sphere_volume.test

<<< native
[ EIdentifier "S"
, ESymbol Rel "="
, ESymbol Open "{"
, ENumber "0"
, ESymbol Rel "\8804"
, EIdentifier "\981"
, ESymbol Rel "\8804"
, ENumber "2"
, EIdentifier "\960"
, ESymbol Pun ","
, ESpace (2 % 9)
, ENumber "0"
, ESymbol Rel "\8804"
, EIdentifier "\952"
, ESymbol Rel "\8804"
, EIdentifier "\960"
, ESymbol Pun ","
, ESpace (2 % 9)
, ENumber "0"
, ESymbol Rel "\8804"
, EIdentifier "\961"
, ESymbol Rel "\8804"
, EIdentifier "R"
, ESymbol Close "}"
, EArray
    [ AlignRight , AlignLeft ]
    [ [ [ EStyled
            TextNormal
            [ EIdentifier "V"
            , EIdentifier "o"
            , EIdentifier "l"
            , EIdentifier "u"
            , EIdentifier "m"
            , EIdentifier "e"
            ]
        ]
      , [ ESymbol Rel "="
        , EUnder False (ESymbol Op "\8749") (EIdentifier "S")
        , ESpace ((-1) % 6)
        , ESuper (EIdentifier "\961") (ENumber "2")
        , EMathOperator "sin"
        , EIdentifier "\952"
        , ESpace (1 % 6)
        , EStyled TextNormal [ EIdentifier "d" ]
        , EIdentifier "\961"
        , ESpace (1 % 6)
        , EStyled TextNormal [ EIdentifier "d" ]
        , EIdentifier "\952"
        , ESpace (1 % 6)
        , EStyled TextNormal [ EIdentifier "d" ]
        , EIdentifier "\981"
        ]
      ]
    , [ []
      , [ ESymbol Rel "="
        , ESubsup
            (ESymbol Op "\8747")
            (ENumber "0")
            (EGrouped [ ENumber "2" , EIdentifier "\960" ])
        , ESpace ((-1) % 6)
        , EStyled TextNormal [ EIdentifier "d" ]
        , EIdentifier "\981"
        , ESpace (1 % 6)
        , ESubsup (ESymbol Op "\8747") (ENumber "0") (EIdentifier "\960")
        , ESpace ((-1) % 6)
        , EMathOperator "sin"
        , EIdentifier "\952"
        , ESpace (1 % 6)
        , EStyled TextNormal [ EIdentifier "d" ]
        , EIdentifier "\952"
        , ESpace (1 % 6)
        , ESubsup (ESymbol Op "\8747") (ENumber "0") (EIdentifier "R")
        , ESpace ((-1) % 6)
        , ESuper (EIdentifier "\961") (ENumber "2")
        , EStyled TextNormal [ EIdentifier "d" ]
        , EIdentifier "\961"
        ]
      ]
    , [ []
      , [ ESymbol Rel "="
        , EIdentifier "\981"
        , ESubsup
            (EScaled (9 % 5) (ESymbol Open "|"))
            (ENumber "0")
            (EGrouped [ ENumber "2" , EIdentifier "\960" ])
        , ESpace (2 % 9)
        , ESymbol Open "("
        , ESymbol Ord "\8722"
        , EMathOperator "cos"
        , EIdentifier "\952"
        , ESymbol Close ")"
        , ESubsup
            (EScaled (9 % 5) (ESymbol Open "|"))
            (ENumber "0")
            (EIdentifier "\960")
        , ESpace (2 % 9)
        , EFraction InlineFrac (ENumber "1") (ENumber "3")
        , ESuper (EIdentifier "\961") (ENumber "3")
        , ESubsup
            (EScaled (9 % 5) (ESymbol Open "|"))
            (ENumber "0")
            (EIdentifier "R")
        ]
      ]
    , [ []
      , [ ESymbol Rel "="
        , ENumber "2"
        , EIdentifier "\960"
        , ESymbol Bin "\215"
        , ENumber "2"
        , ESymbol Bin "\215"
        , EFraction InlineFrac (ENumber "1") (ENumber "3")
        , ESuper (EIdentifier "R") (ENumber "3")
        ]
      ]
    , [ []
      , [ ESymbol Rel "="
        , EFraction InlineFrac (ENumber "4") (ENumber "3")
        , EIdentifier "\960"
        , ESuper (EIdentifier "R") (ENumber "3")
        ]
      ]
    ]
]
>>> starmath
S = left lbrace 0 <= %iphi <= 2%ipi , 0 <= %itheta <= %ipi , 0 <= %irho <= R right rbrace matrix { alignr "Volume" # alignl {} = iiint from S %irho^2 sin %itheta nitalic d%irho nitalic d%itheta nitalic d%iphi ## alignr {} # alignl {} = int_0^{{2%ipi}} nitalic d%iphi int_0^%ipi sin %itheta nitalic d%itheta int_0^R %irho^2 nitalic d%irho ## alignr {} # alignl {} = {left none %iphi right rline}_0^{{2%ipi}} {left none left ( - cos %itheta right ) right rline}_0^%ipi size*0.7 {{alignc 1} over {alignc 3}}{left none %irho^3 right rline}_0^R ## alignr {} # alignl {} = 2%ipi times 2 times size*0.7 {{alignc 1} over {alignc 3}}R^3 ## alignr {} # alignl {} = size*0.7 {{alignc 4} over {alignc 3}}%ipi R^3 }