diffalg[delta_polynomial] - return the delta-polynomial generated by two differential polynomials
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Calling Sequence
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delta_polynomial (p, q, R)
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Parameters
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p, q
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differential polynomials in R
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R
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differential polynomial ring
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Description
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The delta_polynomial command returns the delta-polynomial of p and q, that is
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where phi and psi are the derivation operators of least order such that phi (up) = psi (uq) where up and uq are the leaders of p and q.
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The delta-polynomial is sometimes called the cross-derivative.
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The differential polynomials p and q must not belong to the ground field of R. Their leaders must be derivatives of the same differential indeterminate but not be derivatives of each other. Otherwise, the delta-polynomial is not defined and delta_polynomial returns an error message.
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The command with(diffalg,delta_polynomial) allows the use of the abbreviated form of this command.
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