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RegularChains[ChainTools]

  

IsPrimitive

  

test if a regular chain is primitive

 

Calling Sequence

Parameters

Description

Examples

References

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 satT 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

withRegularChains:withChainTools:

RPolynomialRingx,y,u,v

R:=polynomial_ring

(1)

TEmptyR

T:=regular_chain

(2)

TChainuy+v,xy1,T,R

T:=regular_chain

(3)

EquationsT,R

yx1,uy+v

(4)

IsPrimitiveT,R

true

(5)

UEmptyR

U:=regular_chain

(6)

UChainuy+v,vx+u,U,R

U:=regular_chain

(7)

EquationsU,R

vx+u,uy+v

(8)

IsPrimitiveU,R

false

(9)

References

  

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

See Also

IsIncluded

IsInSaturate

RegularChains

 


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