Under - Maple Help

RegularChains[ChainTools]

 Under
 regular sub-chain with respect to specified variable

 Calling Sequence Under(v, rc, R)

Parameters

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

Description

 • The command Under(v, rc, R) returns the regular chain consisting of the polynomials of rc with main variable strictly less than v.
 • This command is part of the RegularChains[ChainTools] package, so it can be used in the form Under(..) 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][Under](..).

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$
 > $R≔\mathrm{PolynomialRing}\left(\left[x,y,z\right]\right)$
 ${R}{≔}{\mathrm{polynomial_ring}}$ (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)
 > $\mathrm{rc}≔\mathrm{Under}\left(x,T,R\right)$
 ${\mathrm{rc}}{≔}{\mathrm{regular_chain}}$ (4)