def CGB(self):
'''Compute a comprehensive Groebner base.
'''
s = self.pset;
F = s.list;
t = System.currentTimeMillis();
if self.gbsys == None:
self.gbsys = ComprehensiveGroebnerBaseSeq(self.ring.ring.coFac).GBsys(F);
G = self.gbsys.getCGB();
t = System.currentTimeMillis() - t;
print "sequential comprehensive executed in %s ms" % t;
return ParamIdeal(self.ring,"",G,self.gbsys);
def isCGBsystem(self):
'''Test if this is a comprehensive Groebner system.
'''
s = self.pset;
S = self.gbsys;
t = System.currentTimeMillis();
b = ComprehensiveGroebnerBaseSeq(self.ring.ring.coFac).isGBsys(S);
t = System.currentTimeMillis() - t;
print "isCGBsystem executed in %s ms" % t;
return b;
def isCGB(self):
'''Test if this is a comprehensive Groebner base.
'''
s = self.pset;
F = s.list;
t = System.currentTimeMillis();
b = ComprehensiveGroebnerBaseSeq(self.ring.ring.coFac).isGB(F);
t = System.currentTimeMillis() - t;
print "isCGB executed in %s ms" % t;
return b;
def CGBsystem(self):
'''Compute a comprehensive Groebner system.
'''
s = self.pset;
F = s.list;
t = System.currentTimeMillis();
S = ComprehensiveGroebnerBaseSeq(self.ring.ring.coFac).GBsys(F);
t = System.currentTimeMillis() - t;
print "sequential comprehensive system executed in %s ms" % t;
return ParamIdeal(self.ring,None,F,S);
class ParamIdeal:
'''Represents a JAS polynomial ideal with polynomial coefficients.
Methods to compute comprehensive Groebner bases.
'''
def __init__(self,ring,polystr="",list=None,gbsys=None):
'''Parametric ideal constructor.
'''
self.ring = ring;
if list == None and polystr != None:
sr = StringReader( polystr );
tok = GenPolynomialTokenizer(ring.pset.ring,sr);
self.list = tok.nextPolynomialList();
else:
self.list = pylist2arraylist(list);
self.gbsys = gbsys;
self.pset = OrderedPolynomialList(ring.ring,self.list);
def __str__(self):
'''Create a string representation.
'''
if self.gbsys == None:
return str(self.pset);
else:
return str(self.gbsys);
# return str(self.pset) + "\n" + str(self.gbsys);
def optimizeCoeff(self):
'''Optimize the term order on the variables of the coefficients.
'''
p = self.pset;
o = TermOrderOptimization.optimizeTermOrderOnCoefficients(p);
r = Ring("",o.ring);
return ParamIdeal(r,"",o.list);
def optimizeCoeffQuot(self):
'''Optimize the term order on the variables of the quotient coefficients.
'''
p = self.pset;
l = p.list;
r = p.ring;
q = r.coFac;
c = q.ring;
rc = GenPolynomialRing( c, r.nvar, r.tord, r.vars );
#print "rc = ", rc;
lp = PolyUfdUtil.integralFromQuotientCoefficients(rc,l);
#print "lp = ", lp;
pp = PolynomialList(rc,lp);
#print "pp = ", pp;
oq = TermOrderOptimization.optimizeTermOrderOnCoefficients(pp);
oor = oq.ring;
qo = oor.coFac;
cq = QuotientRing( qo );
rq = GenPolynomialRing( cq, r.nvar, r.tord, r.vars );
#print "rq = ", rq;
o = PolyUfdUtil.quotientFromIntegralCoefficients(rq,oq.list);
r = Ring("",rq);
return ParamIdeal(r,"",o);
def toIntegralCoeff(self):
'''Convert rational function coefficients to integral function coefficients.
'''
p = self.pset;
l = p.list;
r = p.ring;
q = r.coFac;
c = q.ring;
rc = GenPolynomialRing( c, r.nvar, r.tord, r.vars );
#print "rc = ", rc;
lp = PolyUfdUtil.integralFromQuotientCoefficients(rc,l);
#print "lp = ", lp;
r = Ring("",rc);
return ParamIdeal(r,"",lp);
def toModularCoeff(self,mf):
'''Convert integral function coefficients to modular function coefficients.
'''
p = self.pset;
l = p.list;
r = p.ring;
c = r.coFac;
#print "c = ", c;
cm = GenPolynomialRing( mf, c.nvar, c.tord, c.vars );
#print "cm = ", cm;
rm = GenPolynomialRing( cm, r.nvar, r.tord, r.vars );
#print "rm = ", rm;
pm = PolyUfdUtil.fromIntegerCoefficients(rm,l);
r = Ring("",rm);
return ParamIdeal(r,"",pm);
def toQuotientCoeff(self):
'''Convert integral function coefficients to rational function coefficients.
'''
p = self.pset;
l = p.list;
r = p.ring;
c = r.coFac;
#print "c = ", c;
q = QuotientRing(c);
#print "q = ", q;
qm = GenPolynomialRing( q, r.nvar, r.tord, r.vars );
#print "qm = ", qm;
pm = PolyUfdUtil.quotientFromIntegralCoefficients(qm,l);
r = Ring("",qm);
return ParamIdeal(r,"",pm);
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 isGB(self):
'''Test if this is a Groebner base.
'''
I = Ideal(self.ring,"",self.pset.list);
return I.isGB();
def CGB(self):
'''Compute a comprehensive Groebner base.
'''
s = self.pset;
F = s.list;
t = System.currentTimeMillis();
if self.gbsys == None:
self.gbsys = ComprehensiveGroebnerBaseSeq(self.ring.ring.coFac).GBsys(F);
G = self.gbsys.getCGB();
t = System.currentTimeMillis() - t;
print "sequential comprehensive executed in %s ms" % t;
return ParamIdeal(self.ring,"",G,self.gbsys);
def CGBsystem(self):
'''Compute a comprehensive Groebner system.
'''
s = self.pset;
F = s.list;
t = System.currentTimeMillis();
S = ComprehensiveGroebnerBaseSeq(self.ring.ring.coFac).GBsys(F);
t = System.currentTimeMillis() - t;
print "sequential comprehensive system executed in %s ms" % t;
return ParamIdeal(self.ring,None,F,S);
def isCGB(self):
'''Test if this is a comprehensive Groebner base.
'''
s = self.pset;
F = s.list;
t = System.currentTimeMillis();
b = ComprehensiveGroebnerBaseSeq(self.ring.ring.coFac).isGB(F);
t = System.currentTimeMillis() - t;
print "isCGB executed in %s ms" % t;
return b;
def isCGBsystem(self):
'''Test if this is a comprehensive Groebner system.
'''
s = self.pset;
S = self.gbsys;
t = System.currentTimeMillis();
b = ComprehensiveGroebnerBaseSeq(self.ring.ring.coFac).isGBsys(S);
t = System.currentTimeMillis() - t;
print "isCGBsystem executed in %s ms" % t;
return b;
def regularRepresentation(self):
'''Convert Groebner system to a representation with regular ring coefficents.
'''
if self.gbsys == None:
return None;
G = PolyUtilApp.toProductRes(self.gbsys.list);
ring = Ring(None,G[0].ring);
return ParamIdeal(ring,None,G);
def regularGB(self):
'''Compute a Groebner base over a regular ring.
'''
s = self.pset;
F = s.list;
t = System.currentTimeMillis();
G = RGroebnerBasePseudoSeq(self.ring.ring.coFac).GB(F);
t = System.currentTimeMillis() - t;
print "sequential regular GB executed in %s ms" % t;
return ParamIdeal(self.ring,None,G);
def isRegularGB(self):
'''Test if this is Groebner base over a regular ring.
'''
s = self.pset;
F = s.list;
t = System.currentTimeMillis();
b = RGroebnerBasePseudoSeq(self.ring.ring.coFac).isGB(F);
t = System.currentTimeMillis() - t;
print "isRegularGB executed in %s ms" % t;
return b;
def stringSlice(self):
'''Get each component (slice) of regular ring coefficients separate.
'''
s = self.pset;
b = PolyUtilApp.productToString(s);
return b;
