class JAS::SimIdeal

Represents a JAS polynomial ideal: PolynomialList and Ideal.

Methods for Groebner bases, ideal sum, intersection and others.

Attributes

list[R]

the Java polynomial list, polynomial ring, and ideal decompositions

primary[R]

the Java polynomial list, polynomial ring, and ideal decompositions

prime[R]

the Java polynomial list, polynomial ring, and ideal decompositions

pset[R]

the Java polynomial list, polynomial ring, and ideal decompositions

ring[R]

the Java polynomial list, polynomial ring, and ideal decompositions

roots[R]

the Java polynomial list, polynomial ring, and ideal decompositions

Public Class Methods

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

SimIdeal constructor.

# File examples/jas.rb, line 2752
def initialize(ring,polystr="",list=nil)
    @ring = ring;
    if list == nil
       sr = StringReader.new( polystr );
       tok = GenPolynomialTokenizer.new(ring::ring,sr);
       @list = tok.nextPolynomialList();
    else
       @list = rbarray2arraylist(list,rec=1);
    end
    #@list = PolyUtil.monic(@list);
    @pset = OrderedPolynomialList.new(@ring.ring,@list);
    #@ideal = Ideal.new(@pset);
    @roots = nil;
    @croots = nil;
    @prime = nil;
    @primary = nil;
    #super(@ring::ring,@list) # non-sense, JRuby extends application.Ideal
end

Public Instance Methods

<=>(other) click to toggle source

Compare two ideals.

# File examples/jas.rb, line 2781
def <=>(other)
    s = Ideal.new(@pset);
    o = Ideal.new(other.pset);
    return s.compareTo(o);
end

==(other) click to toggle source

Test if two ideals are equal.

# File examples/jas.rb, line 2790
def ==(other)
    if not other.is_a? SimIdeal
       return false;
    end
    return (self <=> other) == 0; 
end

CS() click to toggle source

Compute a Characteristic Set.

# File examples/jas.rb, line 3323
def CS()
    s = @pset;
    cofac = s.ring.coFac;
    ff = s.list;
    t = System.currentTimeMillis();
    if cofac.isField()
        gg = CharacteristicSetWu.new().characteristicSet(ff);
    else
        puts "CS not implemented for coefficients #{cofac.toScriptFactory()}\n"; 
        gg = nil;
    end
    t = System.currentTimeMillis() - t;
    puts "sequential char set executed in #{t} ms\n"; 
    return SimIdeal.new(@ring,"",gg);
end

GB() click to toggle source

Compute a Groebner base.

# File examples/jas.rb, line 2823
def GB()
    #if @ideal != nil
    #   return SimIdeal.new(@ring,"",nil,@ideal.GB());
    #end
    cofac = @ring.ring.coFac;
    ff = @pset.list;
    kind = "";
    t = System.currentTimeMillis();
    if cofac.isField()
        #gg = GroebnerBaseSeq.new().GB(ff);
        #gg = GroebnerBaseSeq.new(ReductionSeq.new(),OrderedPairlist.new()).GB(ff);
        gg = GroebnerBaseSeq.new(ReductionSeq.new(),OrderedSyzPairlist.new()).GB(ff);
        #gg = GroebnerBaseSeqIter.new(ReductionSeq.new(),OrderedSyzPairlist.new()).GB(ff);
        kind = "field"
    else
        if cofac.is_a? GenPolynomialRing and cofac.isCommutative()
            gg = GroebnerBasePseudoRecSeq.new(cofac).GB(ff);
            kind = "pseudoRec"
        else
            gg = GroebnerBasePseudoSeq.new(cofac).GB(ff);
            kind = "pseudo"
        end
    end
    t = System.currentTimeMillis() - t;
    puts "sequential(#{kind}) GB executed in #{t} ms\n"; 
    return SimIdeal.new(@ring,"",gg);
end

NF(reducer) click to toggle source

Compute a normal form of this ideal with respect to reducer.

# File examples/jas.rb, line 3064
def NF(reducer)
    s = @pset;
    ff = s.list;
    gg = reducer.list;
    t = System.currentTimeMillis();
    nn = ReductionSeq.new().normalform(gg,ff);
    t = System.currentTimeMillis() - t;
    puts "sequential NF executed in #{t} ms\n"; 
    return SimIdeal.new(@ring,"",nn);
end

complexRoots() click to toggle source

Compute complex roots of 0-dim ideal.

# File examples/jas.rb, line 3243
def complexRoots()
    ii = Ideal.new(@pset);
    @croots = PolyUtilApp.complexAlgebraicRoots(ii);
    for r in @croots
        r.doDecimalApproximation();
    end
    return @croots;
end

complexRootsPrint() click to toggle source

Print decimal approximation of complex roots of 0-dim ideal.

# File examples/jas.rb, line 3255
def complexRootsPrint()
    if @croots == nil
        ii = Ideal.new(@pset);
        @croots = PolyUtilApp.complexAlgebraicRoots(ii);
        for r in @croots
            r.doDecimalApproximation();
        end
    end
    for ic in @croots
        for dc in ic.decimalApproximation()
            puts dc.to_s;
        end
        puts;
    end
end

csReduction(p) click to toggle source

Compute a normal form of polynomial p with respect this characteristic set.

# File examples/jas.rb, line 3362
def csReduction(p)
    s = @pset;
    ff = s.list.clone();
    Collections.reverse(ff); # todo
    if p.is_a? RingElem
        p = p.elem;
    end
    t = System.currentTimeMillis();
    nn = CharacteristicSetWu.new().characteristicSetReduction(ff,p);
    t = System.currentTimeMillis() - t;
    #puts "sequential char set reduction executed in #{t} ms\n"; 
    return RingElem.new(nn);
end

dGB() click to toggle source

Compute an d-Groebner base.

# File examples/jas.rb, line 2912
def dGB()
    s = @pset;
    cofac = s.ring.coFac;
    ff = s.list;
    t = System.currentTimeMillis();
    if cofac.isField()
        gg = GroebnerBaseSeq.new().GB(ff);
    else
        gg = DGroebnerBaseSeq.new().GB(ff)
    end
    t = System.currentTimeMillis() - t;
    puts "sequential d-GB executed in #{t} ms\n"; 
    return SimIdeal.new(@ring,"",gg);
end

decomposition() click to toggle source

Compute irreducible decomposition of this ideal.

# File examples/jas.rb, line 3234
def decomposition()
    ii = Ideal.new(@pset);
    @irrdec = ii.decomposition();
    return @irrdec;
end

distClient(port=4711) click to toggle source

Client for a distributed computation.

# File examples/jas.rb, line 3002
def distClient(port=4711)
    s = @pset;
    e1 = ExecutableServer.new( port );
    e1.init();
    e2 = ExecutableServer.new( port+1 );
    e2.init();
    @exers = [e1,e2];
    return nil;
end

distClientStop() click to toggle source

Client for a distributed computation.

# File examples/jas.rb, line 3016
def distClientStop()
    for es in @exers;
        es.terminate();
    end
    return nil;
end

distGB(th=2,machine="examples/machines.localhost",port=55711) click to toggle source

Compute on a distributed system a Groebner base.

# File examples/jas.rb, line 2983
def distGB(th=2,machine="examples/machines.localhost",port=55711)
    s = @pset;
    ff = s.list;
    t = System.currentTimeMillis();
    # old: gbd = GBDist.new(th,machine,port);
    gbd = GroebnerBaseDistributedEC.new(machine,th,port);
    #gbd = GroebnerBaseDistributedHybridEC.new(machine,th,3,port);
    t1 = System.currentTimeMillis();
    gg = gbd.GB(ff);
    t1 = System.currentTimeMillis() - t1;
    gbd.terminate(false);
    t = System.currentTimeMillis() - t;
    puts "distributed #{th} executed in #{t1} ms (#{t-t1} ms start-up)\n"; 
    return SimIdeal.new(@ring,"",gg);
end

eGB() click to toggle source

Compute an e-Groebner base.

# File examples/jas.rb, line 2876
def eGB()
    s = @pset;
    cofac = s.ring.coFac;
    ff = s.list;
    t = System.currentTimeMillis();
    if cofac.isField()
        gg = GroebnerBaseSeq.new().GB(ff);
    else
        gg = EGroebnerBaseSeq.new().GB(ff)
    end
    t = System.currentTimeMillis() - t;
    puts "sequential e-GB executed in #{t} ms\n"; 
    return SimIdeal.new(@ring,"",gg);
end

eReduction(p) click to toggle source

Compute a e-normal form of p with respect to this ideal.

# File examples/jas.rb, line 3048
def eReduction(p)
    s = @pset;
    gg = s.list;
    if p.is_a? RingElem
        p = p.elem;
    end
    t = System.currentTimeMillis();
    n = EReductionSeq.new().normalform(gg,p);
    t = System.currentTimeMillis() - t;
    puts "sequential eReduction executed in " + str(t) + " ms"; 
    return RingElem.new(n);
end

eliminateRing(ring) click to toggle source

Compute the elimination ideal of this and the given polynomial ring.

# File examples/jas.rb, line 3130
def eliminateRing(ring)
    s = Ideal.new(@pset);
    nn = s.eliminate(ring.ring);
    r = Ring.new( "", nn.getRing() );
    return SimIdeal.new(r,"",nn.getList());
end

interreduced_basis() click to toggle source

Compute a interreduced ideal basis of this.

# File examples/jas.rb, line 3102
def interreduced_basis()
    ff = @pset.list;
    nn = ReductionSeq.new().irreducibleSet(ff);
    return nn.map{ |x| RingElem.new(x) };
end

intersect(id2) click to toggle source

Compute the intersection of this and the given ideal.

# File examples/jas.rb, line 3120
def intersect(id2)
    s1 = Ideal.new(@pset);
    s2 = Ideal.new(id2.pset);
    nn = s1.intersect(s2);
    return SimIdeal.new(@ring,"",nn.getList());
end

intersectRing(ring) click to toggle source

Compute the intersection of this and the given polynomial ring.

# File examples/jas.rb, line 3111
def intersectRing(ring)
    s = Ideal.new(@pset);
    nn = s.intersect(ring.ring);
    return SimIdeal.new(ring,"",nn.getList());
end

inverse(p) click to toggle source

Compute the inverse polynomial modulo this ideal, if it exists.

# File examples/jas.rb, line 3172
def inverse(p)
    if p.is_a? RingElem
        p = p.elem;
    end
    s = Ideal.new(@pset);
    i = s.inverse(p);
    return RingElem.new(i);
end

isCS() click to toggle source

Test for Characteristic Set.

# File examples/jas.rb, line 3342
def isCS()
    s = @pset;
    cofac = s.ring.coFac;
    ff = s.list.clone();
    Collections.reverse(ff); # todo
    t = System.currentTimeMillis();
    if cofac.isField()
        b = CharacteristicSetWu.new().isCharacteristicSet(ff);
    else
        puts "isCS not implemented for coefficients #{cofac.toScriptFactory()}\n"; 
        b = false;
    end
    t = System.currentTimeMillis() - t;
    #puts "sequential is char set executed in #{t} ms\n"; 
    return b;
end

isGB() click to toggle source

Test if this is a Groebner base.

# File examples/jas.rb, line 2854
def isGB()
    s = @pset;
    cofac = s.ring.coFac;
    ff = s.list;
    t = System.currentTimeMillis();
    if cofac.isField()
        b = GroebnerBaseSeq.new().isGB(ff);
    else
        if cofac.is_a? GenPolynomialRing and cofac.isCommutative()
            b = GroebnerBasePseudoRecSeq.new(cofac).isGB(ff);
        else
            b = GroebnerBasePseudoSeq.new(cofac).isGB(ff);
        end
    end
    t = System.currentTimeMillis() - t;
    puts "isGB = #{b} executed in #{t} ms\n"; 
    return b;
end

isONE() click to toggle source

Test if ideal is one.

# File examples/jas.rb, line 2800
def isONE()
    s = Ideal.new(@pset);
    return s.isONE(); 
end

isSyzygy(m) click to toggle source

Test if this is a syzygy of the module in m.

# File examples/jas.rb, line 3393
def isSyzygy(m)
    p = @pset;
    g = p.list;
    l = m.list;
    #puts "l = #{l}"; 
    #puts "g = #{g}"; 
    t = System.currentTimeMillis();
    z = SyzygySeq.new(p.ring.coFac).isZeroRelation( l, g );
    t = System.currentTimeMillis() - t;
    puts "executed isSyzygy in #{t} ms\n"; 
    return z;
end

isZERO() click to toggle source

Test if ideal is zero.

# File examples/jas.rb, line 2808
def isZERO()
    s = Ideal.new(@pset);
    return s.isZERO(); 
end

isdGB() click to toggle source

Test if this is a d-Groebner base.

# File examples/jas.rb, line 2930
def isdGB()
    s = @pset;
    cofac = s.ring.coFac;
    ff = s.list;
    t = System.currentTimeMillis();
    if cofac.isField()
        b = GroebnerBaseSeq.new().isGB(ff);
    else
        b = DGroebnerBaseSeq.new().isGB(ff)
    end
    t = System.currentTimeMillis() - t;
    puts "is d-GB = #{b} executed in #{t} ms\n"; 
    return b;
end

iseGB() click to toggle source

Test if this is an e-Groebner base.

# File examples/jas.rb, line 2894
def iseGB()
    s = @pset;
    cofac = s.ring.coFac;
    ff = s.list;
    t = System.currentTimeMillis();
    if cofac.isField()
        b = GroebnerBaseSeq.new().isGB(ff);
    else
        b = EGroebnerBaseSeq.new().isGB(ff)
    end
    t = System.currentTimeMillis() - t;
    puts "is e-GB = #{b} executed in #{t} ms\n"; 
    return b;
end

lift(p) click to toggle source

Represent p as element of this ideal.

# File examples/jas.rb, line 3078
def lift(p)
    gg = @pset.list;
    z = @ring.ring.getZERO();
    rr = gg.map { |x| z };
    if p.is_a? RingElem
        p = p.elem;
    end
    #t = System.currentTimeMillis();
    if @ring.ring.coFac.isField()
       n = ReductionSeq.new().normalform(rr,gg,p);
    else 
       n = PseudoReductionSeq.new().normalform(rr,gg,p);
    end
    if not n.isZERO()
       raise StandardError, "p ist not a member of the ideal"
    end
    #t = System.currentTimeMillis() - t;
    #puts "sequential reduction executed in " + str(t) + " ms"; 
    return rr.map { |x| RingElem.new(x) };
end

optimize() click to toggle source

Optimize the term order on the variables.

# File examples/jas.rb, line 3184
def optimize()
    p = @pset;
    o = TermOrderOptimization.optimizeTermOrder(p);
    r = Ring.new("",o.ring);
    return SimIdeal.new(r,"",o.list);
end

parGB(th) click to toggle source

Compute in parallel a Groebner base.

# File examples/jas.rb, line 2963
def parGB(th)
    s = @pset;
    ff = s.list;
    cofac = s.ring.coFac;
    if cofac.isField() 
       bbpar = GroebnerBaseParallel.new(th);
    else 
       bbpar = GroebnerBasePseudoParallel.new(th,cofac);
    end
    t = System.currentTimeMillis();
    gg = bbpar.GB(ff);
    t = System.currentTimeMillis() - t;
    bbpar.terminate();
    puts "parallel #{th} executed in #{t} ms\n"; 
    return SimIdeal.new(@ring,"",gg);
end

parUnusedGB(th) click to toggle source

Compute in parallel a Groebner base.

# File examples/jas.rb, line 2948
def parUnusedGB(th)
    s = @pset;
    ff = s.list;
    bbpar = GroebnerBaseSeqPairParallel.new(th);
    t = System.currentTimeMillis();
    gg = bbpar.GB(ff);
    t = System.currentTimeMillis() - t;
    bbpar.terminate();
    puts "parallel-old #{th} executed in #{t} ms\n"; 
    return SimIdeal.new(@ring,"",gg);
end

paramideal() click to toggle source

Create an ideal in a polynomial ring with parameter coefficients.

# File examples/jas.rb, line 2816
def paramideal()
    return ParamIdeal.new(@ring,"",@list);
end

primaryDecomp() click to toggle source

Compute primary decomposition of this ideal.

# File examples/jas.rb, line 3283
    def primaryDecomp()
        ii = Ideal.new(@pset);
##         if @prime == nil:
##             @prime = I.primeDecomposition();
        @primary = ii.primaryDecomposition();
        return @primary;
    end

primeDecomp() click to toggle source

Compute prime decomposition of this ideal.

# File examples/jas.rb, line 3274
def primeDecomp()
    ii = Ideal.new(@pset);
    @prime = ii.primeDecomposition();
    return @prime;
end

radicalDecomp() click to toggle source

Compute radical decomposition of this ideal.

# File examples/jas.rb, line 3225
def radicalDecomp()
    ii = Ideal.new(@pset);
    @radical = ii.radicalDecomposition();
    return @radical;
end

realRoots() click to toggle source

Compute real roots of 0-dim ideal.

# File examples/jas.rb, line 3194
def realRoots()
    ii = Ideal.new(@pset);
    @roots = PolyUtilApp.realAlgebraicRoots(ii);
    for r in @roots
        r.doDecimalApproximation();
    end
    return @roots;
end

realRootsPrint() click to toggle source

Print decimal approximation of real roots of 0-dim ideal.

# File examples/jas.rb, line 3206
def realRootsPrint()
    if @roots == nil
        ii = Ideal.new(@pset);
        @roots = PolyUtilApp.realAlgebraicRoots(ii);
        for r in @roots
            r.doDecimalApproximation();
        end
    end
    for ir in @roots
        for dr in ir.decimalApproximation()
            puts dr.to_s;
        end
        puts;
    end
end

reduction(p) click to toggle source

Compute a normal form of p with respect to this ideal.

# File examples/jas.rb, line 3026
def reduction(p)
    s = @pset;
    gg = s.list;
    if p.is_a? RingElem
        p = p.elem;
    end
    #t = System.currentTimeMillis();
    if @ring.ring.coFac.isField()
       n = ReductionSeq.new().normalform(gg,p);
    else 
       n = PseudoReductionSeq.new().normalform(gg,p);
       #ff = PseudoReductionSeq.New().normalformFactor(gg,p);
       #print "ff.multiplicator = " + str(ff.multiplicator)
    end
    #t = System.currentTimeMillis() - t;
    #puts "sequential reduction executed in " + str(t) + " ms"; 
    return RingElem.new(n);
end

sat(id2) click to toggle source

Compute the saturation of this and the given ideal.

# File examples/jas.rb, line 3140
def sat(id2)
    s1 = Ideal.new(@pset);
    s2 = Ideal.new(id2.pset);
    #nn = s1.infiniteQuotient(s2);
    nn = s1.infiniteQuotientRab(s2);
    mm = nn.getList(); #PolyUtil.monicRec(nn.getList());
    return SimIdeal.new(@ring,"",mm);
end

sum(other) click to toggle source

Compute the sum of this and the ideal.

# File examples/jas.rb, line 3152
def sum(other)
    s = Ideal.new(@pset);
    t = Ideal.new(other.pset);
    nn = s.sum( t );
    return SimIdeal.new(@ring,"",nn.getList());
end

syzygy() click to toggle source

Syzygy of generating polynomials.

# File examples/jas.rb, line 3379
def syzygy()
    p = @pset;
    l = p.list;
    t = System.currentTimeMillis();
    s = SyzygySeq.new(p.ring.coFac).zeroRelations( l );
    t = System.currentTimeMillis() - t;
    puts "executed Syzygy in #{t} ms\n"; 
    m = CommutativeModule.new("",p.ring);
    return SubModule.new(m,"",s);
end

toInteger() click to toggle source

Convert rational coefficients to integer coefficients.

# File examples/jas.rb, line 3294
def toInteger()
    p = @pset;
    l = p.list;
    r = p.ring;
    ri = GenPolynomialRing.new( BigInteger.new(), r.nvar, r.tord, r.vars );
    pi = PolyUtil.integerFromRationalCoefficients(ri,l);
    r = Ring.new("",ri);
    return SimIdeal.new(r,"",pi);
end

toModular(mf) click to toggle source

Convert integer coefficients to modular coefficients.

# File examples/jas.rb, line 3307
def toModular(mf)
    p = @pset;
    l = p.list;
    r = p.ring;
    if mf.is_a? RingElem
        mf = mf.ring;
    end
    rm = GenPolynomialRing.new( mf, r.nvar, r.tord, r.vars );
    pm = PolyUtil.fromIntegerCoefficients(rm,l);
    r = Ring.new("",rm);
    return SimIdeal.new(r,"",pm);
end

to_s() click to toggle source

Create a string representation.

# File examples/jas.rb, line 2774
def to_s()
    return @pset.toScript();
end

univariates() click to toggle source

Compute the univariate polynomials in each variable of this ideal.

# File examples/jas.rb, line 3162
def univariates()
    s = Ideal.new(@pset);
    ll = s.constructUnivariate();
    nn = ll.map {|e| RingElem.new(e) };
    return nn;
end