RegularChains[ChainTools] - Maple Programming Help

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

 > with(RegularChains):
 > R := PolynomialRing([x, y, z]);
 ${R}{≔}{\mathrm{polynomial_ring}}$ (1)
 > with(ChainTools):
 > T := Empty(R):
 > T := Chain([(z+1)*(z+2), y^2+z, (x-z)*(x-y)], T, R);
 ${T}{≔}{\mathrm{regular_chain}}$ (2)
 > Equations(T, R);
 $\left[{{x}}^{{2}}{+}\left({-}{y}{-}{z}\right){}{x}{+}{z}{}{y}{,}{{y}}^{{2}}{+}{z}{,}{{z}}^{{2}}{+}{3}{}{z}{+}{2}\right]$ (3)
 > p1 := Polynomial(x, T, R);
 ${\mathrm{p1}}{≔}{{x}}^{{2}}{-}{x}{}{y}{-}{z}{}{x}{+}{z}{}{y}$ (4)
 > p2 := Polynomial(y, T, R);
 ${\mathrm{p2}}{≔}{{y}}^{{2}}{+}{z}$ (5)
 > p3 := Polynomial(z, T, R);
 ${\mathrm{p3}}{≔}{{z}}^{{2}}{+}{3}{}{z}{+}{2}$ (6)