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genericSymmetricMatrix(R,x,n) -- make a symmetric n by n matrix whose entries on and above the diagonal are the variables of R, starting with the variable x.

Code:

     -- ../../../Macaulay2/m2/genmat.m2:29-36
     genericSymmetricMatrix = (R,first,n) -> (
          first = getIndex(R,first);
          vars := new MutableHashTable;
          nextvar := first;
          scan(0..n-1, i -> scan(i..n-1, j -> (
                         vars#(i,j) = R_nextvar; 
                         nextvar = nextvar+1)));
          matrix table(n,n, (i,j) -> if i>j then vars#(j,i) else vars#(i,j)))

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