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The short product of two power series is the meaningful part of the product of these objects, i.e., i+ j <n a i b j x i+ j . Mulders (AAECC 11 (2000) 69) gives an algorithm to compute a short product faster than the full product in the case of Karatsuba's multiplication (Karatsuba and Ofman, Dokl. Akad. Nauk SSSR 145 (1962) 293 ). This algorithm works by selecting a cutoff point k and performing a full k × k product and two (n − k) × (n − k) short products recursively. Mulders also gives adoi:10.1016/j.jsc.2003.03.001 fatcat:rjkerdngsnfnnoyd2owk6rtdtq