texmath-0.12.5: test/writer/mml/complex1.test
<<< native
[ EArray
[ AlignCenter , AlignCenter ]
[ [ [ EText TextNormal "Bernoulli Trials" ]
, [ EGrouped
[ EGrouped
[ EIdentifier "P"
, ESymbol Open "("
, EIdentifier "E"
, ESymbol Close ")"
]
, ESymbol Rel "="
, EDelimited
"("
")"
[ Right (EFraction NormalFrac (EIdentifier "n") (EIdentifier "k"))
]
, ESubsup (EIdentifier "p") (EGrouped []) (EIdentifier "k")
, ESubsup
(EGrouped
[ ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, EIdentifier "p"
, ESymbol Close ")"
])
(EGrouped [])
(EGrouped [ EIdentifier "n" , ESymbol Bin "-" , EIdentifier "k" ])
]
]
]
, [ [ EText TextNormal "Cauchy-Schwarz Inequality" ]
, [ EGrouped
[ ESubsup
(EDelimited
"("
")"
[ Right
(EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "n"))
, Right (ESubsup (EIdentifier "a") (EIdentifier "k") (EGrouped []))
, Right (ESubsup (EIdentifier "b") (EIdentifier "k") (EGrouped []))
])
(EGrouped [])
(ENumber "2")
, ESymbol Rel "\8804"
, EDelimited
"("
")"
[ Right
(EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "n"))
, Right (ESubsup (EIdentifier "a") (EIdentifier "k") (ENumber "2"))
]
, EDelimited
"("
")"
[ Right
(EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "n"))
, Right (ESubsup (EIdentifier "b") (EIdentifier "k") (ENumber "2"))
]
]
]
]
, [ [ EText TextNormal "Cauchy Formula" ]
, [ EGrouped
[ EIdentifier "f"
, ESymbol Open "("
, EIdentifier "z"
, ESymbol Close ")"
, ESpace (1 % 6)
, ESymbol Bin "\183"
, ESubsup (EIdentifier "Ind") (EIdentifier "\947") (EGrouped [])
, ESymbol Open "("
, EIdentifier "z"
, ESymbol Close ")"
, ESymbol Rel "="
, EFraction
NormalFrac
(ENumber "1")
(EGrouped [ ENumber "2" , EIdentifier "\960" , EIdentifier "i" ])
, EUnderover
False (ESymbol Op "\8750") (EIdentifier "\947") (EGrouped [])
, EFraction
NormalFrac
(EGrouped
[ EIdentifier "f"
, ESymbol Open "("
, EIdentifier "\958"
, ESymbol Close ")"
])
(EGrouped
[ EIdentifier "\958" , ESymbol Bin "-" , EIdentifier "z" ])
, ESpace (1 % 6)
, EIdentifier "d"
, EIdentifier "\958"
]
]
]
, [ [ EText TextNormal "Cross Product" ]
, [ EGrouped
[ ESubsup (EIdentifier "V") (ENumber "1") (EGrouped [])
, ESymbol Bin "\215"
, ESubsup (EIdentifier "V") (ENumber "2") (EGrouped [])
, ESymbol Rel "="
, EDelimited
"|"
"|"
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EIdentifier "i" ]
, [ EIdentifier "j" ]
, [ EIdentifier "k" ]
]
, [ [ EFraction
NormalFrac
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "X" ])
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "u" ])
]
, [ EFraction
NormalFrac
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "Y" ])
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "u" ])
]
, [ ENumber "0" ]
]
, [ [ EFraction
NormalFrac
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "X" ])
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "v" ])
]
, [ EFraction
NormalFrac
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "Y" ])
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "v" ])
]
, [ ENumber "0" ]
]
])
]
]
]
]
, [ [ EText TextNormal "Vandermonde Determinant" ]
, [ EGrouped
[ EDelimited
"|"
"|"
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter , AlignCenter ]
[ [ [ ENumber "1" ]
, [ ENumber "1" ]
, [ ESymbol Ord "\8943" ]
, [ ENumber "1" ]
]
, [ [ ESubsup (EIdentifier "v") (ENumber "1") (EGrouped []) ]
, [ ESubsup (EIdentifier "v") (ENumber "2") (EGrouped []) ]
, [ ESymbol Ord "\8943" ]
, [ ESubsup (EIdentifier "v") (EIdentifier "n") (EGrouped []) ]
]
, [ [ ESubsup (EIdentifier "v") (ENumber "1") (ENumber "2") ]
, [ ESubsup (EIdentifier "v") (ENumber "2") (ENumber "2") ]
, [ ESymbol Ord "\8943" ]
, [ ESubsup (EIdentifier "v") (EIdentifier "n") (ENumber "2") ]
]
, [ [ ESymbol Rel "\8942" ]
, [ ESymbol Rel "\8942" ]
, [ ESymbol Rel "\8945" ]
, [ ESymbol Rel "\8942" ]
]
, [ [ ESubsup
(EIdentifier "v")
(ENumber "1")
(EGrouped [ EIdentifier "n" , ESymbol Bin "-" , ENumber "1" ])
]
, [ ESubsup
(EIdentifier "v")
(ENumber "2")
(EGrouped [ EIdentifier "n" , ESymbol Bin "-" , ENumber "1" ])
]
, [ ESymbol Ord "\8943" ]
, [ ESubsup
(EIdentifier "v")
(EIdentifier "n")
(EGrouped [ EIdentifier "n" , ESymbol Bin "-" , ENumber "1" ])
]
]
])
]
, ESymbol Rel "="
, EUnderover
False
(ESymbol Op "\8719")
(EGrouped
[ ENumber "1"
, ESymbol Rel "\8804"
, EIdentifier "i"
, ESymbol Rel "<"
, EIdentifier "j"
, ESymbol Rel "\8804"
, EIdentifier "n"
])
(EGrouped [])
, ESymbol Open "("
, ESubsup (EIdentifier "v") (EIdentifier "j") (EGrouped [])
, ESymbol Bin "-"
, ESubsup (EIdentifier "v") (EIdentifier "i") (EGrouped [])
, ESymbol Close ")"
]
]
]
, [ [ EText TextNormal "Lorenz Equations" ]
, [ EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EUnderover
False (EIdentifier "x") (EGrouped []) (ESymbol Accent "\729")
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ EIdentifier "\963"
, ESymbol Open "("
, EIdentifier "y"
, ESymbol Bin "-"
, EIdentifier "x"
, ESymbol Close ")"
]
]
]
, [ [ EUnderover
False (EIdentifier "y") (EGrouped []) (ESymbol Accent "\729")
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ EIdentifier "\961"
, EIdentifier "x"
, ESymbol Bin "-"
, EIdentifier "y"
, ESymbol Bin "-"
, EIdentifier "x"
, EIdentifier "z"
]
]
]
, [ [ EUnderover
False (EIdentifier "z") (EGrouped []) (ESymbol Accent "\729")
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ ESymbol Bin "-"
, EIdentifier "\946"
, EIdentifier "z"
, ESymbol Bin "+"
, EIdentifier "x"
, EIdentifier "y"
]
]
]
]
]
]
, [ [ EText TextNormal "Maxwell's Equations" ]
, [ EDelimited
"{"
""
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EGrouped
[ ESymbol Ord "\8711"
, ESpace (0 % 1)
, ESymbol Bin "\215"
, EUnderover
False (EIdentifier "B") (EGrouped []) (ESymbol Accent "\8636")
, ESymbol Bin "-"
, ESpace (1 % 6)
, EFraction NormalFrac (ENumber "1") (EIdentifier "c")
, ESpace (1 % 6)
, EFraction
NormalFrac
(EGrouped
[ ESymbol Ord "\8706"
, ESpace (0 % 1)
, EUnderover
False (EIdentifier "E") (EGrouped []) (ESymbol Accent "\8636")
])
(EGrouped
[ ESymbol Ord "\8706" , ESpace (0 % 1) , EIdentifier "t" ])
]
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ EFraction
NormalFrac
(EGrouped [ ENumber "4" , EIdentifier "\960" ])
(EIdentifier "c")
, ESpace (1 % 6)
, EUnderover
False (EIdentifier "j") (EGrouped []) (ESymbol Accent "\8636")
]
]
]
, [ [ EGrouped
[ ESymbol Ord "\8711"
, ESpace (0 % 1)
, ESymbol Bin "\183"
, EUnderover
False (EIdentifier "E") (EGrouped []) (ESymbol Accent "\8636")
]
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ ENumber "4" , EIdentifier "\960" , EIdentifier "\961" ]
]
]
, [ [ EGrouped
[ ESymbol Ord "\8711"
, ESpace (0 % 1)
, ESymbol Bin "\215"
, EUnderover
False (EIdentifier "E") (EGrouped []) (ESymbol Accent "\8636")
, ESpace (1 % 6)
, ESymbol Bin "+"
, ESpace (1 % 6)
, EFraction NormalFrac (ENumber "1") (EIdentifier "c")
, ESpace (1 % 6)
, EFraction
NormalFrac
(EGrouped
[ ESymbol Ord "\8706"
, ESpace (0 % 1)
, EUnderover
False (EIdentifier "B") (EGrouped []) (ESymbol Accent "\8636")
])
(EGrouped
[ ESymbol Ord "\8706" , ESpace (0 % 1) , EIdentifier "t" ])
]
]
, [ ESymbol Rel "=" ]
, [ EUnderover
False (ENumber "0") (EGrouped []) (ESymbol Accent "\8636")
]
]
, [ [ EGrouped
[ ESymbol Ord "\8711"
, ESpace (0 % 1)
, ESymbol Bin "\183"
, EUnderover
False (EIdentifier "B") (EGrouped []) (ESymbol Accent "\8636")
]
]
, [ ESymbol Rel "=" ]
, [ ENumber "0" ]
]
])
]
]
]
, [ [ EText TextNormal "Einstein Field Equations" ]
, [ EGrouped
[ ESubsup
(EIdentifier "R")
(EGrouped [ EIdentifier "\956" , EIdentifier "\957" ])
(EGrouped [])
, ESymbol Bin "-"
, EFraction NormalFrac (ENumber "1") (ENumber "2")
, ESpace (1 % 6)
, ESubsup
(EIdentifier "g")
(EGrouped [ EIdentifier "\956" , EIdentifier "\957" ])
(EGrouped [])
, ESpace (1 % 6)
, EIdentifier "R"
, ESymbol Rel "="
, EFraction
NormalFrac
(EGrouped [ ENumber "8" , EIdentifier "\960" , EIdentifier "G" ])
(ESubsup (EIdentifier "c") (EGrouped []) (ENumber "4"))
, ESpace (1 % 6)
, ESubsup
(EIdentifier "T")
(EGrouped [ EIdentifier "\956" , EIdentifier "\957" ])
(EGrouped [])
]
]
]
, [ [ EText TextNormal "Ramanujan Identity" ]
, [ EGrouped
[ EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESymbol Open "("
, ESqrt (EGrouped [ EIdentifier "\966" , ESqrt (ENumber "5") ])
, ESymbol Bin "-"
, EIdentifier "\966"
, ESymbol Close ")"
, ESubsup
(EIdentifier "e")
(EGrouped [])
(EFraction NormalFrac (ENumber "25") (EIdentifier "\960"))
])
, ESymbol Rel "="
, ENumber "1"
, ESymbol Bin "+"
, EFraction
NormalFrac
(ESubsup
(EIdentifier "e")
(EGrouped [])
(EGrouped [ ESymbol Bin "-" , ENumber "2" , EIdentifier "\960" ]))
(EGrouped
[ ENumber "1"
, ESymbol Bin "+"
, EFraction
NormalFrac
(ESubsup
(EIdentifier "e")
(EGrouped [])
(EGrouped [ ESymbol Bin "-" , ENumber "4" , EIdentifier "\960" ]))
(EGrouped
[ ENumber "1"
, ESymbol Bin "+"
, EFraction
NormalFrac
(ESubsup
(EIdentifier "e")
(EGrouped [])
(EGrouped [ ESymbol Bin "-" , ENumber "6" , EIdentifier "\960" ]))
(EGrouped
[ ENumber "1"
, ESymbol Bin "+"
, EFraction
NormalFrac
(ESubsup
(EIdentifier "e")
(EGrouped [])
(EGrouped
[ ESymbol Bin "-" , ENumber "8" , EIdentifier "\960" ]))
(EGrouped
[ ENumber "1" , ESymbol Bin "+" , ESymbol Ord "\8230" ])
])
])
])
]
]
]
, [ [ EText TextNormal "Another Ramanujan identity" ]
, [ EGrouped
[ EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "\8734")
, EFraction
NormalFrac
(ENumber "1")
(ESubsup
(ENumber "2")
(EGrouped [])
(EGrouped
[ ESymbol Open "\8970"
, EIdentifier "k"
, ESymbol Bin "\183"
, ESpace (0 % 1)
, EIdentifier "\966"
, ESymbol Close "\8971"
]))
, ESymbol Rel "="
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESubsup (ENumber "2") (EGrouped []) (ENumber "0")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESubsup (ENumber "2") (EGrouped []) (ENumber "1")
, ESymbol Bin "+"
, ESymbol Ord "\8943"
])
])
]
]
]
, [ [ EText TextNormal "Rogers-Ramanujan Identity" ]
, [ EGrouped
[ ENumber "1"
, ESymbol Bin "+"
, EGrouped
[ EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "\8734")
, EFraction
NormalFrac
(ESubsup
(EIdentifier "q")
(EGrouped [])
(EGrouped
[ ESubsup (EIdentifier "k") (EGrouped []) (ENumber "2")
, ESymbol Bin "+"
, EIdentifier "k"
]))
(EGrouped
[ ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, EIdentifier "q"
, ESymbol Close ")"
, ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, ESubsup (EIdentifier "q") (EGrouped []) (ENumber "2")
, ESymbol Close ")"
, ESymbol Ord "\8943"
, ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, ESubsup (EIdentifier "q") (EGrouped []) (EIdentifier "k")
, ESymbol Close ")"
])
]
, ESymbol Rel "="
, EGrouped
[ EUnderover
False
(ESymbol Op "\8719")
(EGrouped [ EIdentifier "j" , ESymbol Rel "=" , ENumber "0" ])
(EIdentifier "\8734")
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, ESubsup
(EIdentifier "q")
(EGrouped [])
(EGrouped
[ ENumber "5" , EIdentifier "j" , ESymbol Bin "+" , ENumber "2" ])
, ESymbol Close ")"
, ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, ESubsup
(EIdentifier "q")
(EGrouped [])
(EGrouped
[ ENumber "5" , EIdentifier "j" , ESymbol Bin "+" , ENumber "3" ])
, ESymbol Close ")"
])
]
, ESymbol Pun ","
, EText TextNormal "\8287\8202"
, EText TextNormal "\8287\8202"
, EGrouped [ EIdentifier "f" , EIdentifier "o" , EIdentifier "r" ]
, ESpace (2 % 9)
, ESymbol Op "|"
, EIdentifier "q"
, ESymbol Op "|"
, ESymbol Rel "<"
, ENumber "1"
, EIdentifier "."
]
]
]
, [ [ EText TextNormal "Commutative Diagram" ]
, [ EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EIdentifier "H" ]
, [ ESymbol Accent "\8592" ]
, [ EIdentifier "K" ]
]
, [ [ ESymbol Rel "\8595" ]
, [ ESpace (0 % 1) ]
, [ ESymbol Rel "\8593" ]
]
, [ [ EIdentifier "H" ]
, [ ESymbol Accent "\8594" ]
, [ EIdentifier "K" ]
]
]
]
]
]
]
>>> mml
<?xml version='1.0' ?>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mtable>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Bernoulli Trials</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<mrow>
<mi>P</mi>
<mo stretchy="false" form="prefix">(</mo>
<mi>E</mi>
<mo stretchy="false" form="postfix">)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo stretchy="true" form="prefix">(</mo>
<mfrac>
<mi>n</mi>
<mi>k</mi>
</mfrac>
<mo stretchy="true" form="postfix">)</mo>
</mrow>
<msubsup>
<mi>p</mi>
<mrow />
<mi>k</mi>
</msubsup>
<msubsup>
<mrow>
<mo stretchy="false" form="prefix">(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>p</mi>
<mo stretchy="false" form="postfix">)</mo>
</mrow>
<mrow />
<mrow>
<mi>n</mi>
<mo>-</mo>
<mi>k</mi>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Cauchy-Schwarz Inequality</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<msubsup>
<mrow>
<mo stretchy="true" form="prefix">(</mo>
<munderover>
<mo>∑</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>a</mi>
<mi>k</mi>
<mrow />
</msubsup>
<msubsup>
<mi>b</mi>
<mi>k</mi>
<mrow />
</msubsup>
<mo stretchy="true" form="postfix">)</mo>
</mrow>
<mrow />
<mn>2</mn>
</msubsup>
<mo>≤</mo>
<mrow>
<mo stretchy="true" form="prefix">(</mo>
<munderover>
<mo>∑</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>a</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo stretchy="true" form="postfix">)</mo>
</mrow>
<mrow>
<mo stretchy="true" form="prefix">(</mo>
<munderover>
<mo>∑</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>b</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo stretchy="true" form="postfix">)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Cauchy Formula</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<mi>f</mi>
<mo stretchy="false" form="prefix">(</mo>
<mi>z</mi>
<mo stretchy="false" form="postfix">)</mo>
<mspace width="0.167em" />
<mo>·</mo>
<msubsup>
<mi>Ind</mi>
<mi>γ</mi>
<mrow />
</msubsup>
<mo stretchy="false" form="prefix">(</mo>
<mi>z</mi>
<mo stretchy="false" form="postfix">)</mo>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mi>i</mi>
</mrow>
</mfrac>
<munderover>
<mo>∮</mo>
<mi>γ</mi>
<mrow />
</munderover>
<mfrac>
<mrow>
<mi>f</mi>
<mo stretchy="false" form="prefix">(</mo>
<mi>ξ</mi>
<mo stretchy="false" form="postfix">)</mo>
</mrow>
<mrow>
<mi>ξ</mi>
<mo>-</mo>
<mi>z</mi>
</mrow>
</mfrac>
<mspace width="0.167em" />
<mi>d</mi>
<mi>ξ</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Cross Product</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<msubsup>
<mi>V</mi>
<mn>1</mn>
<mrow />
</msubsup>
<mo>×</mo>
<msubsup>
<mi>V</mi>
<mn>2</mn>
<mrow />
</msubsup>
<mo>=</mo>
<mrow>
<mo stretchy="true" form="prefix">|</mo>
<mtable>
<mtr>
<mtd columnalign="center">
<mi>i</mi>
</mtd>
<mtd columnalign="center">
<mi>j</mi>
</mtd>
<mtd columnalign="center">
<mi>k</mi>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mfrac>
<mrow>
<mi>∂</mi>
<mi>X</mi>
</mrow>
<mrow>
<mi>∂</mi>
<mi>u</mi>
</mrow>
</mfrac>
</mtd>
<mtd columnalign="center">
<mfrac>
<mrow>
<mi>∂</mi>
<mi>Y</mi>
</mrow>
<mrow>
<mi>∂</mi>
<mi>u</mi>
</mrow>
</mfrac>
</mtd>
<mtd columnalign="center">
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mfrac>
<mrow>
<mi>∂</mi>
<mi>X</mi>
</mrow>
<mrow>
<mi>∂</mi>
<mi>v</mi>
</mrow>
</mfrac>
</mtd>
<mtd columnalign="center">
<mfrac>
<mrow>
<mi>∂</mi>
<mi>Y</mi>
</mrow>
<mrow>
<mi>∂</mi>
<mi>v</mi>
</mrow>
</mfrac>
</mtd>
<mtd columnalign="center">
<mn>0</mn>
</mtd>
</mtr>
</mtable>
<mo stretchy="true" form="postfix">|</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Vandermonde Determinant</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<mrow>
<mo stretchy="true" form="prefix">|</mo>
<mtable>
<mtr>
<mtd columnalign="center">
<mn>1</mn>
</mtd>
<mtd columnalign="center">
<mn>1</mn>
</mtd>
<mtd columnalign="center">
<mi>⋯</mi>
</mtd>
<mtd columnalign="center">
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<msubsup>
<mi>v</mi>
<mn>1</mn>
<mrow />
</msubsup>
</mtd>
<mtd columnalign="center">
<msubsup>
<mi>v</mi>
<mn>2</mn>
<mrow />
</msubsup>
</mtd>
<mtd columnalign="center">
<mi>⋯</mi>
</mtd>
<mtd columnalign="center">
<msubsup>
<mi>v</mi>
<mi>n</mi>
<mrow />
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<msubsup>
<mi>v</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mtd>
<mtd columnalign="center">
<msubsup>
<mi>v</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
</mtd>
<mtd columnalign="center">
<mi>⋯</mi>
</mtd>
<mtd columnalign="center">
<msubsup>
<mi>v</mi>
<mi>n</mi>
<mn>2</mn>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mo>⋮</mo>
</mtd>
<mtd columnalign="center">
<mo>⋮</mo>
</mtd>
<mtd columnalign="center">
<mo>⋱</mo>
</mtd>
<mtd columnalign="center">
<mo>⋮</mo>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<msubsup>
<mi>v</mi>
<mn>1</mn>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mtd>
<mtd columnalign="center">
<msubsup>
<mi>v</mi>
<mn>2</mn>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mtd>
<mtd columnalign="center">
<mi>⋯</mi>
</mtd>
<mtd columnalign="center">
<msubsup>
<mi>v</mi>
<mi>n</mi>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mtd>
</mtr>
</mtable>
<mo stretchy="true" form="postfix">|</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>∏</mo>
<mrow>
<mn>1</mn>
<mo>≤</mo>
<mi>i</mi>
<mo><</mo>
<mi>j</mi>
<mo>≤</mo>
<mi>n</mi>
</mrow>
<mrow />
</munderover>
<mo stretchy="false" form="prefix">(</mo>
<msubsup>
<mi>v</mi>
<mi>j</mi>
<mrow />
</msubsup>
<mo>-</mo>
<msubsup>
<mi>v</mi>
<mi>i</mi>
<mrow />
</msubsup>
<mo stretchy="false" form="postfix">)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Lorenz Equations</mtext>
</mtd>
<mtd columnalign="center">
<mtable>
<mtr>
<mtd columnalign="center">
<munderover>
<mi>x</mi>
<mrow />
<mo accent="true">˙</mo>
</munderover>
</mtd>
<mtd columnalign="center">
<mo>=</mo>
</mtd>
<mtd columnalign="center">
<mrow>
<mi>σ</mi>
<mo stretchy="false" form="prefix">(</mo>
<mi>y</mi>
<mo>-</mo>
<mi>x</mi>
<mo stretchy="false" form="postfix">)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<munderover>
<mi>y</mi>
<mrow />
<mo accent="true">˙</mo>
</munderover>
</mtd>
<mtd columnalign="center">
<mo>=</mo>
</mtd>
<mtd columnalign="center">
<mrow>
<mi>ρ</mi>
<mi>x</mi>
<mo>-</mo>
<mi>y</mi>
<mo>-</mo>
<mi>x</mi>
<mi>z</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<munderover>
<mi>z</mi>
<mrow />
<mo accent="true">˙</mo>
</munderover>
</mtd>
<mtd columnalign="center">
<mo>=</mo>
</mtd>
<mtd columnalign="center">
<mrow>
<mo>-</mo>
<mi>β</mi>
<mi>z</mi>
<mo>+</mo>
<mi>x</mi>
<mi>y</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Maxwell's Equations</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<mo stretchy="true" form="prefix">{</mo>
<mtable>
<mtr>
<mtd columnalign="center">
<mrow>
<mi>∇</mi>
<mspace width="0.0em" />
<mo>×</mo>
<munderover>
<mi>B</mi>
<mrow />
<mo accent="true">↼</mo>
</munderover>
<mo>-</mo>
<mspace width="0.167em" />
<mfrac>
<mn>1</mn>
<mi>c</mi>
</mfrac>
<mspace width="0.167em" />
<mfrac>
<mrow>
<mi>∂</mi>
<mspace width="0.0em" />
<munderover>
<mi>E</mi>
<mrow />
<mo accent="true">↼</mo>
</munderover>
</mrow>
<mrow>
<mi>∂</mi>
<mspace width="0.0em" />
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
<mtd columnalign="center">
<mo>=</mo>
</mtd>
<mtd columnalign="center">
<mrow>
<mfrac>
<mrow>
<mn>4</mn>
<mi>π</mi>
</mrow>
<mi>c</mi>
</mfrac>
<mspace width="0.167em" />
<munderover>
<mi>j</mi>
<mrow />
<mo accent="true">↼</mo>
</munderover>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mrow>
<mi>∇</mi>
<mspace width="0.0em" />
<mo>·</mo>
<munderover>
<mi>E</mi>
<mrow />
<mo accent="true">↼</mo>
</munderover>
</mrow>
</mtd>
<mtd columnalign="center">
<mo>=</mo>
</mtd>
<mtd columnalign="center">
<mrow>
<mn>4</mn>
<mi>π</mi>
<mi>ρ</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mrow>
<mi>∇</mi>
<mspace width="0.0em" />
<mo>×</mo>
<munderover>
<mi>E</mi>
<mrow />
<mo accent="true">↼</mo>
</munderover>
<mspace width="0.167em" />
<mo>+</mo>
<mspace width="0.167em" />
<mfrac>
<mn>1</mn>
<mi>c</mi>
</mfrac>
<mspace width="0.167em" />
<mfrac>
<mrow>
<mi>∂</mi>
<mspace width="0.0em" />
<munderover>
<mi>B</mi>
<mrow />
<mo accent="true">↼</mo>
</munderover>
</mrow>
<mrow>
<mi>∂</mi>
<mspace width="0.0em" />
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
<mtd columnalign="center">
<mo>=</mo>
</mtd>
<mtd columnalign="center">
<munderover>
<mn>0</mn>
<mrow />
<mo accent="true">↼</mo>
</munderover>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mrow>
<mi>∇</mi>
<mspace width="0.0em" />
<mo>·</mo>
<munderover>
<mi>B</mi>
<mrow />
<mo accent="true">↼</mo>
</munderover>
</mrow>
</mtd>
<mtd columnalign="center">
<mo>=</mo>
</mtd>
<mtd columnalign="center">
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Einstein Field Equations</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<msubsup>
<mi>R</mi>
<mrow>
<mi>μ</mi>
<mi>ν</mi>
</mrow>
<mrow />
</msubsup>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mspace width="0.167em" />
<msubsup>
<mi>g</mi>
<mrow>
<mi>μ</mi>
<mi>ν</mi>
</mrow>
<mrow />
</msubsup>
<mspace width="0.167em" />
<mi>R</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>8</mn>
<mi>π</mi>
<mi>G</mi>
</mrow>
<msubsup>
<mi>c</mi>
<mrow />
<mn>4</mn>
</msubsup>
</mfrac>
<mspace width="0.167em" />
<msubsup>
<mi>T</mi>
<mrow>
<mi>μ</mi>
<mi>ν</mi>
</mrow>
<mrow />
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Ramanujan Identity</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<mo stretchy="false" form="prefix">(</mo>
<msqrt>
<mrow>
<mi>φ</mi>
<msqrt>
<mn>5</mn>
</msqrt>
</mrow>
</msqrt>
<mo>-</mo>
<mi>φ</mi>
<mo stretchy="false" form="postfix">)</mo>
<msubsup>
<mi>e</mi>
<mrow />
<mfrac>
<mn>25</mn>
<mi>π</mi>
</mfrac>
</msubsup>
</mrow>
</mfrac>
<mo>=</mo>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<msubsup>
<mi>e</mi>
<mrow />
<mrow>
<mo>-</mo>
<mn>2</mn>
<mi>π</mi>
</mrow>
</msubsup>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<msubsup>
<mi>e</mi>
<mrow />
<mrow>
<mo>-</mo>
<mn>4</mn>
<mi>π</mi>
</mrow>
</msubsup>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<msubsup>
<mi>e</mi>
<mrow />
<mrow>
<mo>-</mo>
<mn>6</mn>
<mi>π</mi>
</mrow>
</msubsup>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<msubsup>
<mi>e</mi>
<mrow />
<mrow>
<mo>-</mo>
<mn>8</mn>
<mi>π</mi>
</mrow>
</msubsup>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mi>…</mi>
</mrow>
</mfrac>
</mrow>
</mfrac>
</mrow>
</mfrac>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Another Ramanujan identity</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<munderover>
<mo>∑</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>∞</mi>
</munderover>
<mfrac>
<mn>1</mn>
<msubsup>
<mn>2</mn>
<mrow />
<mrow>
<mo stretchy="false" form="prefix">⌊</mo>
<mi>k</mi>
<mo>·</mo>
<mspace width="0.0em" />
<mi>φ</mi>
<mo stretchy="false" form="postfix">⌋</mo>
</mrow>
</msubsup>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msubsup>
<mn>2</mn>
<mrow />
<mn>0</mn>
</msubsup>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msubsup>
<mn>2</mn>
<mrow />
<mn>1</mn>
</msubsup>
<mo>+</mo>
<mi>⋯</mi>
</mrow>
</mfrac>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Rogers-Ramanujan Identity</mtext>
</mtd>
<mtd columnalign="center">
<mrow>
<mn>1</mn>
<mo>+</mo>
<mrow>
<munderover>
<mo>∑</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>∞</mi>
</munderover>
<mfrac>
<msubsup>
<mi>q</mi>
<mrow />
<mrow>
<msubsup>
<mi>k</mi>
<mrow />
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mi>k</mi>
</mrow>
</msubsup>
<mrow>
<mo stretchy="false" form="prefix">(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>q</mi>
<mo stretchy="false" form="postfix">)</mo>
<mo stretchy="false" form="prefix">(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>q</mi>
<mrow />
<mn>2</mn>
</msubsup>
<mo stretchy="false" form="postfix">)</mo>
<mi>⋯</mi>
<mo stretchy="false" form="prefix">(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>q</mi>
<mrow />
<mi>k</mi>
</msubsup>
<mo stretchy="false" form="postfix">)</mo>
</mrow>
</mfrac>
</mrow>
<mo>=</mo>
<mrow>
<munderover>
<mo>∏</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>∞</mi>
</munderover>
<mfrac>
<mn>1</mn>
<mrow>
<mo stretchy="false" form="prefix">(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>q</mi>
<mrow />
<mrow>
<mn>5</mn>
<mi>j</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo stretchy="false" form="postfix">)</mo>
<mo stretchy="false" form="prefix">(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>q</mi>
<mrow />
<mrow>
<mn>5</mn>
<mi>j</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</msubsup>
<mo stretchy="false" form="postfix">)</mo>
</mrow>
</mfrac>
</mrow>
<mo>,</mo>
<mtext mathvariant="normal"> </mtext>
<mtext mathvariant="normal"> </mtext>
<mrow>
<mi>f</mi>
<mi>o</mi>
<mi>r</mi>
</mrow>
<mspace width="0.222em" />
<mo>|</mo>
<mi>q</mi>
<mo>|</mo>
<mo><</mo>
<mn>1</mn>
<mi>.</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mtext mathvariant="normal">Commutative Diagram</mtext>
</mtd>
<mtd columnalign="center">
<mtable>
<mtr>
<mtd columnalign="center">
<mi>H</mi>
</mtd>
<mtd columnalign="center">
<mo>←</mo>
</mtd>
<mtd columnalign="center">
<mi>K</mi>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mo>↓</mo>
</mtd>
<mtd columnalign="center">
<mspace width="0.0em" />
</mtd>
<mtd columnalign="center">
<mo>↑</mo>
</mtd>
</mtr>
<mtr>
<mtd columnalign="center">
<mi>H</mi>
</mtd>
<mtd columnalign="center">
<mo>→</mo>
</mtd>
<mtd columnalign="center">
<mi>K</mi>
</mtd>
</mtr>
</mtable>
</mtd>
</mtr>
</mtable>
</math>