SumTools[Hypergeometric][RationalCanonicalForm] - construct four rational canonical forms of a rational function
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Calling Sequence
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RationalCanonicalForm[1](F, n)
RationalCanonicalForm[2](F, n)
RationalCanonicalForm[3](F, n)
RationalCanonicalForm[4](F, n)
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Parameters
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F
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rational function of n
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n
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variable
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Description
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Let F be a rational function of n over a field K of characteristic 0. The RationalCanonicalForm[i](F,n) calling sequence constructs the ith rational canonical forms for F, .
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If the RationalCanonicalForm command is called without an index, the first rational canonical form is constructed.
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1.
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2.
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for all integers k.
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3.
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, .
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Note: E is the automorphism of K(n) defined by .
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If then is minimal.
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If then is minimal.
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Examples
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Check the result from RationalCanonicalForm[1].
Condition 1 is satisfied.
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Condition 2 is satisfied.
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Condition 3 is satisfied.
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Degrees of the kernel:
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The degree of v1 is minimal.
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The degree of u2 is minimal.
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For , the degree of the shell is minimal.
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References
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Abramov, S.A.; Le, H.Q.; and Petkovsek, M. "Rational Canonical Forms and Efficient Representations of Hypergeometric Terms." Proc. ISSAC'2003, pp. 7-14. 2003.
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Abramov, S.A., and Petkovsek, M. "Canonical representations of hypergeometric terms." Proc. FPSAC'2001, pp. 1-10. 2001.
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