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OreTools[Modular][GCRD] - compute the GCRD of two Ore polynomials modulo a prime
OreTools[Modular][LCLM] - compute the LCLM of a sequence of Ore polynomials modulo a prime
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Calling Sequence
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Modular[GCRD](Ore1, Ore2, p, A)
Modular[LCLM](Ore1, Ore2, ..., Orek, p, A)
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Parameters
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Ore1, Ore2, ... Orek
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Ore polynomials; to define an Ore polynomial, use the OrePoly structure
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p
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prime
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A
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Ore ring; to define an Ore ring, use the SetOreRing command
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Description
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The Modular[GCRD](Ore1, Ore2, p, A) calling sequence returns the GCRD of Ore1 and Ore2 modulo the prime p.
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The Modular[LCLM](Ore1, Ore2, ..., Orek, p, A) calling sequence returns the GCRD of Ore1, Ore2, ..., Orek modulo the prime p.
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Examples
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](/support/helpjp/helpview.aspx?si=7374/file06381/math138.png)
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](/support/helpjp/helpview.aspx?si=7374/file06381/math145.png)
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](/support/helpjp/helpview.aspx?si=7374/file06381/math152.png)
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](/support/helpjp/helpview.aspx?si=7374/file06381/math159.png)
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References
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Abramov, S.A.; Le, H.Q.; and Li, Z. "OreTools: a computer algebra library for univariate Ore polynomial rings." Technical Report CS-2003-12. School of Computer Science, University of Waterloo, 2003.
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Li, Z., and Nemes, I. "A modular algorithm for computing greatest common right divisors of Ore polynomials." Proc. of ISSAC'97, pp. 282-289. Edited by W. Kuechlin. ACM Press, 1997.
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