Procedure from library linalg.lib (see linalg_lib).
linalg.lib
sym_gauss(A); A = symmetric matrix
matrix, diagonalisation with symmetric gauss algorithm
Example:
LIB "linalg.lib"; ring r=0,(x),lp; matrix A[2][2]=1,4,4,15; print(A); print(sym_gauss(A));