multiplicitySequence I
multiplicitySequence(i, I)
Given a (graded) ideal I, this function computes the multiplicity sequence as defined in [0]. Specifying Strategy => "genElts" will use the general element method as in [4]: one can specify the "complexity" of the general elements by using the option minTerms.
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The j-multiplicity of I is the l-th number, where l is the analytic spread of I.
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Note that this function does not require the ambient ring to be a polynomial ring:
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One can specify a particular element in the multiplicity sequence:
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There are two conventions in use about the order of the sequence. The current function follows that of [4] and in this setting the j-multiplicity of I appears at the l-th spot, where l is the analytic spread of I. If the ideal I is not graded, this function may produce incorrect results.
The object multiplicitySequence is a method function with options.