HILBERT _ _ _ _ _ _ _ _ _ _ _ _ operator

syntax:

<square\_size> :- a positive integer.

<expr> :- an algebraic expression.

hilbertcomputes the square hilbert matrix of dimension <square\_size>.

This is the symmetric matrix in which the (i,j)'th entry is 1/(i+j-<expr>).

examples:

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 ]