RegularChains[ChainTools] - Maple Programming Help

# Online Help

###### All Products    Maple    MapleSim

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

RegularChains[ChainTools]

 Polynomial
 polynomial of a regular chain with specified main variable

 Calling Sequence Polynomial(v, rc, R)

Parameters

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

Description

 • The command Polynomial(v, rc, R) returns the polynomial of rc with main variable v, otherwise an error is produced.
 • This command is part of the RegularChains[ChainTools] package, so it can be used in the form Polynomial(..) 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][Polynomial](..).

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)
 > $\mathrm{p1}≔\mathrm{Polynomial}\left(x,T,R\right)$
 ${\mathrm{p1}}{≔}{{x}}^{{2}}{-}{x}{}{y}{-}{x}{}{z}{+}{y}{}{z}$ (4)
 > $\mathrm{p2}≔\mathrm{Polynomial}\left(y,T,R\right)$
 ${\mathrm{p2}}{≔}{{y}}^{{2}}{+}{z}$ (5)
 > $\mathrm{p3}≔\mathrm{Polynomial}\left(z,T,R\right)$
 ${\mathrm{p3}}{≔}{{z}}^{{2}}{+}{3}{}{z}{+}{2}$ (6)

 See Also

## Was this information helpful?

 Please add your Comment (Optional) E-mail Address (Optional) What is ? This question helps us to combat spam