def sum(self,other):
'''Compute the sum of this and the ideal.
'''
s = jas.application.Ideal(self.pset);
t = jas.application.Ideal(other.pset);
N = s.sum( t );
return Ideal(self.ring,"",N.getList());
def optimize(self):
'''Optimize the term order on the variables.
'''
p = self.pset;
o = TermOrderOptimization.optimizeTermOrder(p);
r = Ring("",o.ring);
return Ideal(r,"",o.list);
def element(self,polystr):
'''Create an element from a string.
'''
I = Ideal(self, "( " + polystr + " )");
list = I.pset.list;
if len(list) > 0:
return RingElem( list[0] );
def toModular(self,mf):
'''Convert integer coefficients to modular coefficients.
'''
p = self.pset;
l = p.list;
r = p.ring;
rm = GenPolynomialRing( mf, r.nvar, r.tord, r.vars );
pm = PolyUtil.fromIntegerCoefficients(rm,l);
r = Ring("",rm);
return Ideal(r,"",pm);
def toInteger(self):
'''Convert rational coefficients to integer coefficients.
'''
p = self.pset;
l = p.list;
r = p.ring;
ri = GenPolynomialRing( BigInteger(), r.nvar, r.tord, r.vars );
pi = PolyUtil.integerFromRationalCoefficients(ri,l);
r = Ring("",ri);
return Ideal(r,"",pi);
def NF(self,reducer):
'''Compute a normal form of this ideal with respect to reducer.
'''
s = self.pset;
F = s.list;
G = reducer.list;
t = System.currentTimeMillis();
N = ReductionSeq().normalform(G,F);
t = System.currentTimeMillis() - t;
print "sequential NF executed in %s ms" % t;
return Ideal(self.ring,"",N);
def parTwosidedGB(self,th):
'''Compute a two-sided Groebner base in parallel.
'''
s = self.pset;
F = s.list;
bbpar = SolvableGroebnerBaseParallel(th);
t = System.currentTimeMillis();
G = bbpar.twosidedGB(F);
t = System.currentTimeMillis() - t;
bbpar.terminate();
print "parallel %s twosidedGB executed in %s ms" % (th, t);
return Ideal(self.ring,"",G);
def parOldGB(self,th):
'''Compute in parallel a Groebner base.
'''
s = self.pset;
F = s.list;
bbpar = GroebnerBaseParallel(th);
t = System.currentTimeMillis();
G = bbpar.GB(F);
t = System.currentTimeMillis() - t;
bbpar.terminate();
print "parallel-old %s executed in %s ms" % (th, t);
return Ideal(self.ring,"",G);
def distGB(self,th=2,machine="examples/machines.localhost",port=7114):
'''Compute on a distributed system a Groebner base.
'''
s = self.pset;
F = s.list;
t = System.currentTimeMillis();
# G = GroebnerBaseDistributed.Server(F,th);
#G = GBDist(th,machine,port).execute(F);
gbd = GBDist(th,machine,port);
t1 = System.currentTimeMillis();
G = gbd.execute(F);
t1 = System.currentTimeMillis() - t1;
gbd.terminate(0);
t = System.currentTimeMillis() - t;
print "distributed %s executed in %s ms (%s ms start-up)" % (th,t1,t-t1);
return Ideal(self.ring,"",G);
def GB(self):
'''Compute a Groebner base.
'''
s = self.pset;
cofac = s.ring.coFac;
F = s.list;
t = System.currentTimeMillis();
if cofac.isField():
G = GroebnerBaseSeq().GB(F);
else:
v = None;
try:
v = cofac.vars;
except:
pass
if v == None:
G = GroebnerBasePseudoSeq(cofac).GB(F);
else:
G = GroebnerBasePseudoRecSeq(cofac).GB(F);
t = System.currentTimeMillis() - t;
print "sequential GB executed in %s ms" % t;
return Ideal(self.ring,"",G);
def ideal(self,ringstr="",list=None):
'''Create an ideal.
'''
return Ideal(self,ringstr,list);
def isGB(self):
'''Test if this is a Groebner base.
'''
I = Ideal(self.ring,"",self.pset.list);
return I.isGB();
def GB(self):
'''Compute a Groebner base.
'''
I = Ideal(self.ring,"",self.pset.list);
g = I.GB();
return ParamIdeal(g.ring,"",g.pset.list);
def intersect(self,ring):
'''Compute the intersection of this and the given polynomial ring.
'''
s = jas.application.Ideal(self.pset);
N = s.intersect(ring.ring);
return Ideal(self.ring,"",N.getList());
"""
for t in (2, 3, 5, 7, 11, 13, 17, 19, 23, 27, 31, 37, 43):
#for t in (5,7):
r1 = SolvableRing(rs1 % t)
r1c = SolvableRing(rs1c)
#print "SolvableRing: " + str(r1);
#print "SolvableRing: " + str(r1c);
#print;
it = r1.ideal(ps % (t, t))
#print "SolvableIdeal: " + str(it);
#print;
# compute I_{\phi_t} \cap WA_1^opp
x = it.leftGB()
print "seq left x:", x
y = Ideal(x.pset).intersect(r1c.ring)
len = y.list.size()
print "seq left y: ", y
print "seq left y len: ", len
#print;
#-------------------------------------
r2 = SolvableRing(rs2 % t)
r2c = SolvableRing(rs2c % t)
#print "SolvableRing: " + str(r2);
#print "SolvableRing: " + str(r2c);
#print;
ikt = r2.ideal(ps % (t, t))
#print "SolvableIdeal: " + str(ikt);
print
# compute ker(\phi_t)
x = ikt.leftGB()