## Abstract

In this paper we will classify all the minimal bilinear algorithms for computing the coefficients of (∑ i=0 n-1x_{i}u^{i})( ∑ i=0 n-1y_{i}u^{i}) mod Q(u)^{l} where deg Q(u)=j,jl=n and Q(u) is irreducible. The case where l=1 was studied in [1]. For l>1 the main results are that we have to distinguish between two cases: j>1 and j=1. The first case is discussed here while the second is classified in [4]. For j>1 it is shown that up to equivalence every minimal (2n-1 multiplications) bilinear algorithm for computing the coefficients of (∑ i=0 n-1x_{i}u^{i})( ∑ i=0 n-1y_{i}u^{i}) mod Q(u)^{l} is done by first computing the coefficients of (∑ i=0 n-1x_{i}u^{i})( ∑ i=0 n-1y_{i}u^{i}) and then reducing it modulo Q(u)^{l} (similar to the case l = 1, [1]).

Original language | English |
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Pages (from-to) | 17-56 |

Number of pages | 40 |

Journal | Theoretical Computer Science |

Volume | 58 |

Issue number | 1-3 |

DOIs | |

State | Published - Jun 1988 |

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