DifferentialAlgebra[Tools][DifferentialPrem] - the Ritt reduction algorithm
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Calling Sequence
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DifferentialPrem (p,regchain,opts)
DifferentialPrem (p,redset,R,opts)
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Parameters
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p
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a differential polynomial
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regchain
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a regular differential chain
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redset
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a polynomial or a list or a set of differential polynomials
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opts (optional)
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a sequence of options
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Description
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The function call DifferentialPrem (p,redset,R,opts) returns a sequence such that is a power product of initials and separants of redset, is a differential polynomial fully reduced with respect to each element of redset, and, modulo the differential ideal generated by redset. The elements of redset must depend on at least, one derivative and have integer coefficients. All the differential polynomials are regarded as elements of R, or, of its embedding ring, if R is an ideal.
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A differential polynomial p belongs to the differential ideal defined by regchain if and only if, the function call DifferentialPrem (p,regchain) returns a sequence whose second component is zero.
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This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form DifferentialPrem(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][DifferentialPrem](...).
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Options
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The opts arguments may contain one or more of the options below.
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reduction = full, partial or algebraic. Indicates the type of reduction to be performed. Depending on the type of reduction, the differential polynomial satisfies the following properties:
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notation = jet, tjet, diff or Diff. Specifies the notation used for the result of the function call. If not specified, the notation of p is used.
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memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero (no memory out).
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Examples
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The ratio / is equivalent to modulo the differential ideal defined by the regular differential chain, but, it is not the normal form of
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Different modes of reduction are available
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