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MathGroup Archive 2002

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how can I solve this with mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34816] how can I solve this with mathematica?
  • From: daldosch <daldosch at aon.at>
  • Date: Sat, 8 Jun 2002 05:21:28 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

How can I solve the following problem?


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Notebook[{
Cell[BoxData[
    \(c = 
      \(\[Sum]\+\(n = 0\)\%\(X - 1
              \)\(\[Sum]\+\(m = 0\)\%\(Y - 1\){
                s \((n, m)\)*cos \((p \((m + 1\/2)\) \[Pi]\/Y)\)*cos 
                  \((q \((n + 1\/2)\) \[Pi]\/X)\)}\n\t\nX\) = 4\), Y = 4\ , 
    0 \[LessEqual] n \[GreaterEqual] 3, 0 \[LessEqual] m \[GreaterEqual] 3, 
    0 \[LessEqual] p \[GreaterEqual] 3, 
    0 \[LessEqual] q \[GreaterEqual] 3\)], "Input"],

Cell[BoxData[
    \(how\ can\ I\ get\ a\ result\ like\ the\ \(following\ ?\)\)], "Input"],

Cell[BoxData[{
    \(for\ p = 0, q = 0\), 
    \(c \((0, 0)\) = {\n
        s \((0, 0)\)*cos \((0)\)*cos \((0)\) + 
          s \((0, 1)\)*cos \((0)\)*cos \((0)\) + 
          s \((0, 2)\)*cos \((0)\)*cos \((0)\) + 
          s \((0, 3)\)*cos \((0)\)*cos \((0)\) + \n
          s \((1, 0)\)*cos \((0)\)*cos \((0)\) + 
          s \((1, 1)\)*cos \((0)\)*cos \((0)\) + 
          s \((1, 2)\)*cos \((0)\)*cos \((0)\) + 
          s \((1, 3)\)*cos \((0)\)*cos \((0)\) + \n
          s \((2, 0)\)*cos \((0)\)*cos \((0)\) + 
          s \((2, 1)\)*cos \((0)\)*cos \((0)\) + 
          s \((2, 2)\)*cos \((0)\)*cos \((0)\) + 
          s \((2, 3)\)*cos \((0)\)*cos \((0)\) + \n
          s \((3, 0)\)*cos \((0)\)*cos \((0)\) + 
          s \((3, 1)\)*cos \((0)\)*cos \((0)\) + 
          s \((3, 2)\)*cos \((0)\)*cos \((0)\) + 
          s \((3, 3)\)*cos \((0)\)*cos \((0)\)}\n\t\), 
    \(for\ p = 1, q = 0\), 
    \(c = 
      \(\((1, 0)\) = {\n\t
          \(\(\(\(\(\(\({s \((0, 0)\)*cos 
                                \((1 \((0 + 1\/2)\) \[Pi]\/4*cos \((0)\) + 
                                    s \((0, 1)\)*cos 
                                      \((1 \((1 + 1\/2)\) \[Pi]\/4*cos 
                                        \((0)\) + \n\t\t
                                        s \((0, 2)\)*cos 
                                        \((1 \((2 + 1\/2)\) \[Pi]\/4*cos 
                                        \((0)\) + 
                                        s \((0, 3)\)*cos 
                                        \((1 \((3 + 1\/2)\) \[Pi]\/4*cos 
                                        \((0)\) + \n\ \t
                                        s \((1, 0)\)*cos 
                                        \((1 \((0 + 1\/2)\) \[Pi]\/4*cos 
                                        \((0)\) + s \((1, 1)\)*cos 
                                        \((1 \((1 + 1\/2)\) \[Pi]\/4*cos 
                                        \((0)\) + \n\t\ts \((1, 2)\)*cos 
                                        \((1 \((2 + 1\/2)\) \[Pi]\/4*cos \((0)
                                        \) + s \((1, 3)\)*cos \((1 \((3 + 
                                        1\/2)\) \[Pi]\/4*cos \((0)\) + \n\t\ 
                                        s \((2, 0)\)*cos \((1 \((0 + 1\/2)\) 
                                        \[Pi]\/4*cos \((0)\) + s \((2, 
                                        1)\)*cos \((1 \((1 + 1\/2)\) 
                                        \[Pi]\/4*cos \((0)\) + \n\t\ts \((2, 
                                        2)\)*cos \((1 \((2 + 1\/2)\) 
                                        \[Pi]\/4*cos \((0)\) + s \((2, 
                                        3)\)*cos \((1 \((3 + 1\/2)\) 
                                        \[Pi]\/4*cos \((0)\) + \t\n\t\ s 
                                        \((3, 0)\)*cos \((1 \((0 + 1\/2)\) 
                                        \[Pi]\/4*cos \((0)\) + s \((3, 
                                        1)\)*cos \((1 \((1 + 1\/2)\) 
                                        \[Pi]\/4*cos \((0)\) + \n\t\ts \((3, 
                                        2)\)*cos \((1 \((2 + 1\/2)\) 
                                        \[Pi]\/4*cos \((0)\) + s \((3, 
                                        3)\)*cos \((1 \((3 + 1\/2)\) 
                                        \[Pi]\/4*cos 
                                        \((0)
                                        \)\)\)\)\)\)\)\)\)\)\)\)\)\)\)\)\)}
                              \t\t\t\t\n
                            \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\
\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t ... \) ... \) ... 
                        \) ... \) ... \) ... \) ... \)\n\t\t\tfor\ p = 1, 
          q = 1\t\t\t\n\t\t\ts \((0, 0)\)*cos 
              \((1 \((0 + 1\/2)\) \[Pi]\/4*cos 
                  \((1 \((0 + 1\/2)\) \[Pi]\/4 + \n\t\t\t
                      s \((1, 0)\)*cos 
                        \((1 \((0 + 1\/2)\) \[Pi]\/4*cos 
                            \((\(\(\(1 \((1 + 1\/2)\) \[Pi]\/4 ... \) ... 
                                    \) ...  . 
                                \)\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\
\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\)\)\)\)\)\)}], "Input"]
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