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RegularChains[ChainTools]

 IsStronglyNormalized
 check whether a regular chain is strongly normalized

 Calling Sequence IsStronglyNormalized(rc, R)

Parameters

 rc - regular chain of R R - polynomial ring

Description

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

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)
 > $\mathrm{px1}≔x+y+z$
 ${\mathrm{px1}}{:=}{x}{+}{y}{+}{z}$ (4)
 > $\mathrm{px2}≔zx+y+z$
 ${\mathrm{px2}}{:=}{x}{}{z}{+}{y}{+}{z}$ (5)
 > $\mathrm{rc}≔\mathrm{Empty}\left(R\right)$
 ${\mathrm{rc}}{:=}{\mathrm{regular_chain}}$ (6)
 > $\mathrm{rc1}≔\mathrm{Chain}\left(\left[\mathrm{pz},\mathrm{py},\mathrm{px1}\right],\mathrm{rc},R\right)$
 ${\mathrm{rc1}}{:=}{\mathrm{regular_chain}}$ (7)
 > $\mathrm{IsStronglyNormalized}\left(\mathrm{rc1},R\right)$
 ${\mathrm{true}}$ (8)
 > $\mathrm{rc2}≔\mathrm{Chain}\left(\left[\mathrm{pz},\mathrm{py},\mathrm{px2}\right],\mathrm{rc},R\right)$
 ${\mathrm{rc2}}{:=}{\mathrm{regular_chain}}$ (9)
 > $\mathrm{IsStronglyNormalized}\left(\mathrm{rc2},R\right)$
 ${\mathrm{false}}$ (10)