be a power of 2 instead). Say the two integers being multiplied are: {| |m || = ||12||3456||7890||1234||5678||9012 |- |n || = |align=right|9||8765||4321||9876||5432||1098. |} These are much smaller than would normally be processed with Toom–Cook (grade-school multiplication would be faster) but they will serve to illustrate the algorithm. Splitting In Toom-k, we want to split the factors into k parts. The first step is to select the base B = bi, such that the number of digits of both m and n in base B is at most k (e.g., 3 in Toom-3). A typical choice for i is given by: In our example we'll be doing Toom-3, so we choose . We then separate m and n into their base B digits mi, ni: We then use these digits as coefficients in degree- polynomials p and q, with the property that p(B) = m and q(B) = n: The purpose of defining these polynomials is that if we can compute their product , our answer will be . In the case where the numbers being multiplied are of different sizes, it's useful to use different values of k for m and n, which we'll call km and kn. For example, the algorithm "Toom-2.5" refers to Toom–Cook with km = 3 and kn = 2. In this case the i in B = bi is typically chosen by: Evaluation The Toom–Cook approach to computing the polynomial product p(x)q(x) is a commonly used one. Note that a polynomial of degree d is uniquely determined by d + 1 points (for example, a line - polynomial of degree one is specified by two points). The idea is to evaluate p(·) and q(·) at various points. Then multiply their values at these points to get points on the product polynomial. Finally interpolate to find its coefficients. Since , we will need points to determine the final result. Call this d. In the case of Toom-3, d = 5. The algorithm will work no matter what points are chosen (with a few small exceptions, see matrix invertibility requirement in Interpolation), but in the interest of simplifying the algorithm it's better to choose small integer values like 0, 1, −1, and −2. One unusual point value that is frequently used is infinity, written ∞ or 1/0. To "evaluate" a polynomial p at infinity actually means to take the limit of p(x)/xdeg p as x goes