Re: Variables names
- To: mathgroup at smc.vnet.net
- Subject: [mg15086] Re: Variables names
- From: Leszek Sczaniecki <lsczan at concentric.net>
- Date: Thu, 10 Dec 1998 03:13:15 -0500
- Organization: Concentric Internet Services
- References: <74ld6o$sdk@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Way to complicated. Try this
M = Table[ToExpression["A"<>ToString[i]<>ToString[j]], {i, 5}, {j, 5}];
X = Table[ToExpression["x"<>ToString[i]], {i, 5}]; X.M.X // Expand
-Leszek
Andrzej Kozlowski wrote:
> On Sat, Dec 5, 1998, Kim Allemand <kim.allemand at epfl.ch> wrote:
>
> >Hi,
> >I have a square matrix Q of dimension N and would like to generate the
> >quadratic function $\sum_{i,j}q_{ij}x_i x_j$. The problem is how to say
> >to Mathamatica that the variables names are x1, x2, etc. Is it possible
> >to generate variables names in an automatic way? A possibility would be
> >to generate manually a vector NN={x1, x2, x3, ....} of dimension N and
> >then to pick NN[[i]] for the ith variable name, but imagine when
> >N=1000... !!
> >Thanks, Kim
> >
>
> Well, if you don't mind rather messy notation (x111 for x_3 etc) than
> the following will do it:
>
> reindex[i_]:=ToExpression[ToString[i]<>"1"] reindex[i_,0]:=i
> reindex[i_,n_]:=reindex[reindex[i,n-1]]
> indexlist[a_,n_]:=NestList[reindex,reindex[a],n-1]
>
> quadratic[q_,x_,n_]:=
>
> Flatten[Outer[Times,indexlist[x,n],indexlist[x,n]]].Flatten[Array[q,{n,n}]]
>
> In[32]:=
> quadratic[q,x,6]
>
> Out[32]=
> 2
> x1 q[1, 1] + x1 x11 q[1, 2] + x1 x111 q[1, 3] +
>
> x1 x1111 q[1, 4] + x1 x11111 q[1, 5] +
>
> 2
> x1 x111111 q[1, 6] + x1 x11 q[2, 1] + x11 q[2, 2] +
>
> x11 x111 q[2, 3] + x11 x1111 q[2, 4] +
>
> x11 x11111 q[2, 5] + x11 x111111 q[2, 6] +
>
> 2
> x1 x111 q[3, 1] + x11 x111 q[3, 2] + x111 q[3, 3] +
>
> x111 x1111 q[3, 4] + x111 x11111 q[3, 5] +
>
> x111 x111111 q[3, 6] + x1 x1111 q[4, 1] +
>
> 2
> x11 x1111 q[4, 2] + x111 x1111 q[4, 3] + x1111 q[4, 4] +
>
> x1111 x11111 q[4, 5] + x1111 x111111 q[4, 6] +
>
> x1 x11111 q[5, 1] + x11 x11111 q[5, 2] +
>
> x111 x11111 q[5, 3] + x1111 x11111 q[5, 4] +
>
> 2
> x11111 q[5, 5] + x11111 x111111 q[5, 6] +
>
> x1 x111111 q[6, 1] + x11 x111111 q[6, 2] +
>
> x111 x111111 q[6, 3] + x1111 x111111 q[6, 4] +
>
> 2
> x11111 x111111 q[6, 5] + x111111 q[6, 6]
>
> Andrzej Kozlowski
> Toyama International University
> JAPAN
> http://sigma.tuins.ac.jp/
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<tt>Way to complicated. Try this</tt><tt></tt> <p><tt>M =
Table[ToExpression["A"<>ToString[i]<>ToString[j]], {i, 5}, {j,
5}];</tt>
<br><tt>X = Table[ToExpression["x"<>ToString[i]], {i, 5}];</tt>
<br><tt>X.M.X // Expand</tt><tt></tt> <p><tt>-Leszek</tt><tt></tt>
<p>Andrzej Kozlowski wrote:
<blockquote TYPE=CITE>On Sat, Dec 5, 1998, Kim Allemand
<kim.allemand at epfl.ch> wrote:
<p>>Hi,
<br>>I have a square matrix Q of dimension N and would like to generate
the
<br>>quadratic function $\sum_{i,j}q_{ij}x_i x_j$. The problem is how to
say
<br>>to Mathamatica that the variables names are x1, x2, etc. Is it
possible <br>>to generate variables names in an automatic way? A
possibility would be
<br>>to generate manually a vector NN={x1, x2, x3, ....} of dimension N
and
<br>>then to pick NN[[i]] for the ith variable name, but imagine when
<br>>N=1000... !!
<br>>Thanks, Kim
<br>>
<p>Well, if you don't mind rather messy notation (x111 for x_3 etc) than
<br>the following will do it:
<p>reindex[i_]:=ToExpression[ToString[i]<>"1"] reindex[i_,0]:=i
<br>reindex[i_,n_]:=reindex[reindex[i,n-1]]
<br>indexlist[a_,n_]:=NestList[reindex,reindex[a],n-1]
<p>quadratic[q_,x_,n_]:=
<p>Flatten[Outer[Times,indexlist[x,n],indexlist[x,n]]].Flatten[Array[q,{n,n}]]
<p>In[32]:=
<br>quadratic[q,x,6]
<p>Out[32]=
<br> 2
<br>x1 q[1, 1] + x1 x11 q[1, 2] + x1 x111 q[1, 3] + <p> x1
x1111 q[1, 4] + x1 x11111 q[1, 5] +
<p>
2
<br> x1 x111111 q[1, 6] + x1 x11 q[2, 1] + x11 q[2, 2] +
<p> x11 x111 q[2, 3] + x11 x1111 q[2, 4] + <p> x11 x11111
q[2, 5] + x11 x111111 q[2, 6] +
<p>
2
<br> x1 x111 q[3, 1] + x11 x111 q[3, 2] + x111 q[3, 3] +
<p> x111 x1111 q[3, 4] + x111 x11111 q[3, 5] + <p> x111
x111111 q[3, 6] + x1 x1111 q[4, 1] +
<p>
2
<br> x11 x1111 q[4, 2] + x111 x1111 q[4, 3] + x1111 q[4, 4]
+
<p> x1111 x11111 q[4, 5] + x1111 x111111 q[4, 6] + <p> x1
x11111 q[5, 1] + x11 x11111 q[5, 2] + <p> x111 x11111 q[5, 3] +
x1111 x11111 q[5, 4] + <p> 2
<br> x11111 q[5, 5] + x11111 x111111 q[5, 6] + <p> x1
x111111 q[6, 1] + x11 x111111 q[6, 2] + <p> x111 x111111 q[6, 3]
+ x1111 x111111 q[6, 4] +
<p>
2
<br> x11111 x111111 q[6, 5] + x111111 q[6, 6] <p>Andrzej
Kozlowski
<br>Toyama International University
<br>JAPAN
<br><a
href="http://sigma.tuins.ac.jp/";>http://sigma.tuins.ac.jp/</a></blockquote>
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