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OreTools[Modular][RightPseudoQuotient] - compute the right pseudo-quotient of two Ore polynomials modulo a prime
OreTools[Modular][RightPseudoRemainder] - compute the right pseudo-remainder of two Ore polynomials modulo a prime
OreTools[Modular][RightQuotient] - compute the right quotient of two Ore polynomials modulo a prime
OreTools[Modular][RightRemainder] - compute the right remainder of two Ore polynomials modulo a prime
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Calling Sequence
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Modular[RightPseudoQuotient](Ore1, Ore2, p, A, 'm', 'R')
Modular[RightPseudoRemainder](Ore1, Ore2, p, 'm', 'Q')
Modular[RightQuotient](Ore1, Ore2, p, A, 'R')
Modular[RightRemainder](Ore1, Ore2, p, A, 'Q')
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Parameters
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Ore1, Ore2
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two 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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m, Q, R
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unevaluated names
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Description
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The Modular[RightPseudoQuotient](Ore1, Ore2, p, A, 'm', 'R') calling sequence computes the right pseudo-quotient of Ore1 and Ore2 modulo the prime p. If the fifth (optional) argument is present, it is assigned the multiplier. If the sixth (optional) argument is present, it is assigned the right pseudo-remainder of Ore1 and Ore2.
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The Modular[RightPseudoRemainder](Ore1, Ore2, p, A, 'm', 'Q') calling sequence computes the right pseudo-remainder of Ore1 and Ore2 modulo the prime p. If the fifth (optional) argument is present, it is assigned the multiplier. If the sixth (optional) argument is present, it is assigned the right pseudo-quotient of Ore1 and Ore2.
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The Modular[RightQuotient](Ore1, Ore2, p, A, ''R') calling sequence computes the right quotient of Ore1 and Ore2 modulo the prime p. If the fifth (optional) argument is present, it is assigned the right remainder of Ore1 and Ore2.
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The Modular[RightRemainder](Ore1, Ore2, p, A, 'Q') calling sequence computes the right remainder of Ore1 and Ore2 modulo the prime p. If the fifth (optional) argument is present, it is assigned the right quotient of Ore1 and Ore2.
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Examples
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](/support/helpjp/helpview.aspx?si=7372/file06379/math195.png)
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](/support/helpjp/helpview.aspx?si=7372/file06379/math202.png)
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Check the results.
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](/support/helpjp/helpview.aspx?si=7372/file06379/math211.png)
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](/support/helpjp/helpview.aspx?si=7372/file06379/math218.png)
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, R, 19)](/support/helpjp/helpview.aspx?si=7372/file06379/math225.png)
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](/support/helpjp/helpview.aspx?si=7372/file06379/math232.png)
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Check the results.
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](/support/helpjp/helpview.aspx?si=7372/file06379/math241.png)
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, R, 11)](/support/helpjp/helpview.aspx?si=7372/file06379/math248.png)
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](/support/helpjp/helpview.aspx?si=7372/file06379/math255.png)
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| (12) |
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