RegularChains[ChainTools] - Maple Help

Home : Support : Online Help : Mathematics : Factorization and Solving Equations : RegularChains : ChainTools Subpackage : RegularChains/ChainTools/IsEmptyChain

RegularChains[ChainTools]

 IsEmptyChain
 test if a regular chain is empty

 Calling Sequence IsEmptyChain(rc, R)

Parameters

 rc - regular chain of R R - polynomial ring

Description

 • The command IsEmptyChain(rc, R) returns true if and only if rc is the empty regular chain of R.
 • This command is part of the RegularChains[ChainTools] package, so it can be used in the form IsEmptyChain(..) 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][IsEmptyChain](..).

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)
 > $T≔\mathrm{Empty}\left(R\right)$
 ${T}{:=}{\mathrm{regular_chain}}$ (2)
 > $T≔\mathrm{Chain}\left(\left[\left(z+1\right)\left(z+2\right),{y}^{2}+z,\left(x-z\right)\left(x-y\right)\right],T,R\right)$
 ${T}{:=}{\mathrm{regular_chain}}$ (3)
 > $\mathrm{Equations}\left(T,R\right)$
 $\left[{{x}}^{{2}}{+}\left({-}{y}{-}{z}\right){}{x}{+}{z}{}{y}{,}{{y}}^{{2}}{+}{z}{,}{{z}}^{{2}}{+}{3}{}{z}{+}{2}\right]$ (4)
 > $\mathrm{IsEmptyChain}\left(T,R\right)$
 ${\mathrm{false}}$ (5)