to infinity. Consequently, p(∞) is always the value of its highest-degree coefficient (in the example above coefficient m2). In our Toom-3 example, we will use the points 0, 1, −1, −2, and ∞. These choices simplify evaluation, producing the formulas: and analogously for q. In our example, the values we get are: {| |- |p(0) || = || m0 || = || 56789012 || = ||align="right"| 56789012 |- |p(1) || = || m0 + m1 + m2 || = || 56789012 + 78901234 + 123456 || = ||align="right"| 135813702 |- |p(−1) || = || m0 − m1 + m2 || = || 56789012 − 78901234 + 123456 || = ||align="right"| −21988766 |- |p(−2) || = || m0 − 2m1 + 4m2 || = || 56789012 − 2 × 78901234 + 4 × 123456 || = ||align="right"| −100519632 |- |p(∞) || = || m2 || = || 123456 || = ||align="right"| 123456 |- |q(0) || = || n0 || = || 54321098 || = ||align="right"| 54321098 |- |q(1) || = || n0 + n1 + n2 || = || 54321098 + 43219876 + 98765 || = ||align="right"| 97639739 |- |q(−1) || = || n0 − n1 + n2 || = || 54321098 − 43219876 + 98765 || = ||align="right"| 11199987 |- |q(−2) || = || n0 − 2n1 + 4n2 || = || 54321098 − 2 × 43219876 + 4 × 98765 || = ||align="right"| −31723594 |- |q(∞) || = || n2 || = || 98765 || = ||align="right"| 98765. |} As shown, these values may be negative. For the purpose of later explanation, it will be useful to view this evaluation process as a matrix-vector multiplication, where each row of the matrix contains powers of one of the evaluation points, and the vector contains the coefficients of the polynomial: The dimensions of the matrix are d by km for p and d by kn for q. The row for infinity is always all zero except for a 1 in the last column. Faster evaluation Multipoint evaluation can be obtained faster than with the above formulas. The number of elementary operations (addition/subtraction) can be reduced. The sequence given by Bodrato for Toom-3, executed here over the first operand (polynomial p) of the running example is the following: {| |- |p0 || ← || m0 + m2 || = || 56789012 + 123456 || = ||align="right"| 56912468 |- |p(0) || = ||