print; rel = [d, x, x * d + 1 ]; print "relations: = " + str([ str(f) for f in rel ]); print; r = SolvPolyRing( PolyRing(QQ(),"a,b",PolyRing.lex),"x,d", PolyRing.lex, rel); print "Ring: " + str(r); print; p1 = 2 * x * d**2 + a * x * d; p2 = x * d**3 + b * x**2 * d - b * x; p3 = x * d**2 - a * x; f = r.paramideal( "", [p1,p2,p3] ); print "ParamIdeal: " + str(f); print; #exit(); #startLog(); gs = f.CGBsystem(); print "CGBsystem: " + str(gs); print; #exit(); bg = gs.isCGBsystem(); print "isCGBsystem: " + str(bg); print;
rel = [d1, x1, x1 * d1 + 1, d2, x2, x2 * d2 + 1 ]; print "relations: = " + str([ str(f) for f in rel ]); print; r = SolvPolyRing( PolyRing(QQ(),"a,b",PolyRing.lex),"x1,x2,d1,d2", PolyRing.lex, rel); print "Ring: " + str(r); print; p1 = a * x1 * d1**2 * d2 + (a+1) * x1 * x2 * d2; p2 = x2**2 * d2 + b * x1; p3 = d1 * d2**2; f = r.paramideal( "", [p1,p2,p3] ); print "ParamIdeal: " + str(f); print; #exit(); #startLog(); gs = f.CGBsystem(); print "CGBsystem: " + str(gs); print; #exit(); #bg = gs.isCGBsystem(); #print "isCGBsystem: " + str(bg); #print;
print "comm Ring: " + str(rc); print; rel = [y, x, x * y + 1]; print "relations: = " + str([ str(f) for f in rel ]); print; r = SolvPolyRing( PolyRing(QQ(),"(u,v)",PolyRing.lex),"(x,y)", PolyRing.lex, rel); print "Ring: " + str(r); print; p1 = v * x * y + x; p2 = u * y**2 + x**2; f = r.paramideal( "", [p1,p2] ); print "ParamIdeal: " + str(f); print; #sys.exit(); #startLog(); gs = f.CGBsystem(); print "CGBsystem: " + str(gs); print; #sys.exit(); print "isCGBsystem: " + str(gs.isCGBsystem());