CoCoA » CoCoALib

This was the error, found by Ashkan Nikseresht (nice feedback! thanks!)

/* */ K::=ZZ/(2);
/* */ Use S::=K[a,b,x,y];
/* */ al:=a^2+a+1;
/* */ be1:=b^2 +(a)*b +(1);
/* */ J:=ideal(al, be1, (x-a)^2,(y-b^2));
/* */ IsPrimary(J);
true
/* */ Iz:=Elim([a,b],J);
/* */ Iz;
ideal(x^4 +x^2 +1,  x^2*y +y^2 +1,  y^3 +x^2 +y^2 +1)
/* */ Use R::=K[x,y];
/* */ phi:=PolyAlgebraHom(S,R,[0,0,x,y]);
/* */ I1:=ideal(apply(phi,gens(Iz)));
/* */ I1;
ideal(x^4 +x^2 +1,  x^2*y +y^2 +1,  y^3 +x^2 +y^2 +1)
/* */ radi:=Radical(I1);
/* */ IsMaximal(radi);
true
/* */ IsPrimary(I1);
false

I added the test to exbugs.cocoa5

I like the suggestion to change the fn to void. Still we should discuss it when I'm there.
Also we should look to see if there are other similar fns whose design should be changed.

As a safety feature we could put CoCoA_ASSERT(!IsUncertain3(myPrimaryFlag)) after the call.

Even "better" we could implement as follows: main fn calls the one that does the work, then
makes the assertion. While this is safer (since you cannot forget to write the assertion
after every call), it seems to complicate the impl more than I'd like.

As a compromise, we could put assertions just before every return in the fn which actually does the work (and hope that we do not forget one).