# procedures E_I, E_II, E_III;  packable
# Copyright: Erich Kaltofen

alias(E_I = `refpkg/E_I`, E_II = `refpkg/E_II`, E_III = `refpkg/E_III`);

`refpkg/E_I` := proc(n, i, j)
   # create an n times n elementary matrix of the first kind
   # matrix swaps row (col) i and j
   RETURN(linalg[swaprow](array(identity, 1..n,1..n), i, j));
end:

`refpkg/E_II` := proc(n, i, alpha)
   # create an n times n elementary matrix of the second kind
   # matrix multiplies row (col) i with alpha
   RETURN(linalg[mulrow](array(identity, 1..n,1..n), i, alpha));
end:

`refpkg/E_III` := proc(n, i, j, alpha)
   # create an n times n elementary matrix of the third kind
   # matrix adds alpha*row i (col j) to row j (col i)
   RETURN(linalg[addrow](array(identity, 1..n,1..n), i, j, alpha));
   end: