The command RationalMapImage(F, RM, R, S) returns a constructible set cs which is the image of the variety $V\left(F\right)$ under the rational map RM.

If H is specified, let $W$ be the variety defined by the product of polynomials in H. The command RationalMapImage(F, H, RM, R, S) returns the image of the constructible set $V$-$W$ under the rational map RM.

The command RationalMapImage(CS, RM, R, S) returns the image of the constructible set CS under the rational map RM.

Both rings R and S should be over the same ground field.

The variable sets of R and S should be disjoint.

The number of polynomials in RM is equal to the number of variables of ring S.

$\mathrm{with}\left(\mathrm{RegularChains}\right)\:$

$\mathrm{with}\left(\mathrm{ConstructibleSetTools}\right)\:$

$S≔\mathrm{PolynomialRing}\left(\left[t\right]\right)$

$S≔\mathrm{polynomial\_ring}$

$T≔\mathrm{PolynomialRing}\left(\left[x\,y\right]\right)$

$T≔\mathrm{polynomial\_ring}$

$F≔\left[\right]$

$F≔\left[\right]$

$\mathrm{RM}≔\left[\frac{t^3-6t^2+9t-2}{2t^4-16t^3+40t^2-32t+9}\,\frac{t^2-4t+4}{2t^4-16t^3+40t^2-32t+9}\right]$

$\mathrm{RM}≔\left[\frac{t^3-6t^2+9t-2}{2t^4-16t^3+40t^2-32t+9}\,\frac{t^2-4t+4}{2t^4-16t^3+40t^2-32t+9}\right]$

$\mathrm{cs}≔\mathrm{RationalMapImage}\left(F\,\mathrm{RM}\,S\,T\right)$

$\mathrm{cs}≔\mathrm{constructible\_set}$

$\mathrm{Info}\left(\mathrm{cs}\,T\right)$

$\left[\left[2x^4-3y{x}^2+y^4-2y^3+y^2\right]\,\left[y\,\left(10y+2\right)x^2+2y^3-y^2-y\,\left(964y^6-480y^5-6858y^4-4328y^3-888y^2-72y-2\right)x^2-88y^8+2104y^7-2316y^6-943y^5+892y^4+318y^3+32y^2+y\right]\right],\left[\left[x\,y-1\right]\,\left[1\right]\right],\left[\left[x\,y\right]\,\left[1\right]\right]$