class JAS::ParamIdeal

Represents a JAS polynomial ideal with polynomial coefficients.

Methods to compute comprehensive Groebner bases.

Public Class Methods

new(ring,polystr="",list=nil,gbsys=nil) click to toggle source

Parametric ideal constructor.

     # File examples/jas.rb
3713 def initialize(ring,polystr="",list=nil,gbsys=nil)
3714     @ring = ring;
3715     if list == nil and polystr != nil
3716        sr = StringReader.new( polystr );
3717        tok = GenPolynomialTokenizer.new(ring.ring,sr);
3718        @list = tok.nextPolynomialList();
3719     else
3720        @list = rbarray2arraylist(list,rec=1);
3721     end
3722     @gbsys = gbsys;
3723     @pset = OrderedPolynomialList.new(ring.ring,@list);
3724 end

Public Instance Methods

CGB() click to toggle source

Compute a comprehensive Groebner base.

     # File examples/jas.rb
3850 def CGB()
3851     s = @pset;
3852     ff = s.list;
3853     t = System.currentTimeMillis();
3854     if @gbsys == nil
3855         @gbsys = ComprehensiveGroebnerBaseSeq.new(@ring.ring.coFac).GBsys(ff);
3856     end
3857     gg = @gbsys.getCGB();
3858     t = System.currentTimeMillis() - t;
3859     puts "sequential comprehensive executed in #{t} ms\n"; 
3860     return ParamIdeal.new(@ring,"",gg,@gbsys);
3861 end

CGBsystem() click to toggle source

Compute a comprehensive Groebner system.

     # File examples/jas.rb
3866 def CGBsystem()
3867     s = @pset;
3868     ff = s.list;
3869     t = System.currentTimeMillis();
3870     ss = ComprehensiveGroebnerBaseSeq.new(@ring.ring.coFac).GBsys(ff);
3871     t = System.currentTimeMillis() - t;
3872     puts "sequential comprehensive system executed in #{t} ms\n"; 
3873     return ParamIdeal.new(@ring,nil,ff,ss);
3874 end

GB() click to toggle source

Compute a Groebner base.

     # File examples/jas.rb
3833 def GB()
3834     ii = SimIdeal.new(@ring,"",@pset.list);
3835     g = ii.GB();
3836     return ParamIdeal.new(g.ring,"",g.pset.list);
3837 end

isCGB() click to toggle source

Test if this is a comprehensive Groebner base.

     # File examples/jas.rb
3879 def isCGB()
3880     s = @pset;
3881     ff = s.list;
3882     t = System.currentTimeMillis();
3883     b = ComprehensiveGroebnerBaseSeq.new(@ring.ring.coFac).isGB(ff);
3884     t = System.currentTimeMillis() - t;
3885     puts "isCGB = #{b} executed in #{t} ms\n"; 
3886     return b;
3887 end

isCGBsystem() click to toggle source

Test if this is a comprehensive Groebner system.

     # File examples/jas.rb
3892 def isCGBsystem()
3893     s = @pset;
3894     ss = @gbsys;
3895     t = System.currentTimeMillis();
3896     b = ComprehensiveGroebnerBaseSeq.new(@ring.ring.coFac).isGBsys(ss);
3897     t = System.currentTimeMillis() - t;
3898     puts "isCGBsystem = #{b} executed in #{t} ms\n"; 
3899     return b;
3900 end

isGB() click to toggle source

Test if this is a Groebner base.

     # File examples/jas.rb
3842 def isGB()
3843     ii = SimIdeal.new(@ring,"",@pset.list);
3844     return ii.isGB();
3845 end

isRegularGB() click to toggle source

Test if this is Groebner base over a regular ring.

     # File examples/jas.rb
3944 def isRegularGB()
3945     s = @pset;
3946     ff = s.list;
3947     t = System.currentTimeMillis();
3948     b = RGroebnerBasePseudoSeq.new(@ring.ring.coFac).isGB(ff);
3949     t = System.currentTimeMillis() - t;
3950     puts "isRegularGB = #{b} executed in #{t} ms\n"; 
3951     return b;
3952 end

optimizeCoeff() click to toggle source

Optimize the term order on the variables of the coefficients.

     # File examples/jas.rb
3741 def optimizeCoeff()
3742     p = @pset;
3743     o = TermOrderOptimization.optimizeTermOrderOnCoefficients(p);
3744     r = Ring.new("",o.ring);
3745     return ParamIdeal.new(r,"",o.list);
3746 end

optimizeCoeffQuot() click to toggle source

Optimize the term order on the variables of the quotient coefficients.

     # File examples/jas.rb
3751 def optimizeCoeffQuot()
3752     p = @pset;
3753     l = p.list;
3754     r = p.ring;
3755     q = r.coFac;
3756     c = q.ring;
3757     rc = GenPolynomialRing.new( c, r.nvar, r.tord, r.vars );
3758     #puts "rc = ", rc;
3759     lp = PolyUfdUtil.integralFromQuotientCoefficients(rc,l);
3760     #puts "lp = ", lp;
3761     pp = PolynomialList.new(rc,lp);
3762     #puts "pp = ", pp;
3763     oq = TermOrderOptimization.optimizeTermOrderOnCoefficients(pp);
3764     oor = oq.ring;
3765     qo = oor.coFac;
3766     cq = QuotientRing.new( qo );
3767     rq = GenPolynomialRing.new( cq, r.nvar, r.tord, r.vars );
3768     #puts "rq = ", rq;
3769     o = PolyUfdUtil.quotientFromIntegralCoefficients(rq,oq.list);
3770     r = Ring.new("",rq);
3771     return ParamIdeal.new(r,"",o);
3772 end

regularGB() click to toggle source

Compute a Groebner base over a regular ring.

     # File examples/jas.rb
3931 def regularGB()
3932     s = @pset;
3933     ff = s.list;
3934     t = System.currentTimeMillis();
3935     gg = RGroebnerBasePseudoSeq.new(@ring.ring.coFac).GB(ff);
3936     t = System.currentTimeMillis() - t;
3937     puts "sequential regular GB executed in #{t} ms\n"; 
3938     return ParamIdeal.new(@ring,nil,gg);
3939 end

regularRepresentation() click to toggle source

Convert Groebner system to a representation with regular ring coefficents.

     # File examples/jas.rb
3905 def regularRepresentation()
3906     if @gbsys == nil
3907         return nil;
3908     end
3909     gg = PolyUtilApp.toProductRes(@gbsys.list);
3910     ring = Ring.new(nil,gg[0].ring);
3911     return ParamIdeal.new(ring,nil,gg);
3912 end

regularRepresentationBC() click to toggle source

Convert Groebner system to a boolean closed representation with regular ring coefficents.

     # File examples/jas.rb
3917 def regularRepresentationBC()
3918     if @gbsys == nil
3919         return nil;
3920     end
3921     gg = PolyUtilApp.toProductRes(@gbsys.list);
3922     ring = Ring.new(nil,gg[0].ring);
3923     res = RReductionSeq.new();
3924     gg = res.booleanClosure(gg);
3925     return ParamIdeal.new(ring,nil,gg);
3926 end

stringSlice() click to toggle source

Get each component (slice) of regular ring coefficients separate.

     # File examples/jas.rb
3957 def stringSlice()
3958     s = @pset;
3959     b = PolyUtilApp.productToString(s);
3960     return b;
3961 end

toIntegralCoeff() click to toggle source

Convert rational function coefficients to integral function coefficients.

     # File examples/jas.rb
3777 def toIntegralCoeff()
3778     p = @pset;
3779     l = p.list;
3780     r = p.ring;
3781     q = r.coFac;
3782     c = q.ring;
3783     rc = GenPolynomialRing.new( c, r.nvar, r.tord, r.vars );
3784     #puts "rc = ", rc;
3785     lp = PolyUfdUtil.integralFromQuotientCoefficients(rc,l);
3786     #puts "lp = ", lp;
3787     r = Ring.new("",rc);
3788     return ParamIdeal.new(r,"",lp);
3789 end

toModularCoeff(mf) click to toggle source

Convert integral function coefficients to modular function coefficients.

     # File examples/jas.rb
3794 def toModularCoeff(mf)
3795     p = @pset;
3796     l = p.list;
3797     r = p.ring;
3798     c = r.coFac;
3799     #puts "c = ", c;
3800     if mf.is_a? RingElem
3801         mf = mf.ring;
3802     end
3803     cm = GenPolynomialRing.new( mf, c.nvar, c.tord, c.vars );
3804     #puts "cm = ", cm;
3805     rm = GenPolynomialRing.new( cm, r.nvar, r.tord, r.vars );
3806     #puts "rm = ", rm;
3807     pm = PolyUfdUtil.fromIntegerCoefficients(rm,l);
3808     r = Ring.new("",rm);
3809     return ParamIdeal.new(r,"",pm);
3810 end

toQuotientCoeff() click to toggle source

Convert integral function coefficients to rational function coefficients.

     # File examples/jas.rb
3815 def toQuotientCoeff()
3816     p = @pset;
3817     l = p.list;
3818     r = p.ring;
3819     c = r.coFac;
3820     #puts "c = ", c;
3821     q = QuotientRing.new(c);
3822     #puts "q = ", q;
3823     qm = GenPolynomialRing.new( q, r.nvar, r.tord, r.vars );
3824     #puts "qm = ", qm;
3825     pm = PolyUfdUtil.quotientFromIntegralCoefficients(qm,l);
3826     r = Ring.new("",qm);
3827     return ParamIdeal.new(r,"",pm);
3828 end

to_s() click to toggle source

Create a string representation.

     # File examples/jas.rb
3729     def to_s()
3730         if @gbsys == nil
3731             return @pset.toScript();
3732         else
3733             return @pset.toScript() + "\n" + @gbsys.toScript();
3734 #            return @pset.toScript() + "\n" + @gbsys.to_s;
3735         end
3736     end