RegularChains[ChainTools]
Polynomial
polynomial of a regular chain with specified main variable
Calling Sequence
Parameters
Description
Examples
Polynomial(v, rc, R)
v

variable of R
rc
regular chain of R
R
polynomial ring
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](..).
$\mathrm{with}\left(\mathrm{RegularChains}\right)\:$
$R\u2254\mathrm{PolynomialRing}\left(\left[x\,y\,z\right]\right)$
${R}{\u2254}{\mathrm{polynomial\_ring}}$
$\mathrm{with}\left(\mathrm{ChainTools}\right)\:$
$T\u2254\mathrm{Empty}\left(R\right)\:$
$T\u2254\mathrm{Chain}\left(\left[\left(z+1\right)\left(z+2\right)\,{y}^{2}+z\,\left(xz\right)\left(xy\right)\right]\,T\,R\right)$
${T}{\u2254}{\mathrm{regular\_chain}}$
$\mathrm{Equations}\left(T\,R\right)$
$\left[{{x}}^{{2}}{+}\left({}{y}{}{z}\right){}{x}{+}{z}{}{y}{\,}{{y}}^{{2}}{+}{z}{\,}{{z}}^{{2}}{+}{3}{}{z}{+}{2}\right]$
$\mathrm{p1}\u2254\mathrm{Polynomial}\left(x\,T\,R\right)$
${\mathrm{p1}}{\u2254}{{x}}^{{2}}{}{x}{}{y}{}{z}{}{x}{+}{z}{}{y}$
$\mathrm{p2}\u2254\mathrm{Polynomial}\left(y\,T\,R\right)$
${\mathrm{p2}}{\u2254}{{y}}^{{2}}{+}{z}$
$\mathrm{p3}\u2254\mathrm{Polynomial}\left(z\,T\,R\right)$
${\mathrm{p3}}{\u2254}{{z}}^{{2}}{+}{3}{}{z}{+}{2}$
See Also
Chain
Cut
Empty
Equations
IsAlgebraic
PolynomialRing
RegularChains
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