where is the bug; does intersect() not respect monomial ordering?

[kroeker@…]

intersect sets attribute "isSB" while it is not true?

Here is the example:

ring rng = 0,(xp,xl,xh),dp;

ideal I=
-4*xp*xh+3*xl^2,
4*xp^2*xh-9*xl*xh,
xp^2*xl-3*xp*xh;

def J = intersect(I,I);
J;
//J[1]=3*xl^2-4*xp*xh
//J[2]=4*xp^2*xh-9*xl*xh
//J[3]=xp^2*xl-3*xp*xh

attrib(J); // attr:isSB, type int
attrib(J,"isSB"); // =1, 
groebner(J);
//_[1]=3*xl^2-4*xp*xh
//_[2]=4*xp^2*xh-9*xl*xh
//_[3]=xp^2*xl-3*xp*xh


ring rng = 0,(xp,xl,xh),lp;

ideal I= -4*xp*xh+3*xl^2, 4*xp^2*xh-9*xl*xh, xp^2*xl-3*xp*xh;

def J = intersect(I,I);
J;
//J[1]=-4*xp*xh+3*xl^2
//J[2]=4*xp^2*xh-9*xl*xh
//J[3]=xp^2*xl-3*xp*xh

attrib(J); // attr:isSB, type int
attrib(J,"isSB"); // =1, incorrect ?

groebner(J);
//_[1]=xl^4-4*xl*xh^2
//_[2]=4*xp*xh-3*xl^2
//_[3]=xp*xl^2-3*xl*xh
//_[4]=xp^2*xl-3*xp*xh

reduce(groebner(J),J);
//_[1]=y^4-4*y*z^2
//_[2]=0
//_[3]=x*y^2-3*y*z
//_[4]=0

[kroeker@…]

Remark: bug was found by throwing random ideals at radEHV and looking at the primary decomposition of the result (of course not by hand!) Since the isSB attrib (set by intersect in radEHV) is probably incorrect (didn't check) , primdecGTZ gives an invalid and unexpected result: ( [4][1][2] <> [4][2][2] )

> ring rng = 0,(xp,xl,xh),lp;
// ** redefining rng **
> 
. ideal I= -4*xp*xh+3*xl^2, 4*xp^2*xh-9*xl*xh, xp^2*xl-3*xp*xh;
> ideal rIehv = radEHV(I);
//options: redSB intStrategy redefine loadLib usage prompt
//options: redSB intStrategy redefine loadLib usage prompt
> primdecGTZ(rIehv);
// ** redefining gnir1 **
[1]:
   [1]:
      _[1]=xh
      _[2]=xl
   [2]:
      _[1]=xh
      _[2]=xl
[2]:
   [1]:
      _[1]=xl^3-4*xh^2
      _[2]=4*xp*xh-3*xl^2
      _[3]=xp*xl-3*xh
      _[4]=4*xp^2-9*xl
   [2]:
      _[1]=xl^3-4*xh^2
      _[2]=4*xp*xh-3*xl^2
      _[3]=xp*xl-3*xh
      _[4]=4*xp^2-9*xl
[3]:
   [1]:
      _[1]=xl
      _[2]=xp
   [2]:
      _[1]=xl
      _[2]=xp
[4]:
   [1]:
      _[1]=xh
      _[2]=xl^2
      _[3]=xp
   [2]:
      _[1]=xp
      _[2]=xl
      _[3]=xh
> 

[hannes]

the result of intersect is a generating set. see 0a6bb08c6f0682a52c5e101d9181d755a4c063c9