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We present a simple and fast algorithm to test the thermodynamic stability and determine the necessary chemical environment for the production of a multiternary material, relative to competing phases and compounds formed from the constituent elements. If the material is found to be stable, the region of stability, in terms of the constituent elemental chemical potentials, is determined from the intersection points of hypersurfaces in an (n− 1)-dimensional chemical potential space, where n is the number of atomic species in the material. The input required is the free energy of formation of the material itself, and that of all competing phases. Output consists of the result of the test of stability, the intersection points in the chemical potential space and the competing phase to which they relate, and, for two-and three-dimensional spaces, a file which may be used for visualization of the stability region. We specify the use of the …