Algorithm for constructing symmetry-adapted functions

Reduce the equations by Gaussian elimination from right to left. 

Use back-substitution to determine the solution whose leading coefficient corresponds to the rightmost undetermined pivot element. Set this coefficient to unity. 

Append this solution vector to the set of equations and remove elements to the right of the new pivot element by Gauss elimination. 

Repeat to obtain a trapezoidal array of m orthogonal null vectors xfU), each with leading coefficient unity. 

The last line is the projection of the first basis function. 

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