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RegularChains[ConstructibleSetTools][RationalMapPreimage] - compute the preimage of a variety under a polynomial map
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Calling Sequence
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RationalMapPreimage(F, RM, R, S)
RationalMapPreimage(F, H, RM, R, S)
RationalMapPreimage(CS, RM, R, S)
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Parameters
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F
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list of polynomials of S
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RM
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a list of rational functions in R
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R
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a polynomial ring (source)
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S
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a polynomial ring (target)
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H
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list of polynomials
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CS
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constructible set
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Description
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The command RationalMapPreimage(F, RM, R, S) returns a constructible set cs over R. cs is the preimage of the variety  under the rational map RM.
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The command RationalMapPreimage(CS, RM, R, S) returns the preimage of the constructible set CS under the rational map RM.
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Both rings R and S should be over the same ground field.
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The variable sets of R and S should be disjoint.
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The number of rational functions in RM is equal to the number of variables of ring S.
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Examples
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![R := PolynomialRing([x, y, z])](/support/helpjp/helpview.aspx?si=6409/file06482/math183.png)
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![S := PolynomialRing([s, t])](/support/helpjp/helpview.aspx?si=6409/file06482/math190.png)
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Note that the rational map should be a list of rational functions of R. Also, the number of polynomials in RM equals the number of variables of S.
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![RM := [x^2/(x+y), y^2/(x+y)]](/support/helpjp/helpview.aspx?si=6409/file06482/math205.png)
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![RM := [x^2/(x+y), y^2/(x+y)]](/support/helpjp/helpview.aspx?si=6409/file06482/math208.png)
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![F := [s-1, t-1]](/support/helpjp/helpview.aspx?si=6409/file06482/math212.png)
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![F := [s-1, t-1]](/support/helpjp/helpview.aspx?si=6409/file06482/math215.png)
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![[[x-2, y-2], [1]]](/support/helpjp/helpview.aspx?si=6409/file06482/math229.png)
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