print "Ideal: " + str(f) print startLog() rg = f.GB() print "seq GB:", rg print #p = t**16 + 272 * t**12 - 7072 * t**8 + 3207424 * t**4 + 12960000; p = t - x - 2 * y #p = p * (y**4 + 4); p = abs(p) n = f.reduction(p) print "p = %s, n = %s " % (p, n) print n = rg.reduction(p) print "p = %s, n = %s " % (p, n) print N = rg.lift(p) print "p = %s, N = %s " % (p, [str(a) for a in N]) print pp = sum([ci * RingElem(ni) for ci, ni in zip(N, rg.list)]) print "N * rg == p:", pp == p #terminate();
ff = [ a*c, b*c ]; print "ff = " + str([ str(f) for f in ff ]); print ii = pt.ideal( "", ff ); print "SolvableIdeal: " + str(ii); print; #exit(0); rgl = ii.leftGB(); print "seq left GB: " + str(rgl); print "isLeftGB: " + str(rgl.isLeftGB()); print; p = RingElem(rgl.list.get(0)); print "p = " + str(p); print "c-p = " + str(c-p); #print "monic(p) = " + str(p.monic()); pp = p * p; print "p*p = " + str(pp); print "p*y*z = " + str(p*y*z); print "p*t = " + str(p*t); print "t*p = " + str(t*p); print; #no: fl = [ p, p*x ]; # x non existent #fl = [ p, p*y ]; #no: fl = [ p, p*z ]; #fl = [ p, p*t, p*y ]; #bad: fl = [ p, p*t, p*p ];
r = WordPolyRing(PolyRing(ZZ(), "a, c, b", PolyRing.lex), "y2, y1, z1, z2, x")
print "Ring: " + str(r)
print
one, a, c, b, y2, y1, z1, z2, x = r.gens()
p1 = x + 2 * y1 * z1 + 3 * a * y1**2 + 5 * y1**4 + 2 * c * y1
p2 = x + 2 * y2 * z2 + 3 * a * y2**2 + 5 * y2**4 + 2 * c * y2
p3 = 2 * z2 + 6 * a * y2 + 20 * y2**3 + 2 * c
p4 = 3 * z1**2 + y1**2 + b
p5 = 3 * z2**2 + y2**2 + b
F = [p1, p2, p3, p4, p5]
# make all variables commute
cm = [RingElem(q) for q in r.ring.commute()]
print "commute: " + str([str(q) for q in cm])
print
g = r.ideal("", F + cm)
print "Ideal: " + str(g)
print
startLog()
rg = g.GB()
print "GB: " + str(rg)
print
bg = rg.isGB()
print "isGB: " + str(bg)
if False:
rg = f.parGB(tnum)
for th in range(tnum, 0, -1):
rg = f.parGB(th)
#print "par Output:", rg;
#print;
rg = f.GB()
#print "seq Output:", rg;
print
arri = arris_algorithm()
ggv1 = ggv_first_implementation()
ff5 = f5z()
F = [RingElem(e) for e in f.list]
print "F:", str([str(e) for e in F])
print
if False:
##gg = staglinbasis(F);
#gg = staglinbasis(F);
t = System.currentTimeMillis()
gg = staglinbasis(F)
t = System.currentTimeMillis() - t
print "stag executed in " + str(t) + " milliseconds"
if not r.ideal(list=gg).isGB():
print "stag no GB"
print "stag Output:" + str([str(ggg) for ggg in gg])
print
print ii = pt.ideal( "", ff ); print "SolvableIdeal: " + str(ii); print; #exit(0); #startLog(); rgl = ii.leftGB(); print "seq left GB: " + str(rgl); print "isLeftGB: " + str(rgl.isLeftGB()); print; #p = RingElem(rgl.list.get(0)); p = RingElem(rgl.list[0]); print "p = " + str(p); print "c = " + str(c); #print "c-p = " + str(c-p); d = c.monic(); print "d=monic(c) = " + str(d); print "d-p = " + str(d-p); print; #exit(0); #no: fl = [ p, p*x ]; # x non existent #no: fl = [ p, p*z ]; #bad: fl = [ p, p*t, p*p ]; #bad: fl = [ p, p*p ]; #fl = [ p, p*t ];
print "x: " + str(x);
print "x == b: " + str(x == b);
print;
L, U, P = a.decompLU();
print "P: " + str(P);
print;
if P.elem.size() != 0:
print "L: " + str(L);
print;
print "U: " + str(U);
print;
Us = RingElem(a.elem.getUpperScaled());
print "scale(U): " + str(Us);
print;
x = a.solveLU(P, c);
print "x: " + str(x);
print "x == b: " + str(x == b);
print;
d = a.determinant(P)
print "det(A): " + str(d) + " ~= " + str(d.elem.getDecimal());
#print "det(A): " + str(d) + " ~= " + str(d.elem.getSymmetricVal());
print;
print
ii = pt.ideal("", ff)
print "SolvableIdeal: " + str(ii)
print
#exit(0);
startLog()
rgl = ii.leftGB()
print "seq left GB: " + str(rgl)
print "isLeftGB: " + str(rgl.isLeftGB())
print
#p = RingElem(rgl.list.get(0));
p = RingElem(rgl.list[0])
print "p = " + str(p)
print "c = " + str(c)
print "c-p = " + str(c - p)
d = c.monic()
print "d = " + str(d)
print "d-p = " + str(d - p)
#print "monic(p) = " + str(p.monic());
#pp = p * p;
#print "p*p = " + str(pp);
#print "p*y*z = " + str(p*y*z);
#print "p*t = " + str(p*t);
#print "t*p = " + str(t*p);
print
#exit(0);