diffalg[reduced] - test if a differential polynomial is reduced with respect to a set of differential polynomials
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Calling Sequence
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reduced (p, F, R, code)
reduced (p, P, code)
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Parameters
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p
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differential polynomial in R
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F
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differential polynomial or list/set of differential polynomials in R
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R
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differential polynomial ring
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code
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(optional) name; 'fully' or 'partially'
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P
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characterizable differential ideal
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Description
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The function reduced returns true if p is reduced with respect to F or with respect to the equations of P. It returns false otherwise.
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A differential polynomial p is said to be partially reduced with respect to a polynomial q if no proper derivative of the leader of q appears in p.
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A differential polynomial p is said to be fully reduced with respect to a polynomial q if it is partially reduced with respect to q and if its degree in the leader of q is less than the degree of q in this leader.
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A differential polynomial p is said to be reduced with respect to a set of differential polynomials F if it is reduced with respect to each element of F.
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If code is omitted, it is assumed to be 'fully'.
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The command with(diffalg,reduced) 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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