RegularChains[ParametricSystemTools] - Maple Programming Help

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RegularChains[ParametricSystemTools]

 BelongsTo
 find constructible sets containing a given point

 Calling Sequence BelongsTo(pt, lcs, R)

Parameters

 pt - point with rational coefficients lcs - list of constructible sets R - polynomial ring

Description

 • The command BelongsTo(pt, lcs, R) returns the indices of constructible sets in lcs which contain the point pt.
 • pt is given by a list of rational numbers; $\mathrm{nops}\left(\mathrm{pt}\right)$ must be equal to the number of variables of R.
 • This command is part of the RegularChains[ParametricSystemTools] package, so it can be used in the form BelongsTo(..) 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][BelongsTo](..).

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$
 > $\mathrm{with}\left(\mathrm{ConstructibleSetTools}\right):$
 > $\mathrm{with}\left(\mathrm{ParametricSystemTools}\right):$
 > $R≔\mathrm{PolynomialRing}\left(\left[x,y\right]\right)$
 ${R}{:=}{\mathrm{polynomial_ring}}$ (1)
 > $S≔\mathrm{PolynomialRing}\left(\left[s,t\right]\right)$
 ${S}{:=}{\mathrm{polynomial_ring}}$ (2)
 > $\mathrm{MP}≔\left[{x}^{2},{y}^{2}\right]$
 ${\mathrm{MP}}{:=}\left[{{x}}^{{2}}{,}{{y}}^{{2}}\right]$ (3)
 > $F≔\left[s-1,t-1\right]$
 ${F}{:=}\left[{s}{-}{1}{,}{t}{-}{1}\right]$ (4)
 > $\mathrm{cs1}≔\mathrm{PolynomialMapPreimage}\left(F,\mathrm{MP},R,S\right)$
 ${\mathrm{cs1}}{:=}{\mathrm{constructible_set}}$ (5)
 > $\mathrm{Info}\left(\mathrm{cs1},R\right)$
 $\left[\left[{x}{+}{1}{,}{y}{-}{1}\right]{,}\left[{1}\right]\right]{,}\left[\left[{x}{-}{1}{,}{y}{-}{1}\right]{,}\left[{1}\right]\right]{,}\left[\left[{x}{+}{1}{,}{y}{+}{1}\right]{,}\left[{1}\right]\right]{,}\left[\left[{x}{-}{1}{,}{y}{+}{1}\right]{,}\left[{1}\right]\right]$ (6)
 > $\mathrm{pt}≔\left[\frac{1}{2},\frac{1}{3}\right]$
 ${\mathrm{pt}}{:=}\left[\frac{{1}}{{2}}{,}\frac{{1}}{{3}}\right]$ (7)
 > $\mathrm{cs2}≔\mathrm{GeneralConstruct}\left(\left[2x-1,3y-1\right],\left[1\right],R\right)$
 ${\mathrm{cs2}}{:=}{\mathrm{constructible_set}}$ (8)
 > $\mathrm{BelongsTo}\left(\mathrm{pt},\left[\mathrm{cs1},\mathrm{cs2}\right],R\right)$
 $\left[{2}\right]$ (9)