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RegularChains[ChainTools]

 IsAlgebraic
 test if a variable is algebraic with respect to a regular chain

 Calling Sequence IsAlgebraic(v, rc, R)

Parameters

 v - variable of of R rc - regular chain of R R - polynomial ring

Description

 • The command IsAlgebraic(v, rc, R) returns true if v is algebraic with respect to rc, false otherwise.
 • This command is part of the RegularChains[ChainTools] package, so it can be used in the form IsAlgebraic(..) only after executing the command with(RegularChains[ChainTools]).  However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][IsAlgebraic](..).

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$
 > $R≔\mathrm{PolynomialRing}\left(\left[x,y,z,t\right]\right)$
 ${R}{≔}{\mathrm{polynomial_ring}}$ (1)
 > $\mathrm{with}\left(\mathrm{ChainTools}\right):$
 > $T≔\mathrm{Empty}\left(R\right):$
 > $T≔\mathrm{Chain}\left(\left[\left(z+1\right)\left(z+2\right),{y}^{2}+z,\left(x-z\right)\left(x-y\right)\right],T,R\right)$
 ${T}{≔}{\mathrm{regular_chain}}$ (2)
 > $\mathrm{Equations}\left(T,R\right)$
 $\left[{{x}}^{{2}}{+}\left({-}{y}{-}{z}\right){}{x}{+}{z}{}{y}{,}{{y}}^{{2}}{+}{z}{,}{{z}}^{{2}}{+}{3}{}{z}{+}{2}\right]$ (3)
 > $\mathrm{IsAlgebraic}\left(x,T,R\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsAlgebraic}\left(t,T,R\right)$
 ${\mathrm{false}}$ (5)

 See Also

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