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- W4285100391 abstract "We propose a new computational proof for the division algorithm that, using vector algebra, generalizes the remainder theorem to divisions for polynomials of any degree over a generic integral domain. Then, we extend this result to calculate the pseudo-divisions. Later, starting from the previous theorems, we obtain some algorithms that calculate the pseudo-remainder and the pseudo-quotient while avoiding long division. Finally, we provide examples and comparisons indicating that these algorithms are efficient in divisions by sparse polynomials and their divisors, as cyclotomic polynomials." @default.
- W4285100391 created "2022-07-14" @default.
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- W4285100391 date "2022-06-24" @default.
- W4285100391 modified "2023-09-25" @default.
- W4285100391 title "A vectorial approach to generalize the remainder theorem" @default.
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- W4285100391 doi "https://doi.org/10.52846/ami.v49i1.1478" @default.
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