diffalg[differential_sprem] - return sparse pseudo remainder of a differential polynomial
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Calling Sequence
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differential_sprem (q, L, R, 'h')
differential_sprem (q, C, 'h')
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Parameters
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q
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differential polynomial in R
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L
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list or a set of differential polynomials in R
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C
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characterizable differential ideal
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R
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differential polynomial ring
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h
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(optional) name
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Description
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The function differential_sprem is an implementation of Ritt's reduction algorithm. It is an extension of the pseudo-remainder algorithm to differential polynomials.
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The function differential_sprem returns a differential polynomial r such that
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(a)
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(b) No proper derivative of the leaders of the elements of appears in .
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(d) The differential polynomial h is a power product of factors of the initials and the separants of the elements of A.
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The differential_sprem(q, L, R, 'h') calling sequence returns an error message if contains 0. If contains a non zero element of the ground field of R, it returns zero.
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The differential_sprem(q, C, 'h') calling sequence requires that q belong to the differential ring in which C is defined.
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The function rewrite_rules shows how the equations of C are interpreted by the pseudo-reduction algorithm.
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Then r is zero if and only if q belongs to C.
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The command with(diffalg,differential_sprem) allows the use of the abbreviated form of this command.
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Examples
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Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.
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Differential pseudo-division by a single differential polynomial:
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Reduction according to a characterizable differential ideal:
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