Ewald summation rewrites the interaction potential as the sum of two terms, φ φ ( r ) = d e f φ φ s r ( r ) + φ φ ℓ ℓ r ( r ) , where φ φ s r ( r ) represents the short-range term whose sum quickly converges in real space and φ φ ℓ ℓ r ( r ) represents the long-range term whose sum quickly converges in Fourier (reciprocal) space. The long-ranged part should be finite for all arguments (most notably r = 0) but may have any convenient mathematical form, most typically a Gaussian distribution. The method assumes that the short-range part can be summed easily; hence, the problem becomes the summation of the long-range term. Due to the use of the Fourier sum, the method implicitly assumes that the system under study is infinitely periodic (a sensible assumption for the interiors of crystals). One repeating unit of this hypothetical periodic system is called a unit cell. One such cell is chosen as the "central cell" for reference and the remaining cells are called images.