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RegularChains[ChainTools]

 IsZeroDimensional
 check whether a regular chain is zero-dimensional

 Calling Sequence IsZeroDimensional(rc, R)

Parameters

 rc - regular chain of R R - polynomial ring

Description

 • The command IsZeroDimensional(rc, R) returns true if rc is zero-dimensional false otherwise.
 • This command is part of the RegularChains[ChainTools] package, so it can be used in the form IsZeroDimensional(..) 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][IsZeroDimensional](..).

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$
 > $\mathrm{with}\left(\mathrm{ChainTools}\right):$
 > $R≔\mathrm{PolynomialRing}\left(\left[x,y,z\right]\right)$
 ${R}{≔}{\mathrm{polynomial_ring}}$ (1)
 > $\mathrm{pz}≔\left(z-1\right)\left(z-2\right)$
 ${\mathrm{pz}}{≔}\left({z}{-}{1}\right){}\left({z}{-}{2}\right)$ (2)
 > $\mathrm{py}≔{y}^{2}+z$
 ${\mathrm{py}}{≔}{{y}}^{{2}}{+}{z}$ (3)
 > $\mathrm{px}≔x+y+z$
 ${\mathrm{px}}{≔}{x}{+}{y}{+}{z}$ (4)
 > $\mathrm{rc}≔\mathrm{Empty}\left(R\right)$
 ${\mathrm{rc}}{≔}{\mathrm{regular_chain}}$ (5)
 > $\mathrm{rc1}≔\mathrm{Chain}\left(\left[\mathrm{pz}\right],\mathrm{rc},R\right)$
 ${\mathrm{rc1}}{≔}{\mathrm{regular_chain}}$ (6)
 > $\mathrm{IsZeroDimensional}\left(\mathrm{rc1},R\right)$
 ${\mathrm{false}}$ (7)
 > $\mathrm{rc2}≔\mathrm{Chain}\left(\left[\mathrm{pz},\mathrm{py},\mathrm{px}\right],\mathrm{rc},R\right)$
 ${\mathrm{rc2}}{≔}{\mathrm{regular_chain}}$ (8)
 > $\mathrm{IsZeroDimensional}\left(\mathrm{rc2},R\right)$
 ${\mathrm{true}}$ (9)

 See Also