The Power of Vocabulary: The Case of Cyclotomic Polynomials - Computer Science > Symbolic ComputationReport as inadecuate




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Abstract: We observe that the vocabulary used to construct the -answer- to problems incomputer algebra can have a dramatic effect on the computational complexity ofsolving that problem. We recall a formalization of this observation and explainthe classic example of sparse polynomial arithmetic. For this case, we showthat it is possible to extend the vocabulary so as reap the benefits ofconciseness whilst avoiding the obvious pitfall of repeating the problemstatement as the -solution-.It is possible to extend the vocabulary either by irreducible cyclotomics orby $x^n-1$: we look at the options and suggest that the pragmatist might optfor both.



Author: Jacques Carette, James H. Davenport

Source: https://arxiv.org/







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