texmath-0.12.5: test/writer/eqn/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" ]
]
]
]
]
]
]
>>> eqn
matrix{
ccol{ {roman "Bernoulli Trials"} above {roman "Cauchy-Schwarz Inequality"} above {roman "Cauchy Formula"} above {roman "Cross Product"} above {roman "Vandermonde Determinant"} above {roman "Lorenz Equations"} above {roman "Maxwell's Equations"} above {roman "Einstein Field Equations"} above {roman "Ramanujan Identity"} above {roman "Another Ramanujan identity"} above {roman "Rogers-Ramanujan Identity"} above {roman "Commutative Diagram"} }
ccol{ {{P ( E )} = left ( n over k right ) p sub {} sup k {( 1 - p )} sub {} sup {n - k}} above {{left ( sum from {k = 1} to n a sub k sup {} b sub k sup {} right )} sub {} sup 2 <= left ( sum from {k = 1} to n a sub k sup 2 right ) left ( sum from {k = 1} to n b sub k sup 2 right )} above {f ( z ) ^ cdot Ind sub gamma sup {} ( z ) = 1 over {2 pi i} \[u222E] from gamma to {} {f ( xi )} over {xi - z} ^ d xi} above {V sub 1 sup {} times V sub 2 sup {} = left | matrix{
ccol{ i above {{partial X} over {partial u}} above {{partial X} over {partial v}} }
ccol{ j above {{partial Y} over {partial u}} above {{partial Y} over {partial v}} }
ccol{ k above 0 above 0 }
} right |} above {left | matrix{
ccol{ 1 above {v sub 1 sup {}} above {v sub 1 sup 2} above \[u22EE] above {v sub 1 sup {n - 1}} }
ccol{ 1 above {v sub 2 sup {}} above {v sub 2 sup 2} above \[u22EE] above {v sub 2 sup {n - 1}} }
ccol{ \[u22EF] above \[u22EF] above \[u22EF] above \[u22F1] above \[u22EF] }
ccol{ 1 above {v sub n sup {}} above {v sub n sup 2} above \[u22EE] above {v sub n sup {n - 1}} }
} right | = prod from {1 <= i < j <= n} to {} ( v sub j sup {} - v sub i sup {} )} above {matrix{
ccol{ {{x from {}} to \[u02D9]} above {{y from {}} to \[u02D9]} above {{z from {}} to \[u02D9]} }
ccol{ = above = above = }
ccol{ {sigma ( y - x )} above {rho x - y - x z} above {- beta z + x y} }
}} above {left { matrix{
ccol{ {grad fwd 0 times {B from {}} to \[u21BC] - ^ 1 over c ^ {partial fwd 0 {E from {}} to \[u21BC]} over {partial fwd 0 t}} above {grad fwd 0 cdot {E from {}} to \[u21BC]} above {grad fwd 0 times {E from {}} to \[u21BC] ^ + ^ 1 over c ^ {partial fwd 0 {B from {}} to \[u21BC]} over {partial fwd 0 t}} above {grad fwd 0 cdot {B from {}} to \[u21BC]} }
ccol{ = above = above = above = }
ccol{ {{4 pi} over c ^ {j from {}} to \[u21BC]} above {4 pi rho} above {{0 from {}} to \[u21BC]} above 0 }
} right ""} above {R sub {mu nu} sup {} - 1 over 2 ^ g sub {mu nu} sup {} ^ R = {8 pi G} over {c sub {} sup 4} ^ T sub {mu nu} sup {}} above {1 over {( sqrt {varphi sqrt 5} - varphi ) e sub {} sup {25 over pi}} = 1 + {e sub {} sup {- 2 pi}} over {1 + {e sub {} sup {- 4 pi}} over {1 + {e sub {} sup {- 6 pi}} over {1 + {e sub {} sup {- 8 pi}} over {1 + ...}}}}} above {sum from {k = 1} to inf 1 over {2 sub {} sup {\[u230A] k cdot fwd 0 varphi \[u230B]}} = 1 over {2 sub {} sup 0 + 1 over {2 sub {} sup 1 + \[u22EF]}}} above {1 + {sum from {k = 1} to inf {q sub {} sup {k sub {} sup 2 + k}} over {( 1 - q ) ( 1 - q sub {} sup 2 ) \[u22EF] ( 1 - q sub {} sup k )}} = {prod from {j = 0} to inf 1 over {( 1 - q sub {} sup {5 j + 2} ) ( 1 - q sub {} sup {5 j + 3} )}} , roman " " roman " " {f o r} ~ | q | < 1 .} above {matrix{
ccol{ H above \[u2193] above H }
ccol{ <- above {fwd 0} above -> }
ccol{ K above \[u2191] above K }
}} }
}