incorrect radical entry in a primdecSY() decomposition

[kroeker@…]

example for incorrect radical entry in a primdecSY() decomposition, see second component:

LIB("primdec.lib");
ring rng = (0),(xm,xp,xw,xo,xj,xd,xn,xz),dp;

ideal I = -2*xj+19*xo^2,
18*xw*xz+19*xd,
-13*xp*xd*xz-16*xo,
-2*xj*xn^2+9*xn,
23*xm-8*xj,
-17*xm*xn+17*xm*xo,
-18*xn*xz+3*xj,
23*xm*xp*xn-30*xw*xn,
-6*xm*xw,
23*xj*xd*xz+4*xd*xz,
16*xm*xw+14*xj,
-20*xp*xj*xn+27*xz^2,
23*xp*xw+14*xm*xd,
7*xm*xj+29*xo*xd*xn;


list  L = primdecSY (I);
ideal pc2 = L[2][1];
pc2;
ideal rpc2 = L[2][2]; // incorrect!!
rpc2;

radical(L[2][1]); 

idealsEqual( radical(pc2), rpc2 ); // = 0!
///////////////////////////////////////////
// same with groebner(I):
L = primdecSY (groebner(I) );
pc2 = L[2][1];
rpc2 = L[2][2];
radical(L[2][1]);
idealsEqual( radical(pc2), rpc2 ); //ok!

output

. list  L = primdecSY (I);
> ideal pc2 = L[2][1];
> pc2;

pc2[1]=xn
pc2[2]=xd
pc2[3]=xj
pc2[4]=xo
pc2[5]=xw
pc2[6]=xm
pc2[7]=xz^2

> ideal rpc2 = L[2][2];
> rpc2;

rpc2[1]=xz
rpc2[2]=xn
rpc2[3]=xd
rpc2[4]=xj
rpc2[5]=xo
rpc2[6]=xw
rpc2[7]=xp
rpc2[8]=xm

> radical(L[2][1]);

_[1]=xz
_[2]=xn
_[3]=xd
_[4]=xj
_[5]=xo
_[6]=xw
_[7]=xm

> . idealsEqual( radical(pc2), rpc2 ); // = 0!
0

[hannes]

fixed by mlee with 948667d52839562086cf444b0a31a259e43e6b41