0_{\\it a}"
✔ should be discovered "0_{\\cal a}"
✔ should be discovered "0_{\\bf a}"
✔ should be discovered "0_{\\bf }"
✔ should be discovered "{\\frac {\\operatorname {d} u_{x}}{\\operatorname {d} t}}"
✔ should be discovered "\\ce{H2O}"
✔ should be discovered "a_{\\ce{H2O}}"
✔ should be discovered "\\mathbb{\\ce{H2O}}"
✔ should be discovered "\\ce{\\underbrace{a}_{b}}"
✔ should be discovered "\\phantom{a}"
✔ should be discovered "\\hphantom{a}"
✔ should be discovered "\\vphantom{a}"
✔ should be discovered "{{ab}}"
✔ should be discovered "\\rm sgn"
✔ should be discovered "\\dot{q_{i}}"
Infix Node test
✔ Should not create an empty Infix
✔ Should not create a Infix with one argument
✔ Should not create a Infix with incorrect type
✔ Should create an basic function
✔ Should create exactly on set of curlies
✔ Should extract identifiers
Baseclass Node test
✔ Should not create an empty literal
✔ Should not create a literal with more than one argument
✔ Should not create a literal with incorrect type
✔ Should create an literal with only one argument
✔ Should render within node base class
✔ Should extract identifier modifications
✔ Identifier modifications should report extra space
✔ Should extract subscripts
Lr Node test
✔ Should not create an empty Lr
✔ Should not create a Lr with one argument
✔ Should not create a Lr with incorrect type
✔ Should create a basic function
✔ Should create exactly one set of curlies
✔ Should extract identifiers
Matrix Node test
✔ Should require two arguments
✔ Should require check second argument for nested arrays
✔ Should create an instance of TexNode
✔ Should render
✔ Should not create extra curlies
✔ Should extract identifiers
Mhchem Node test
✔ Should not create an empty Mhchem
✔ Should not create a Mhchem with one argument
✔ Should not create a Mhchem with incorrect type
✔ Should create a basic function
✔ Should create curlies
✔ Should extract identifiers
Parse and render with new classes
✔ 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: "\\text{x}"
✔ should parse: "\\Big("
✔ should parse: "\\begin{alignedat} { 3 } a & b & c \\end{alignedat}"
✔ should parse: "\\cal x"
✔ should parse: "\\binom{A}{B}"
✔ should parse: "\\sideset{_\\dagger^*}{_\\dagger^*}"
✔ should parse: "\\sqrt[3]{2}"
✔ should parse chem: "\\ce{CO2 + C -> 2 CO}"
✔ should parse chem: "\\ce{CO2 + \\underbrace{a}_{b} -> 2 CO}"
✔ should parse chem: "\\ce{\\begin{math}n\\end{math}H2O}"
✔ in qID1 should be discovered "W(2, k) > 2^k/k^\\varepsilon"
✔ in qID2 should be discovered "(X,\\Sigma)"
✔ in qID3 should be discovered "(p-1)!^n"
✔ in qID4 should be discovered "f_c(z) = z^2 + c"
✔ in qID5 should be discovered "\\forall x \\, \\forall y \\, P(x,y) \\Leftrightarrow \\forall y \\, \\forall x \\, P(x,y)"
✔ in qID6 should be discovered "\\alpha(x)"
✔ in qID7 should be discovered "\\alpha(x)"
✔ in qID8 should be discovered "\\alpha(x)"
✔ in qID9 should be discovered "|{\\Psi}\\rangle=\\sum_{i_1,i_2,\\alpha_1,\\alpha_2}\\Gamma^{[1]i_1}_{\\alpha_1}\\lambda^{[1]}_{\\alpha_1}\\Gamma^{[2]i_2}_{\\alpha_1\\alpha_2}\\lambda^{[2]}_{{\\alpha}_2}|{i_1i_2}\\rangle|{\\Phi^{[3..N]}_{\\alpha_2}}\\rangle"
✔ in qID10 should be discovered "z*x\\le y"
✔ in qID11 should be discovered " \\frac{d}{dx}\\left( \\log_c x\\right) = {1 \\over x \\ln c} , \\qquad c > 0, c \\ne 1"
✔ in qID12 should be discovered "\\theta = n \\times 137.508^\\circ,"
✔ in qID13 should be discovered "s_V(\\mathcal{R})"
✔ in qID14 should be discovered "\\ell(m)"
✔ in qID15 should be discovered "bx-x^2"
✔ in qID16 should be discovered "\\omega_{k}"
✔ in qID17 should be discovered "\\mathbf{m}_1"
✔ in qID18 should be discovered "r_{ij}"
✔ in qID19 should be discovered " Z = \\sum_{j} g_j \\cdot \\mathrm{e}^{- \\beta E_j}"
✔ in qID20 should be discovered "S'"
✔ in qID21 should be discovered "S'"
✔ in qID22 should be discovered "\\text{Ker} (k_* - l_*) \\cong \\text{Im} (i_*, j_*)."
✔ in qID23 should be discovered "D(G,H) = \\sum_{i=1}^{29} | F_i(G) - F_i(H) |"
✔ in qID24 should be discovered " E_\\text{k} = E_t + E_\\text{r} \\, "
✔ in qID25 should be discovered "\\lambda(L(B)) \\leq d"
✔ in qID26 should be discovered "L\\left(C\\right) \\leq L\\left(T\\right)"
✔ in qID27 should be discovered "v = \\frac{c}{n}"
✔ in qID28 should be discovered "\\sigma_y^2(\\tau) = \\frac{2\\pi^2\\tau}{3}h_{-2}"
✔ in qID29 should be discovered " R_{s\\ normal} = \\sqrt{ \\frac{\\omega \\mu_0} {2 \\sigma} }"
✔ in qID30 should be discovered " \\phi_1 = -30^\\circ...+30^\\circ"
✔ in qID31 should be discovered "T_c"
✔ in qID32 should be discovered "T_c"
✔ in qID33 should be discovered "T_c"
✔ in qID34 should be discovered "P_1(X)=P(X)/(X-\\alpha_1)"
✔ in qID35 should be discovered "= \\frac{k}{n}."
✔ in qID36 should be discovered "n = \\prod_{i=1}^r p_i^{a_i}"
✔ in qID37 should be discovered "H(j \\omega) = \\mathcal{F}\\{h(t)\\}"
✔ in qID38 should be discovered "\\pi/4"
✔ in qID39 should be discovered "(x+y)^n = \\sum_{k=0}^n {n \\choose k}x^{n-k}y^k = \\sum_{k=0}^n {n \\choose k}x^{k}y^{n-k}.\n"
✔ in qID40 should be discovered "\\ [A]_t = -kt + [A]_0"
✔ in qID41 should be discovered "q^{42}"
✔ in qID42 should be discovered "\\alpha(d) \\le \\left(\\sqrt{3/2} + \\varepsilon\\right)^d"
✔ in qID43 should be discovered " f^{\\mu} = - 8\\pi { G \\over { 3 c^4 } } \\left ( {A \\over 2} T_{\\alpha \\beta} + {B \\over 2} T \\eta_{\\alpha \\beta} \\right ) \\left ( \\delta^{\\mu}_{\\nu} + u^{\\mu} u_{\\nu} \\right ) u^{\\alpha} x^{\\nu} u^{\\beta} "
✔ in qID44 should be discovered " \\frac{D_g u_g}{Dt} - f_{0}v_a - \\beta y v_g = 0 "
✔ in qID45 should be discovered "I_c"
✔ in qID46 should be discovered "\\, A \\mapsto M\\alpha(A)M^{-1} ,"
✔ in qID47 should be discovered "\\Gamma_{\\infty}"
✔ in qID48 should be discovered "Y = \\beta T_8 + I X"
✔ in qID49 should be discovered " \\mu (A)= \\begin{cases} 1 & \\mbox{ if } 0 \\in A \\\\ \n 0 & \\mbox{ if } 0 \\notin A.\n\\end{cases}"
✔ in qID50 should be discovered "\\lambda_{in}"
✔ in qID51 should be discovered "rpm_{motor}"
✔ in qID52 should be discovered "\\underbrace{u_1(\\mathbf{x},z_1)=v_1+\\dot{u}_x}_{\\text{By definition of }v_1}=\\overbrace{-\\frac{\\partial V_x}{\\partial \\mathbf{x}}g_x(\\mathbf{x})-k_1(\\underbrace{z_1-u_x(\\mathbf{x})}_{e_1})}^{v_1} \\, + \\, \\overbrace{\\frac{\\partial u_x}{\\partial \\mathbf{x}}(\\underbrace{f_x(\\mathbf{x})+g_x(\\mathbf{x})z_1}_{\\dot{\\mathbf{x}} \\text{ (i.e., } \\frac{\\operatorname{d}\\mathbf{x}}{\\operatorname{d}t} \\text{)}})}^{\\dot{u}_x \\text{ (i.e., } \\frac{ \\operatorname{d}u_x }{\\operatorname{d}t} \\text{)}}"
✔ in qID53 should be discovered "E \\left[ \\hat{\\sigma}^2\\right]= \\frac{n-1}{n} \\sigma^2"
✔ in qID54 should be discovered "\\mathsf{fv}"
✔ in qID55 should be discovered "\\sum_x \\sum_y I(x,y) \\,\\!"
✔ in qID56 should be discovered "\\boldsymbol{F}_r"
✔ in qID57 should be discovered "0\\rightarrow B\\rightarrow A\\oplus B\\rightarrow A\\rightarrow0."
✔ in qID58 should be discovered "(\\nabla_Y T)(\\alpha_1, \\alpha_2, \\ldots, X_1, X_2, \\ldots) =Y(T(\\alpha_1,\\alpha_2,\\ldots,X_1,X_2,\\ldots))"
✔ in qID59 should be discovered " \\sum_{n \\in \\mathbb{Z}^d} |\\psi(t,n)|^2 |n| \\leq C "
✔ in qID60 should be discovered " p = {\\frac{-x\\pm\\sqrt{x^2-4(\\frac{-gx^2}{2v^2})(\\frac{-gx^2}{2v^2}-y)}}{2(\\frac{-gx^2}{2v^2}) }}"
✔ in qID61 should be discovered "\\left\\{ z \\in H: \\left| z \\right| > 1,\\, \\left| \\,\\mbox{Re}(z) \\,\\right| < \\frac{1}{2} \\right\\}"
✔ in qID62 should be discovered "T-\\lambda I"
✔ in qID63 should be discovered "\n y\\left( x \\right) = {\\mathop{\\rm sgn}} \\left( {{\\rho }} \\right)\\frac{{{\\sigma _y}}}{{{\\sigma _x}}}\\left( {x - {\\mu _x}} \\right) + {\\mu _y}.\n "
✔ in qID64 should be discovered "x=b \\ "
✔ in qID65 should be discovered "H^1(K)=\\sqrt{2}"
✔ in qID66 should be discovered "P_i = \\mbox{head}(E_K (S_{i-1}), x) \\oplus C_i"
✔ in qID67 should be discovered "\\frac{ \\partial f}{ \\partial x} = f_x = \\partial_x f."
✔ in qID68 should be discovered " P_x = P - \\{ a\\mid a \\geq x\\} "
✔ in qID69 should be discovered "\\eta = \\frac{ work\\ done } {heat\\ absorbed} = \\frac{ Q1-Q2 }{ Q1}"
✔ in qID70 should be discovered "df = {\\partial f \\over \\partial x}dx + {\\partial f \\over \\partial y}dy = pdx + vdy"
✔ in qID71 should be discovered "h_{r,s}"
✔ in qID72 should be discovered " K^M_*(k) := T^*(k^\\times)/(a\\otimes (1-a)) "
✔ in qID73 should be discovered "\\{C : K_X \\cdot C = 0\\}"
✔ in qID74 should be discovered "\\Theta \\wedge\n(d\\Theta)^n \\neq 0"
✔ in qID75 should be discovered "D\\left(\\rho u_i\\right)/Dt\\approx0"
✔ in qID76 should be discovered " z_{t} = \\lambda_{1}z_{t-1} + \\varepsilon_{t} "
✔ in qID77 should be discovered "b_3"
✔ in qID78 should be discovered "b_3"
✔ in qID79 should be discovered " \\Delta W = \\int_{V_1}^{V_2} p \\mathrm{d}V \\,\\!"
✔ in qID80 should be discovered "\\dim f(Z) > n"
✔ in qID81 should be discovered "\\frac{d}{dt} \\log_e t = \\frac{1}{t}."
✔ in qID82 should be discovered "h_i : X \\to \\{-1,+1\\}"
✔ in qID83 should be discovered "2\\le seqs \\le6"
✔ in qID84 should be discovered " F = \\{ (x,y) : x \\in \\mathcal{R}^b,\\, y \\in \\mathcal{R}^n,\\; x=y \\}."
✔ in qID85 should be discovered "X_i(\\omega)=\\omega_i"
✔ in qID86 should be discovered "\n{\\partial{L}\\over \\partial q_i} = {\\mathrm{d} \\over \\mathrm{d}t}{\\partial{L}\\over \\partial{\\dot{q_i}}}.\n"
✔ in qID87 should be discovered "x_7"
✔ in qID88 should be discovered "\\Pi_n"
✔ in qID89 should be discovered "\\sigma^2 = X^TVX,"
✔ in qID90 should be discovered "\\int_{\\mathbb{R}^n}f\\,dx = \\int_0^\\infty\\left\\{\\int_{\\partial B(x_0;r)} f\\,dS\\right\\}\\,dr."
✔ in qID91 should be discovered "\n\\{x, p_x\\}_{DB} = \\{y, p_y\\}_{DB} = \\frac{1}{2}\n"
✔ in qID92 should be discovered "G_{k, \\sigma} (y)= 1-(1+ky/\\sigma)^{-1/k} "
✔ in qID93 should be discovered "L(H_B) \\otimes C(X)"
✔ in qID94 should be discovered "\\pi_i = 2^{-N} \\tbinom Ni"
✔ in qID95 should be discovered "(\\sqrt{p_1}, \\cdots ,\\sqrt{p_n})"
✔ in qID96 should be discovered "\\boldsymbol{s}"
✔ in qID97 should be discovered "\\mathbf{J^TW\\ \\Delta y}"
✔ in qID98 should be discovered "\\bar V^*"
✔ in qID99 should be discovered "\\;\\frac{(n+\\delta-1)(n+\\delta-2)\\cdots n}{(\\delta-1)!}\\;"
✔ in qID100 should be discovered "y_k[n]"
Array Node test
- Should create an instance of Array
✔ Should create an instance of TexNode
✔ Should concatenate its input
✔ Should create exactly one pair of curlies
✔ Should extract identifiers
✔ Should extract identifiers from the argument.
✔ Should extract split identifiers
✔ Should not confuse integrals and identifiers
✔ Should not confuse integral d with d identifier
✔ Should not confuse upright integral d with d identifier
✔ Should extract identifier modifications
✔ Should extract subscripts
Baseclass Node test
✔ Should create an empty node
✔ Should create a node with am empty string
✔ Should create a hello world node
✔ Should create a nested hello world node
✔ Should not accept integers as arguments
✔ Should add curlies
✔ Should not nest curlies
✔ Should produce empty curlies
✔ Should extract identifiers
✔ Should contain a method stub for extracting identifier modifications
✔ Should contain a method stub for extracting subscripts
Uq Node test
✔ Should not create an empty Uq
✔ Should not create a Uq with one argument
✔ Should not create a Uq with incorrect type
✔ Should create an basic Uq
✔ Should create an empty base Uq
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"
texutil to json
1) should be idempotent
Tokens
✔ 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 "\\frac2b"
tree2d3json
✔ 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 "\\frac2b"
✔ should correctly render "b^2"
Array Tree
✔ should correctly render ""
✔ should correctly render "3+\\frac1{7+\\frac1{15+\\dots}}"
✔ should correctly render "\\ce{H2O}"
1565 passing (7m)
1 pending
1 failing
1) texutil to json
should be idempotent:
AssertionError [ERR_ASSERTION]: '922733f37807ff43a21df618a6dbaa18845cf71fda5c7ac74f76bfc03252a038' == '26fd55c8eb0c62af6b2a9e541073aa5b4430ff606671cd4cb4fb590667ce0bc2'
+ expected - actual
-922733f37807ff43a21df618a6dbaa18845cf71fda5c7ac74f76bfc03252a038
+26fd55c8eb0c62af6b2a9e541073aa5b4430ff606671cd4cb4fb590667ce0bc2
at Context.<anonymous> (test/texutil.js:87:16)
at processImmediate (node:internal/timers:466:21)
--- end ---
Traceback (most recent call last):
File "/venv/lib/python3.9/site-packages/runner-0.1.0-py3.9.egg/runner/__init__.py", line 1400, in main
libup.run(args.repo, args.output, args.branch)
File "/venv/lib/python3.9/site-packages/runner-0.1.0-py3.9.egg/runner/__init__.py", line 1338, in run
self.npm_upgrade(plan)
File "/venv/lib/python3.9/site-packages/runner-0.1.0-py3.9.egg/runner/__init__.py", line 1049, in npm_upgrade
self.npm_test()
File "/venv/lib/python3.9/site-packages/runner-0.1.0-py3.9.egg/runner/__init__.py", line 287, in npm_test
self.check_call(['npm', 'test'])
File "/venv/lib/python3.9/site-packages/runner-0.1.0-py3.9.egg/runner/shell2.py", line 54, in check_call
res.check_returncode()
File "/usr/lib/python3.9/subprocess.py", line 460, in check_returncode
raise CalledProcessError(self.returncode, self.args, self.stdout,
subprocess.CalledProcessError: Command '['/usr/bin/npm', 'test']' returned non-zero exit status 1.