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RegularChains[ParametricSystemTools][DiscriminantSet] - compute the discriminant set of a variety
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Calling Sequence
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DiscriminantSet(F, d, R)
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Parameters
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F
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list of polynomials
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d
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number of parameters
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R
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polynomial ring
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Description
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The command DiscriminantSet(F, d, R) returns the discriminant set of a polynomial system with respect to a positive integer, which is a constructible set.
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d is positive and less than the number of variables in R.
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Given a positive integer d, the last d variables will be regarded as parameters.
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A point P is in the discriminant set of F if and only if after specializing F at P, the polynomial system F has no solution or an infinite number of solutions.
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This command is part of the RegularChains[ParametricSystemTools] package, so it can be used in the form DiscriminantSet(..) only after executing the command with(RegularChains[ParametricSystemTools]). However, it can always be accessed through the long form of the command by using RegularChains[ParametricSystemTools][DiscriminantSet](..).
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Examples
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![R := PolynomialRing([x, a, b, c])](/support/helpjp/helpview.aspx?si=6423/file06516/math114.png)
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Consider the following general quadratic polynomial F.
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You can see that when F as a univariate polynomial in x has no solution (over the complex number field) or has infinitely many number solutions.
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![ds := DiscriminantSet([F], 3, R)](/support/helpjp/helpview.aspx?si=6423/file06516/math138.png)
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![[[a, b], [1]]](/support/helpjp/helpview.aspx?si=6423/file06516/math155.png)
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The first case indicates that there are infinite number of solutions; the second one indicates that there is no solution.
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Download Help Document
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