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
3525 def initialize(ring,polystr="",list=nil,gbsys=nil)
3526     @ring = ring;
3527     if list == nil and polystr != nil
3528        sr = StringReader.new( polystr );
3529        tok = GenPolynomialTokenizer.new(ring.ring,sr);
3530        @list = tok.nextPolynomialList();
3531     else
3532        @list = rbarray2arraylist(list,rec=1);
3533     end
3534     @gbsys = gbsys;
3535     @pset = OrderedPolynomialList.new(ring.ring,@list);
3536 end

Public Instance Methods

CGB() click to toggle source

Compute a comprehensive Groebner base.

     # File examples/jas.rb
3662 def CGB()
3663     s = @pset;
3664     ff = s.list;
3665     t = System.currentTimeMillis();
3666     if @gbsys == nil
3667         @gbsys = ComprehensiveGroebnerBaseSeq.new(@ring.ring.coFac).GBsys(ff);
3668     end
3669     gg = @gbsys.getCGB();
3670     t = System.currentTimeMillis() - t;
3671     puts "sequential comprehensive executed in #{t} ms\n"; 
3672     return ParamIdeal.new(@ring,"",gg,@gbsys);
3673 end

CGBsystem() click to toggle source

Compute a comprehensive Groebner system.

     # File examples/jas.rb
3678 def CGBsystem()
3679     s = @pset;
3680     ff = s.list;
3681     t = System.currentTimeMillis();
3682     ss = ComprehensiveGroebnerBaseSeq.new(@ring.ring.coFac).GBsys(ff);
3683     t = System.currentTimeMillis() - t;
3684     puts "sequential comprehensive system executed in #{t} ms\n"; 
3685     return ParamIdeal.new(@ring,nil,ff,ss);
3686 end

GB() click to toggle source

Compute a Groebner base.

     # File examples/jas.rb
3645 def GB()
3646     ii = SimIdeal.new(@ring,"",@pset.list);
3647     g = ii.GB();
3648     return ParamIdeal.new(g.ring,"",g.pset.list);
3649 end

isCGB() click to toggle source

Test if this is a comprehensive Groebner base.

     # File examples/jas.rb
3691 def isCGB()
3692     s = @pset;
3693     ff = s.list;
3694     t = System.currentTimeMillis();
3695     b = ComprehensiveGroebnerBaseSeq.new(@ring.ring.coFac).isGB(ff);
3696     t = System.currentTimeMillis() - t;
3697     puts "isCGB = #{b} executed in #{t} ms\n"; 
3698     return b;
3699 end

isCGBsystem() click to toggle source

Test if this is a comprehensive Groebner system.

     # File examples/jas.rb
3704 def isCGBsystem()
3705     s = @pset;
3706     ss = @gbsys;
3707     t = System.currentTimeMillis();
3708     b = ComprehensiveGroebnerBaseSeq.new(@ring.ring.coFac).isGBsys(ss);
3709     t = System.currentTimeMillis() - t;
3710     puts "isCGBsystem = #{b} executed in #{t} ms\n"; 
3711     return b;
3712 end

isGB() click to toggle source

Test if this is a Groebner base.

     # File examples/jas.rb
3654 def isGB()
3655     ii = SimIdeal.new(@ring,"",@pset.list);
3656     return ii.isGB();
3657 end

isRegularGB() click to toggle source

Test if this is Groebner base over a regular ring.

     # File examples/jas.rb
3756 def isRegularGB()
3757     s = @pset;
3758     ff = s.list;
3759     t = System.currentTimeMillis();
3760     b = RGroebnerBasePseudoSeq.new(@ring.ring.coFac).isGB(ff);
3761     t = System.currentTimeMillis() - t;
3762     puts "isRegularGB = #{b} executed in #{t} ms\n"; 
3763     return b;
3764 end

optimizeCoeff() click to toggle source

Optimize the term order on the variables of the coefficients.

     # File examples/jas.rb
3553 def optimizeCoeff()
3554     p = @pset;
3555     o = TermOrderOptimization.optimizeTermOrderOnCoefficients(p);
3556     r = Ring.new("",o.ring);
3557     return ParamIdeal.new(r,"",o.list);
3558 end

optimizeCoeffQuot() click to toggle source

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

     # File examples/jas.rb
3563 def optimizeCoeffQuot()
3564     p = @pset;
3565     l = p.list;
3566     r = p.ring;
3567     q = r.coFac;
3568     c = q.ring;
3569     rc = GenPolynomialRing.new( c, r.nvar, r.tord, r.vars );
3570     #puts "rc = ", rc;
3571     lp = PolyUfdUtil.integralFromQuotientCoefficients(rc,l);
3572     #puts "lp = ", lp;
3573     pp = PolynomialList.new(rc,lp);
3574     #puts "pp = ", pp;
3575     oq = TermOrderOptimization.optimizeTermOrderOnCoefficients(pp);
3576     oor = oq.ring;
3577     qo = oor.coFac;
3578     cq = QuotientRing.new( qo );
3579     rq = GenPolynomialRing.new( cq, r.nvar, r.tord, r.vars );
3580     #puts "rq = ", rq;
3581     o = PolyUfdUtil.quotientFromIntegralCoefficients(rq,oq.list);
3582     r = Ring.new("",rq);
3583     return ParamIdeal.new(r,"",o);
3584 end

regularGB() click to toggle source

Compute a Groebner base over a regular ring.

     # File examples/jas.rb
3743 def regularGB()
3744     s = @pset;
3745     ff = s.list;
3746     t = System.currentTimeMillis();
3747     gg = RGroebnerBasePseudoSeq.new(@ring.ring.coFac).GB(ff);
3748     t = System.currentTimeMillis() - t;
3749     puts "sequential regular GB executed in #{t} ms\n"; 
3750     return ParamIdeal.new(@ring,nil,gg);
3751 end

regularRepresentation() click to toggle source

Convert Groebner system to a representation with regular ring coefficents.

     # File examples/jas.rb
3717 def regularRepresentation()
3718     if @gbsys == nil
3719         return nil;
3720     end
3721     gg = PolyUtilApp.toProductRes(@gbsys.list);
3722     ring = Ring.new(nil,gg[0].ring);
3723     return ParamIdeal.new(ring,nil,gg);
3724 end

regularRepresentationBC() click to toggle source

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

     # File examples/jas.rb
3729 def regularRepresentationBC()
3730     if @gbsys == nil
3731         return nil;
3732     end
3733     gg = PolyUtilApp.toProductRes(@gbsys.list);
3734     ring = Ring.new(nil,gg[0].ring);
3735     res = RReductionSeq.new();
3736     gg = res.booleanClosure(gg);
3737     return ParamIdeal.new(ring,nil,gg);
3738 end

stringSlice() click to toggle source

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

     # File examples/jas.rb
3769 def stringSlice()
3770     s = @pset;
3771     b = PolyUtilApp.productToString(s);
3772     return b;
3773 end

toIntegralCoeff() click to toggle source

Convert rational function coefficients to integral function coefficients.

     # File examples/jas.rb
3589 def toIntegralCoeff()
3590     p = @pset;
3591     l = p.list;
3592     r = p.ring;
3593     q = r.coFac;
3594     c = q.ring;
3595     rc = GenPolynomialRing.new( c, r.nvar, r.tord, r.vars );
3596     #puts "rc = ", rc;
3597     lp = PolyUfdUtil.integralFromQuotientCoefficients(rc,l);
3598     #puts "lp = ", lp;
3599     r = Ring.new("",rc);
3600     return ParamIdeal.new(r,"",lp);
3601 end

toModularCoeff(mf) click to toggle source

Convert integral function coefficients to modular function coefficients.

     # File examples/jas.rb
3606 def toModularCoeff(mf)
3607     p = @pset;
3608     l = p.list;
3609     r = p.ring;
3610     c = r.coFac;
3611     #puts "c = ", c;
3612     if mf.is_a? RingElem
3613         mf = mf.ring;
3614     end
3615     cm = GenPolynomialRing.new( mf, c.nvar, c.tord, c.vars );
3616     #puts "cm = ", cm;
3617     rm = GenPolynomialRing.new( cm, r.nvar, r.tord, r.vars );
3618     #puts "rm = ", rm;
3619     pm = PolyUfdUtil.fromIntegerCoefficients(rm,l);
3620     r = Ring.new("",rm);
3621     return ParamIdeal.new(r,"",pm);
3622 end

toQuotientCoeff() click to toggle source

Convert integral function coefficients to rational function coefficients.

     # File examples/jas.rb
3627 def toQuotientCoeff()
3628     p = @pset;
3629     l = p.list;
3630     r = p.ring;
3631     c = r.coFac;
3632     #puts "c = ", c;
3633     q = QuotientRing.new(c);
3634     #puts "q = ", q;
3635     qm = GenPolynomialRing.new( q, r.nvar, r.tord, r.vars );
3636     #puts "qm = ", qm;
3637     pm = PolyUfdUtil.quotientFromIntegralCoefficients(qm,l);
3638     r = Ring.new("",qm);
3639     return ParamIdeal.new(r,"",pm);
3640 end

to_s() click to toggle source

Create a string representation.

     # File examples/jas.rb
3541     def to_s()
3542         if @gbsys == nil
3543             return @pset.toScript();
3544         else
3545             return @pset.toScript() + "\n" + @gbsys.toScript();
3546 #            return @pset.toScript() + "\n" + @gbsys.to_s;
3547         end
3548     end