Re: how can I solve this with mathematica?
- To: mathgroup at smc.vnet.net
- Subject: [mg34883] Re: [mg34816] how can I solve this with mathematica?
- From: Tomas Garza <tgarza01 at prodigy.net.mx>
- Date: Tue, 11 Jun 2002 05:00:59 -0400 (EDT)
- References: <200206080921.FAA26123@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Easy. But you must first learn to use the proper parentheses and brackets
following the conventions in Mathematica.
In[1]:=
c = Sum[s[n, m]*Cos[p*(m + 1/2)*(Pi/Y)]*Cos[q*(n + 1/2)*(Pi/X)], {n, 0, X -
1}, {m, 0, Y - 1}];
In[2]:=
c /. {X -> 4, Y -> 4, p -> 0, q -> 0}
Out[2]=
s[0, 0] + s[0, 1] + s[0, 2] + s[0, 3] + s[1, 0] + s[1, 1] + s[1, 2] + s[1,
3] + s[2, 0] +
s[2, 1] + s[2, 2] + s[2, 3] + s[3, 0] + s[3, 1] + s[3, 2] + s[3, 3]
In[3]:=
c /. {X -> 4, Y -> 4, p -> 1, q -> 0}
Out[3]=
Cos[Pi/8]*s[0, 0] + Cos[(3*Pi)/8]*s[0, 1] + Cos[(5*Pi)/8]*s[0, 2] +
Cos[(7*Pi)/8]*s[0, 3] +
Cos[Pi/8]*s[1, 0] + Cos[(3*Pi)/8]*s[1, 1] + Cos[(5*Pi)/8]*s[1, 2] +
Cos[(7*Pi)/8]*s[1, 3] +
Cos[Pi/8]*s[2, 0] + Cos[(3*Pi)/8]*s[2, 1] + Cos[(5*Pi)/8]*s[2, 2] +
Cos[(7*Pi)/8]*s[2, 3] +
Cos[Pi/8]*s[3, 0] + Cos[(3*Pi)/8]*s[3, 1] + Cos[(5*Pi)/8]*s[3, 2] +
Cos[(7*Pi)/8]*s[3, 3]
etc.
Tomas Garza
Mexico City
----- Original Message -----
From: "daldosch" <daldosch at aon.at>
To: mathgroup at smc.vnet.net
Subject: [mg34883] [mg34816] how can I solve this with mathematica?
> How can I solve the following problem?
>
>
> (***********************************************************************
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> Mathematica-Compatible Notebook
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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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>
>
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>
>
>
> (***********************************************************************
> End of Mathematica Notebook file.
> ***********************************************************************)
>
- References:
- how can I solve this with mathematica?
- From: daldosch <daldosch@aon.at>
- how can I solve this with mathematica?