RegularChains[ChainTools] - Maple Programming Help

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RegularChains[ChainTools]

 Cut
 split a chain by a variable

 Calling Sequence Cut(v, rc, R)

Parameters

 v - variable of of R rc - regular chain of R R - polynomial ring out_top - unevaluated name out_pv - unevaluated name out_sub_rc - unevaluated name

Description

 • The command Cut(v, rc, R) returns $\left[\mathrm{alg_v},\mathrm{top},\mathrm{pv},\mathrm{sub_rc}\right]$ where $\mathrm{alg_v}$ is true if and only if v is an algebraic variable of rc, that is, if there exists a polynomial of rc with v as main variables.
 • Moreover, top is assigned to the list of polynomials of rc with main variable strictly greater than v, ordered by increasing main variable.
 • pv is assigned to the polynomial of rc with main variable v. If no such polynomial exists, pv is left unchanged.
 • sub_rc is the regular chain under the variable v, i.e. composed of the polynomials of rc with main variable strictly lower than v.
 • This command is part of the RegularChains[ChainTools] package, so it can be used in the form Cut(..) 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][Cut](..).

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$
 > $R≔\mathrm{PolynomialRing}\left(\left[x,y,z\right]\right)$
 ${R}{:=}{\mathrm{polynomial_ring}}$ (1)
 > $\mathrm{with}\left(\mathrm{ChainTools}\right):$
 > $\mathrm{rc}≔\mathrm{Empty}\left(R\right)$
 ${\mathrm{rc}}{:=}{\mathrm{regular_chain}}$ (2)
 > $\mathrm{rc}≔\mathrm{Chain}\left(\left[z+1,y+2,x+3\right],\mathrm{rc},R\right)$
 ${\mathrm{rc}}{:=}{\mathrm{regular_chain}}$ (3)
 > $\mathrm{res}≔\mathrm{Cut}\left(x,\mathrm{rc},R\right);$$\mathrm{Equations}\left({\mathrm{res}}_{4},R\right)$
 ${\mathrm{res}}{:=}\left[{\mathrm{true}}{,}\left[{}\right]{,}{x}{+}{3}{,}{\mathrm{regular_chain}}\right]$
 $\left[{y}{+}{2}{,}{z}{+}{1}\right]$ (4)
 > $\mathrm{res}≔\mathrm{Cut}\left(y,\mathrm{rc},R\right);$$\mathrm{Equations}\left({\mathrm{res}}_{4},R\right)$
 ${\mathrm{res}}{:=}\left[{\mathrm{true}}{,}\left[{x}{+}{3}\right]{,}{y}{+}{2}{,}{\mathrm{regular_chain}}\right]$
 $\left[{z}{+}{1}\right]$ (5)
 > $\mathrm{res}≔\mathrm{Cut}\left(z,\mathrm{rc},R\right);$$\mathrm{Equations}\left({\mathrm{res}}_{4},R\right)$
 ${\mathrm{res}}{:=}\left[{\mathrm{true}}{,}\left[{y}{+}{2}{,}{x}{+}{3}\right]{,}{z}{+}{1}{,}{\mathrm{regular_chain}}\right]$
 $\left[{}\right]$ (6)