differing solution sets / varieties in 3.0.3 vs. 3.1.0

[seelisch]

On the following example, 3.0.3 yields 21 solutions, whereas 3.1.0 returns just 7. (And: These 7 are not contained in the former 21.):

LIB "solve.lib";

ring r=0,(x,y,z,z(1),z(2)),dp; poly N1=-x4+x3*y-x2*y2+x*y3-x2*z2+x*y*z2+x3-x2*y+x*y2-y3+x*z2-y*z2+16*x2-16*x*y-16*x+16*y+10*z(1)+7*z(2); poly N2=-x3*y-x*y3+x2*y*z+y3*z-x*y*z2+y*z3+2*x3+2*x*y2-2*x2*z-2*y2*z+2*x*z2-2*z3+16*x*y-16*y*z-32*x+32*z-7*z(1)+2*z(2); poly N3=x4*z-x3*y*z+x2*y2*z-x*y3*z-x3*z2+x2*y*z2-x*y2*z2+y3*z2+x2*z3-x*y*z3-x*z4+y*z4-3*x4+3*x3*y-3*x2*y2+3*x*y3+3*x3*z-3*x2*y*z+3*x*y2*z-3*y3*z-3*x2*z2+3*x*y*z2+3*x*z3-3*y*z3-16*x2*z+16*x*y*z+16*x*z2-16*y*z2+48*x2-48*x*y-48*x*z+48*y*z+z(1)+5*z(2); poly N4=-3*x+3*y+2*z+z(1)-8; poly N5=6*x-8*y+9*z+z(2)+2; ideal N=N1,N2,N3,N4,N5; def s = solve(N); setring s; SOL;

[hannes]

interred turned out to be unstable with inexact coeffs