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<A NAME=hilbert>

<TITLE>hilbert</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>HILBERT</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
<P>
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 <P> <H3> 
syntax: </H3>
<em>hilbert</em>(&lt;square\_size&gt;,&lt;expr&gt;) 
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<P>
<P>
&lt;square\_size&gt; :- a positive integer. 
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&lt;expr&gt; :- an algebraic expression. 
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<P>
<em>hilbert</em>computes the square hilbert matrix of dimension 
&lt;square\_size&gt;. 
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This is the symmetric matrix in which the (i,j)'th entry is 
1/(i+j-&lt;expr&gt;). 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>

hilbert(3,y+x); 

  [    - 1          - 1          - 1    ]
  [-----------  -----------  -----------]
  [ x + y - 2    x + y - 3    x + y - 4 ]
  [                                     ]
  [    - 1          - 1          - 1    ]
  [-----------  -----------  -----------]
  [ x + y - 3    x + y - 4    x + y - 5 ]
  [                                     ]
  [    - 1          - 1          - 1    ]
  [-----------  -----------  -----------]
  [ x + y - 4    x + y - 5    x + y - 6 ]

</TT></PRE><P>