Knuth–Eve algorithm: Difference between revisions

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While any <math>t \geq \text{Re}(r_2)</math> can work, it is possible to remove one addition during evaluation if <math>t</math> is also chosen such that two roots of <math>p(x + t)</math> are symmetric about the origin. In that case, <math>\alpha_1</math> can be chosen such that the shifted polynomial has a factor of <math>x^2 - \alpha_1</math>, so <math>\gamma_1 = 0</math>. It is always possible to find such a <math>t</math>.<ref name="eve1964"/>
 
One possible algorithm for choosing <math>t</math> is:{{cn|date=July 2025}}
 
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=== Evaluation step ===