RegularChains[ChainTools] - Maple Programming Help

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RegularChains[ChainTools]

 IsPrimitive
 test if a regular chain is primitive

 Calling Sequence IsPrimitive(T, R)

Parameters

 T - regular chain of R R - polynomial ring

Description

 • The command IsPrimitive(T, R) returns true if T is primitive; false otherwise.
 • If the regular chain T is primitive then the ideal generated by T equals the saturated ideal $\mathrm{sat}\left(T\right)$ of T.
 • For the definition of primitivity and the algorithm, see the paper "When does T equal sat(T)?" by Francois Lemaire, Marc Moreno Maza, Wei Pan and Yuzhen Xie, 2008.

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$$\mathrm{with}\left(\mathrm{ChainTools}\right):$
 > $R≔\mathrm{PolynomialRing}\left(\left[x,y,u,v\right]\right)$
 ${R}{≔}{\mathrm{polynomial_ring}}$ (1)
 > $T≔\mathrm{Empty}\left(R\right)$
 ${T}{≔}{\mathrm{regular_chain}}$ (2)
 > $T≔\mathrm{Chain}\left(\left[uy+v,xy-1\right],T,R\right)$
 ${T}{≔}{\mathrm{regular_chain}}$ (3)
 > $\mathrm{Equations}\left(T,R\right)$
 $\left[{y}{}{x}{-}{1}{,}{u}{}{y}{+}{v}\right]$ (4)
 > $\mathrm{IsPrimitive}\left(T,R\right)$
 ${\mathrm{true}}$ (5)
 > $U≔\mathrm{Empty}\left(R\right)$
 ${U}{≔}{\mathrm{regular_chain}}$ (6)
 > $U≔\mathrm{Chain}\left(\left[uy+v,vx+u\right],U,R\right)$
 ${U}{≔}{\mathrm{regular_chain}}$ (7)
 > $\mathrm{Equations}\left(U,R\right)$
 $\left[{v}{}{x}{+}{u}{,}{u}{}{y}{+}{v}\right]$ (8)
 > $\mathrm{IsPrimitive}\left(U,R\right)$
 ${\mathrm{false}}$ (9)

References

 Lemaire, F.; Moreno Maza, M.; Pan, W.; and Xie, Y. "When does (T) equal Sat(T)?." Proc. ISSAC 2008. Linz, 2008.