class JAS::RingElem

    # File examples/jas.rb
547 def initialize(elem)
548     if elem.is_a? RingElem
549         @elem = elem.elem;
550     else
551         @elem = elem;
552     end
553     begin
554         @ring = @elem.factory();
555     rescue
556         @ring = @elem;
557     end
558     @elem.freeze
559     @ring.freeze
560     self.freeze
561 end

    # File examples/jas.rb
918 def %(other)
919     s,o = coercePair(self,other);
920     return RingElem.new( s.elem.remainder( o.elem ) ); 
921 end

    # File examples/jas.rb
873 def *(other)
874     #puts "* self  type(#{self.elem}) = #{self.elem.class}\n";
875     #puts "* other type(#{other.elem}) = #{other.elem.class}\n";
876     s,o = coercePair(self,other);
877     #puts "* s = #{s}, o = #{o}, s*o = #{s.elem.multiply(o.elem)}\n";
878     if s.elem.is_a? GenMatrix and o.elem.is_a? GenVector
879        return RingElem.new( BasicLinAlg.new().rightProduct(o.elem, s.elem) );
880     end;
881     if s.elem.is_a? GenVector and o.elem.is_a? GenMatrix
882        return RingElem.new( BasicLinAlg.new().leftProduct(s.elem, o.elem) );
883     end;
884     return RingElem.new( s.elem.multiply( o.elem ) ); 
885 end

    # File examples/jas.rb
957 def **(other)
958     #puts "pow other type(#{other}) = #{other.class}";
959     if other.is_a? Integer
960         n = other;
961     else
962         if other.is_a? RingElem
963             n = other.elem;
964             if n.is_a? BigRational
965               #puts "#{n.numerator()} / #{n.denominator()}, other.elem = #{n}"
966               #todo (x**n.n)/(x**(-n.d))
967               if n.numerator().is_a? BigInteger
968                 n = n.numerator().intValue() / n.denominator().intValue();
969               else
970                 n = n.numerator() / n.denominator();
971               end
972             end
973             if n.is_a? BigInteger 
974                 n = n.intValue();
975             end
976         end
977     end
978     if isFactory()
979         p = Power.new(@elem).power( @elem, n );
980     else
981         p = Power.new(@elem.factory()).power( @elem, n );
982         #puts "@elem**#{n} = #{p}, @elem = #{@elem}"
983         #puts "@elem.ring = #{@elem.ring.toScript()}";
984     end
985     return RingElem.new( p ); 
986 end

    # File examples/jas.rb
890 def +(other)
891     #puts "+ self  type(#{self}) = #{self.elem.class}\n";
892     #puts "+ other type(#{other}) = #{other.elem.class}\n";
893     s,o = coercePair(self,other);
894     return RingElem.new( s.elem.sum( o.elem ) ); 
895 end

    # File examples/jas.rb
658 def +@()
659     return self; 
660 end

    # File examples/jas.rb
900 def -(other)
901     #puts "+ self  type(#{self}) = #{self.elem.class}\n";
902     #puts "+ other type(#{other}) = #{other.elem.class}\n";
903     s,o = coercePair(self,other);
904     return RingElem.new( s.elem.subtract( o.elem ) ); 
905 end

    # File examples/jas.rb
651 def -@()
652     return RingElem.new( @elem.negate() ); 
653 end

    # File examples/jas.rb
910 def /(other)
911     s,o = coercePair(self,other);
912     return RingElem.new( s.elem.divide( o.elem ) ); 
913 end

    # File examples/jas.rb
840 def <=>(other)
841     #s,o = coercePair(other);
842     s,o = self, other
843     return s.elem.compareTo( o.elem ); 
844 end

    # File examples/jas.rb
849 def ==(other)
850     if not other.is_a? RingElem
851        return false;
852     end
853     return (self <=> other) == 0; 
854 end

    # File examples/jas.rb
926 def [](i,j)
927     return get(i,j);
928 end

    # File examples/jas.rb
950 def ^(other)
951     return nil;
952 end

    # File examples/jas.rb
644 def abs()
645     return RingElem.new( @elem.abs() ); 
646 end

     # File examples/jas.rb
1307 def algebraicRoots(eps=nil)
1308     a = @elem;
1309     if eps.is_a? RingElem
1310         eps = eps.elem;
1311     end
1312     begin
1313         if eps == nil
1314             ar = RootFactory.algebraicRoots( a );
1315         else
1316             ar = RootFactory.algebraicRoots( a, eps );
1317         end
1318         #no: ar = ar.map{ |y| RingElem.new(y) };
1319         return RingElem.new(ar); #??
1320     rescue => e
1321         puts "error " + str(e)
1322         return nil
1323     end
1324 end

     # File examples/jas.rb
1650 def base_ring()
1651     begin
1652         ev = @elem.ring.coFac;
1653     rescue
1654         return nil;
1655     end
1656     return RingElem.new(ev);
1657 end

     # File examples/jas.rb
1593 def call(num)
1594     if num == 0 
1595         return zero();
1596     end
1597     if num == 1
1598         return one();
1599     end
1600     return RingElem.new( @ring.fromInteger(num) );
1601 end

     # File examples/jas.rb
1536 def coefficients()
1537     a = @elem;
1538     ll = a.coefficientIterator().map { |c| RingElem.new(c) }; 
1539     return ll
1540 end

    # File examples/jas.rb
665 def coerce(other)
666     s,o = coercePair(self,other);
667     return [o,s]; # keep order for non-commutative
668 end

    # File examples/jas.rb
703 def coerceElem(other)
704     #puts "self  type(#{self}) = #{self.class}\n";
705     #puts "other type(#{other}) = #{other.class}\n";
706     #not ok: if other.is_a? RingElem other = other.elem; end
707     if @elem.is_a? GenVector
708         if other.is_a? Array 
709             o = rbarray2arraylist(other,@elem.factory().coFac,rec=1);
710             o = GenVector.new(@elem.factory(),o);
711             return RingElem.new( o );
712             end
713     end
714     if @elem.is_a? GenMatrix
715         #puts "other #{@ring} #{other.factory()}\n";
716         if other.is_a? Array 
717             o = rbarray2arraylist(other,@elem.factory().coFac,rec=2);
718             o = GenMatrix.new(@elem.factory(),o);
719             return RingElem.new( o );
720             end
721         if other.is_a? RingElem and other.elem.is_a? GenVector
722             #puts "other vec #{other.factory()} #{other}\n";
723             #o = rbarray2arraylist(other,other.factory().coFac,rec=1);
724             #o = GenVector.new(other.factory().coFac, o);
725             o = other;
726             return o; #RingElem.new( o );
727             end
728     end
729     if other.is_a? RingElem
730         if (isPolynomial() and not other.isPolynomial()) or (isAlgNum() and not other.isAlgNum())
731             #puts "other pol.parse(#{@ring})\n";
732             o = @ring.parse( other.elem.toString() ); # not toScript()
733             return RingElem.new( o );
734         end
735         #puts "other type(#{other}) = #{other.class}\n";
736         return other;
737     end
738     #puts "--1";
739     if other.is_a? Array
740        # assume BigRational or BigComplex
741        # assume self will be compatible with them. todo: check this
742        puts "other type(#{other})_3 = #{other.class}\n";
743        o = makeJasArith(other);
744        puts "other type(#{o})_4 = #{o.class}\n";
745        ##o = BigRational.new(other[0],other[1]);
746        if isPolynomial()
747             o = @ring.parse( o.toString() ); # not toScript();
748             #o = o.elem;
749        elsif @elem.is_a? BigComplex
750             o = CC( o );
751             o = o.elem;
752        elsif @elem.is_a? BigQuaternion
753             o = Quat( o );
754             o = o.elem;
755        elsif @elem.is_a? BigOctonion
756             o = Oct( Quat(o) );
757             o = o.elem;
758        elsif @elem.is_a? Product
759             o = RR(@ring, @elem.multiply(o) ); # valueOf
760             #puts "o = #{o}";
761             o = o.elem;
762        end
763        puts "other type(#{o})_5 = #{o.class}\n";
764        return RingElem.new(o);
765     end
766     # test if @elem is a factory itself
767     if isFactory()
768         if other.is_a? Integer
769             o = @elem.fromInteger(other);
770         elsif other.is_a? Rational 
771             o = @elem.fromInteger( other.numerator );
772             o = o.divide( @elem.fromInteger( other.denominator ) );
773         elsif other.is_a? Float # ?? what to do ??
774             o = @elem.parse( other.to_s );
775             ##o = @elem.fromInteger( other.to_i );
776         else
777             puts "unknown other type(#{other})_1 = #{other.class}\n";
778             o = @elem.parse( other.to_s );
779         end
780         return RingElem.new(o);
781     end
782     # @elem has a ring factory
783     if other.is_a? Integer
784         o = @elem.factory().fromInteger(other);
785     elsif other.is_a? Rational 
786         o = @elem.factory().fromInteger( other.numerator );
787         o = o.divide( @elem.factory().fromInteger( other.denominator ) );
788     elsif other.is_a? Float # ?? what to do ??
789             o = @elem.factory().parse( other.to_s );
790             if @elem.is_a? Product
791                 o = RR(@ring, @elem.idempotent().multiply(o) ); # valueOf
792                 o = o.elem;
793             end
794     else
795             puts "unknown other type(#{other})_2 = #{other.class}\n";
796             o = @elem.factory().parse( other.to_s );
797     end
798     return RingElem.new(o);
799 end

    # File examples/jas.rb
673 def coercePair(a,b)
674     #puts "a type(#{a}) = #{a.class}\n";
675     #puts "b type(#{b}) = #{b.class}\n";
676     begin
677         if not a.isPolynomial() and b.isPolynomial()
678            #puts "b = " + str(b.isPolynomial());
679            s = b.coerceElem(a);
680            o = b;
681         else if not a.isAlgNum() and b.isAlgNum()
682                 #puts "b = " + str(b.isAlgNum());
683                 s = b.coerceElem(a);
684                 o = b;
685              else
686                 s = a;
687                 o = a.coerceElem(b);
688              end
689         end
690     rescue => e
691            #puts "e #{e.message}, a = #{a}";
692         s = a;
693         o = a.coerceElem(b);
694     end
695     #puts "s type(#{s}) = #{s.class}\n";
696     #puts "o type(#{o}) = #{o.class}\n";
697     return [s,o];
698 end

     # File examples/jas.rb
1265 def complexRoots(eps=nil)
1266     a = @elem;
1267     if eps.is_a? RingElem
1268         eps = eps.elem;
1269     end
1270     cmplx = false;
1271     begin
1272         x = a.ring.coFac.getONE().getRe();
1273         cmplx = true;
1274     rescue => e
1275         #pass;
1276     end
1277     begin
1278         if eps == nil
1279             #rr = ComplexRootsSturm.new(a.ring.coFac).complexRoots( a );
1280             if cmplx
1281                rr = RootFactory.complexAlgebraicNumbersComplex( a );
1282             else 
1283                rr = RootFactory.complexAlgebraicNumbers( a );
1284             end
1285             #R = [ r.centerApprox() for r in R ];
1286         else
1287             ## rr = ComplexRootsSturm.new(a.ring.coFac).complexRoots( a, eps );
1288             ## rr = [ r.centerApprox() for r in rr ];
1289             ##rr = ComplexRootsSturm.new(a.ring.coFac).approximateRoots( a, eps );
1290             if cmplx
1291                rr = RootFactory.complexAlgebraicNumbersComplex( a, eps );
1292             else
1293                rr = RootFactory.complexAlgebraicNumbers( a, eps );
1294             end
1295         end
1296         rr = rr.map{ |y| RingElem.new(y) };
1297         return rr;
1298     rescue => e
1299         puts "error " + str(e)
1300         return nil
1301     end
1302 end

     # File examples/jas.rb
1405 def contFrac(prec)
1406     a = @elem;
1407     if a.is_a? RealAlgebraicNumber
1408        b = prec;
1409        if b.is_a? RingElem
1410           b = b.elem;
1411        end
1412        if b < 1
1413           b = 1;
1414        end
1415        d = RealArithUtil.continuedFraction(a, b);
1416        return d;
1417     end
1418     if a.is_a? BigRational
1419        d = ArithUtil.continuedFraction(a);
1420        return d;
1421     end
1422     raise ArgumentError, "type " + str(a.class) + " not supported"
1423 end

     # File examples/jas.rb
1429 def contFracApprox(lst)
1430     if lst == nil
1431        d = BigRational::ZERO; 
1432        return RingElem.new( d );
1433     end
1434     nb = ArithUtil.continuedFractionApprox(lst);
1435     return RingElem.new( nb );
1436 end

     # File examples/jas.rb
1545 def cpp()
1546     a = @elem;
1547     r = a.coeffPrimitivePart();
1548     return RingElem.new(r);
1549 end

     # File examples/jas.rb
1347 def decimalRoots(eps=nil)
1348     a = @elem;
1349     if eps.is_a? RingElem
1350         eps = eps.elem;
1351     end
1352     if a.is_a? Java::EduJasRoot::AlgebraicRoots
1353         a = a.p;
1354     end
1355     begin
1356         d = RootFactory.decimalRoots( a, eps );
1357         return RingElem.new(d); # ??
1358     rescue => e
1359         puts "error " + str(e)
1360         return nil
1361     end
1362 end

     # File examples/jas.rb
1455 def decompLU()
1456     a = @elem;
1457     p = LinAlg.new().decompositionLU(a);
1458     uu = a.getUpper();
1459     ll = a.getLower();
1460     return [ RingElem.new(ll), RingElem.new(uu), RingElem.new(p) ];
1461 end

     # File examples/jas.rb
1638 def degree()
1639     begin
1640         ev = @elem.degree();
1641     rescue
1642         return nil;
1643     end
1644     return ev;
1645 end

     # File examples/jas.rb
1483 def determinant(p=nil)
1484     a = @elem;
1485     la = LinAlg.new();
1486     if p == nil
1487       p = la.decompositionLU(a);
1488     end;
1489     if p.is_a? RingElem
1490        p = p.elem;
1491     end
1492     if p.isEmpty()
1493       d = @ring.coFac.getZERO();
1494     else
1495       d = la.determinantLU(a,p);
1496     end;
1497     return RingElem.new(d);
1498 end

     # File examples/jas.rb
1111 def differentiate(r=nil)
1112     begin
1113         if r != nil
1114             e = @elem.differentiate(r);
1115         else
1116             e = @elem.differentiate();
1117         end
1118     rescue
1119         e = @elem.factory().getZERO();
1120     end
1121     return RingElem.new( e );
1122 end

     # File examples/jas.rb
1681 def divides(other)
1682     s,o = coercePair(self,other);
1683     return o.elem.remainder( s.elem ).isZERO(); 
1684 end

    # File examples/jas.rb
991 def equal?(other)
992     o = other;
993     if other.is_a? RingElem
994         o = other.elem;
995     end
996     return @elem.equals(o)
997 end

     # File examples/jas.rb
1033 def evaluate(a)
1034     #puts "self  type(#{@elem}) = #{@elen.class}";
1035     #puts "a     type(#{a}) = #{a.class}";
1036     x = nil;
1037     if a.is_a? RingElem
1038         x = a.elem;
1039     end
1040     if a.is_a? Array 
1041         # assume BigRational or BigComplex
1042         # assume self will be compatible with them. todo: check this
1043         #x = makeJasArith(a);
1044         x = rbarray2arraylist(a);
1045     else
1046         x = rbarray2arraylist([a]);
1047     end
1048     begin
1049         if @elem.is_a? UnivPowerSeries
1050            e = @elem.evaluate(x[0]);
1051         else if @elem.is_a? MultiVarPowerSeries
1052               e = @elem.evaluate(x);
1053            else  
1054               #puts "x     = " + x[0].getClass().getSimpleName().to_s;
1055               x = x.map{ |p| p.leadingBaseCoefficient() };
1056               e = PolyUtil.evaluateAll(@ring.coFac, @elem, x);
1057            end
1058         end
1059     rescue => e
1060         raise RuntimeError, e.to_s; 
1061         e = 0;            
1062     end
1063     return RingElem.new( e );
1064 end

     # File examples/jas.rb
1186 def factors()
1187     a = @elem;
1188     if isPolynomial()
1189        factor = Ring.getEngineFactor(@ring); 
1190        if factor == nil 
1191           raise NotImplementedError, "factors not implemented for " + @ring.to_s;
1192        end
1193        cf = @ring.coFac;
1194        if cf.is_a? GenPolynomialRing
1195            e = factor.recursiveFactors( a );
1196        else
1197            e = factor.factors( a );
1198        end
1199        ll = {};
1200        for k in e.keySet()
1201            i = e.get(k);
1202            ll[ RingElem.new( k ) ] = i;
1203        end
1204        return ll;
1205     else
1206        raise NotImplementedError, "factors not implemented for " + a.to_s;
1207     end
1208 end

     # File examples/jas.rb
1214     def factorsAbsolute()
1215         a = @elem;
1216         if isPolynomial()
1217            factor = Ring.getEngineFactor(@ring); 
1218            if factor == nil 
1219               raise NotImplementedError, "factors not implemented for " + @ring.to_s;
1220            end
1221            begin
1222                ll = factor.factorsAbsolute( a );
1223 ##             ll = {};
1224 ##             for a in e.keySet()
1225 ##                 i = e.get(a);
1226 ##                 ll[ RingElem.new( a ) ] = i;
1227                return ll;
1228            rescue => e
1229                raise RuntimeError, "error factorsAbsolute " + @ring.to_s;
1230            end
1231         else
1232            raise NotImplementedError, "factors not implemented for " + a.to_s;
1233         end
1234     end

     # File examples/jas.rb
1002 def factory()
1003     fac = @elem.factory();
1004     begin
1005         nv = fac.nvar;
1006     rescue
1007         return RingElem.new(fac);
1008     end
1009     #return PolyRing(fac.coFac,fac.getVars(),fac.tord);
1010     return RingElem.new(fac);
1011 end

     # File examples/jas.rb
1139 def gcd(b)
1140     a = @elem;
1141     if b.is_a? RingElem
1142         b = b.elem;
1143     else
1144         b = element( b );
1145         b = b.elem;
1146     end
1147     if isPolynomial()
1148        engine = Ring.getEngineGcd(@ring); 
1149        return RingElem.new( engine.gcd(a,b) );
1150     else
1151        return RingElem.new( a.gcd(b) );
1152     end
1153 end

     # File examples/jas.rb
1016 def gens()
1017     ll = @elem.factory().generators();
1018     #puts "L = #{ll}";
1019     nn = ll.map {|e| RingElem.new(e) };
1020     return nn;
1021 end

    # File examples/jas.rb
933 def get(i,j)
934     if not elem.is_a? GenMatrix
935       raise "no matrix " + ring.to_s
936     end
937     if i.is_a? RingElem
938       i = i.elem;
939     end
940     if j.is_a? RingElem
941       j = j.elem;
942     end
943     e = elem.get(i,j);
944     return RingElem.new( e );
945 end

     # File examples/jas.rb
1691 def ideal(list)
1692     r = Ring.new("",ring=self.ring); #,fast=true
1693     return r.ideal("",list=list);
1694 end

     # File examples/jas.rb
1071 def integrate(a=0,r=nil)
1072     #puts "self  type(#{@elem}) = #{@elem.class}";
1073     #puts "a     type(#{a}) = #{a.class}";
1074     x = nil;
1075     if a.is_a? RingElem
1076         x = a.elem;
1077     end
1078     if a.is_a? Array 
1079         # assume BigRational or BigComplex
1080         # assume self will be compatible with them. todo: check this
1081         x = makeJasArith(a);
1082     end
1083     # power series
1084     begin 
1085         if r != nil
1086             e = @elem.integrate(x,r);
1087         else
1088             e = @elem.integrate(x);
1089         end
1090         return RingElem.new( e );
1091     rescue
1092         #pass;
1093     end
1094     cf = @elem.ring;
1095     begin
1096         cf = cf.ring;
1097     rescue
1098         #pass;
1099     end
1100     # rational function
1101     integrator = ElementaryIntegration.new(cf.coFac);
1102     ei = integrator.integrate(@elem); 
1103     return ei;
1104 end

     # File examples/jas.rb
1554 def interiorLeftProduct(other)
1555     #puts "* self  type(#{self.elem}) = #{self.elem.class}\n";
1556     #puts "* other type(#{other.elem}) = #{other.elem.class}\n";
1557     s,o = coercePair(self,other);
1558     #puts "* s = #{s}, o = #{o}, s*o = #{s.elem.multiply(o.elem)}\n";
1559     return RingElem.new( s.elem.interiorLeftProduct( o.elem ) );
1560 end

     # File examples/jas.rb
1565 def interiorRightProduct(other)
1566     #puts "* self  type(#{self.elem}) = #{self.elem.class}\n";
1567     #puts "* other type(#{other.elem}) = #{other.elem.class}\n";
1568     s,o = coercePair(self,other);
1569     #puts "* s = #{s}, o = #{o}, s*o = #{s.elem.multiply(o.elem)}\n";
1570     return RingElem.new( s.elem.interiorRightProduct( o.elem ) );
1571 end

    # File examples/jas.rb
828 def isAlgNum()
829     begin
830         nv = @elem.ring.ring.nvar; #coFac
831     rescue
832         return false;
833     end
834     return true;
835 end

    # File examples/jas.rb
804 def isFactory()
805     f = @elem.factory();
806     if @elem == f
807         return true;
808     else
809         return false;
810     end
811 end

    # File examples/jas.rb
623 def isONE()
624     return @elem.isONE();
625 end

    # File examples/jas.rb
816 def isPolynomial()
817     begin
818         nv = @elem.ring.coFac; #nvar;
819     rescue
820         return false;
821     end
822     return true;
823 end

    # File examples/jas.rb
602 def isZERO()
603     return @elem.isZERO();
604 end

     # File examples/jas.rb
1662 def is_field()
1663     return @ring.isField();
1664 end

     # File examples/jas.rb
1619 def lc()
1620     c = @elem.leadingBaseCoefficient();
1621     return RingElem.new(c);
1622 end

    # File examples/jas.rb
859 def len()
860     return self.elem.length(); 
861 end

     # File examples/jas.rb
1609 def lm()
1610     ev = @elem.leadingExpVector();
1611     return ev;
1612 end

     # File examples/jas.rb
1630 def lt()
1631     ev = @elem.leadingMonomial();
1632     return Monomial.new(ev);
1633 end

     # File examples/jas.rb
1026 def monic()
1027     return RingElem.new( @elem.monic() ); 
1028 end

     # File examples/jas.rb
1727 def monomial_divides(a,b)
1728     #print "JAS a = " + str(a) + ", b = " + str(b);
1729     if a.is_a? RingElem
1730         a = a.elem;
1731     end
1732     if a.is_a? GenPolynomial
1733         a = a.leadingExpVector();
1734     end
1735     if not a.is_a? ExpVector
1736         raise ArgumentError, "No ExpVector given " + str(a) + ", " + str(b)
1737     end
1738     if b == nil
1739         return False;
1740     end
1741     if b.is_a? RingElem
1742         b = b.elem;
1743     end
1744     if b.is_a? GenPolynomial
1745         b = b.leadingExpVector();
1746     end
1747     if not b.is_a? ExpVector
1748         raise ArgumentError, "No ExpVector given " + str(a) + ", " + str(b)
1749     end
1750     return a.divides(b);
1751 end

     # File examples/jas.rb
1775 def monomial_lcm(e,f)
1776     if e.is_a? RingElem
1777         e = e.elem;
1778     end
1779     if f.is_a? RingElem
1780         f = f.elem;
1781     end
1782     # assume JAS ExpVector
1783     c = e.lcm(f);
1784     return c;
1785 end

     # File examples/jas.rb
1758 def monomial_pairwise_prime(e,f)
1759     if e.is_a? RingElem
1760         e = e.elem;
1761     end
1762     if f.is_a? RingElem
1763         f = f.elem;
1764     end
1765     # assume JAS ExpVector
1766     c = e.gcd(f);
1767     return c.isZERO();
1768 end

     # File examples/jas.rb
1701 def monomial_quotient(a,b,coeff=false)
1702     if a.is_a? RingElem
1703         a = a.elem;
1704     end
1705     if b.is_a? RingElem
1706         b = b.elem;
1707     end
1708     if coeff == false
1709         if a.is_a? GenPolynomial
1710             return RingElem.new( a.divide(b) );
1711         else
1712             return RingElem.new( GenPolynomial.new(@ring, a.subtract(b)) );
1713         end
1714     else
1715         # assume JAS Monomial
1716         c = a.coefficient().divide(b.coefficient());
1717         e = a.exponent().subtract(b.exponent())
1718         return RingElem.new( GenPolynomial.new(@ring, c, e) );
1719     end
1720 end

     # File examples/jas.rb
1671 def monomials()
1672     ev = @elem.getMap().keySet();
1673     return ev;
1674 end

     # File examples/jas.rb
1526 def nullSpace()
1527     a = @elem;
1528     r = LinAlg.new().nullSpaceBasis(a);
1529     return r;
1530 end

    # File examples/jas.rb
866 def object_id()
867     return @elem.hashCode(); 
868 end

    # File examples/jas.rb
616 def one()
617     return RingElem.new( @elem.factory().getONE() );
618 end

    # File examples/jas.rb
630 def one?()
631     return @elem.isONE();
632 end

     # File examples/jas.rb
1584 def parent()
1585     return factory();
1586 end

     # File examples/jas.rb
1129 def random(n=3)
1130     if n.is_a? RingElem
1131        n = n.elem
1132     end
1133     return RingElem.new( @elem.factory().random(n) );
1134 end

     # File examples/jas.rb
1516 def rank()
1517     a = @elem;
1518     r = LinAlg.new().rankRE(a);
1519     return r;
1520 end

     # File examples/jas.rb
1239 def realRoots(eps=nil)
1240     a = @elem;
1241     if eps.is_a? RingElem
1242         eps = eps.elem;
1243     end
1244     begin
1245         if eps == nil
1246             #rr = RealRootsSturm.new().realRoots( a );
1247             rr = RootFactory.realAlgebraicNumbers( a )
1248         else
1249             rr = RootFactory.realAlgebraicNumbers( a, eps );
1250             ## rr = RealRootsSturm.new().realRoots( a, eps );
1251             ## rr = [ r.toDecimal() for r in rr ];
1252             #rr = RealRootsSturm.new().approximateRoots(a,eps);
1253         end
1254         rr = rr.map{ |e| RingElem.new(e) };
1255         return rr;
1256     rescue => e
1257         puts "error " + str(e)
1258         return nil
1259     end
1260 end

     # File examples/jas.rb
1792 def reduce(ff)
1793     s = @elem;
1794     fe = ff.map {|e| e.elem };
1795     n = ReductionSeq.new().normalform(fe,s);
1796     return RingElem.new(n);
1797 end

     # File examples/jas.rb
1386 def rootReduce(other)
1387     a = @elem;
1388     b = other;
1389     if b.is_a? RingElem
1390         b = b.elem;
1391     end
1392     begin #Java::EduJasApplication::
1393         d = RootFactoryApp.rootReduce( a, b );
1394         return RingElem.new(d); # ??
1395     rescue => e
1396         puts "error " + str(e)
1397         return nil
1398     end
1399 end

     # File examples/jas.rb
1329 def rootRefine(eps=nil)
1330     r = @elem;
1331     if eps.is_a? RingElem
1332         eps = eps.elem;
1333     end
1334     begin
1335         RootFactory.rootRefine( r, eps );
1336         #no: ar = ar.map{ |y| RingElem.new(y) };
1337         return RingElem.new(r); # ??
1338     rescue => e
1339         puts "error " + str(e)
1340         return nil
1341     end
1342 end

     # File examples/jas.rb
1367 def rootsOfUnity()
1368     a = @elem;
1369     begin #Java::EduJasApplication::
1370         if a.is_a? AlgebraicRootsPrimElem
1371            d = RootFactoryApp.rootsOfUnity( a );
1372         else
1373            d = RootFactory.rootsOfUnity( a );
1374         end
1375         return RingElem.new(d); # ??
1376     rescue => e
1377         puts "error " + str(e)
1378         return nil
1379     end
1380 end

     # File examples/jas.rb
1504 def rowEchelon()
1505     a = @elem;
1506     la = LinAlg.new();
1507     re = la.rowEchelonForm(a);
1508     res = la.rowEchelonFormSparse(re);
1509     return RingElem.new(res);
1510 end

    # File examples/jas.rb
637 def signum()
638     return @elem.signum();
639 end

     # File examples/jas.rb
1442 def solve(b)
1443     a = @elem;
1444     if b.is_a? RingElem
1445        b = b.elem;
1446     end
1447     x = LinAlg.new().solve(a,b);
1448     return RingElem.new(x);
1449 end

     # File examples/jas.rb
1467 def solveLU(p, b)
1468     a = @elem;
1469     if b.is_a? RingElem
1470        b = b.elem;
1471     end
1472     if p.is_a? RingElem
1473        p = p.elem;
1474     end
1475     x = LinAlg.new().solveLU(a,p,b);
1476     return RingElem.new(x);
1477 end

     # File examples/jas.rb
1158 def squarefreeFactors()
1159     a = @elem;
1160     if isPolynomial()
1161        sqf = Ring.getEngineSqf(@ring); 
1162        if sqf == nil 
1163           raise NotImplementedError, "squarefreeFactors not implemented for " + @ring.to_s;
1164        end
1165        cf = @ring.coFac;
1166        if cf.is_a? GenPolynomialRing
1167          e = sqf.recursiveSquarefreeFactors( a );
1168        else
1169          e = sqf.squarefreeFactors( a );
1170        end
1171        ll = {};
1172        for k in e.keySet()
1173            i = e.get(k);
1174            ll[ RingElem.new( k ) ] = i;
1175        end
1176        return ll;
1177     else
1178        raise NotImplementedError, "squarefreeFactors not implemented for " + a.to_s;
1179     end
1180 end

    # File examples/jas.rb
577 def to_f()
578     e = @elem;
579     if e.is_a? BigInteger
580         e = BigRational(e);
581     end
582     if e.is_a? BigRational
583         e = BigDecimal(e);
584     end
585     if e.is_a? BigDecimal
586         e = e.toString();
587     end
588     e = e.to_f();
589     return e;
590 end

    # File examples/jas.rb
566 def to_s()
567     begin 
568        return @elem.toScript();
569     rescue 
570        return @elem.to_s(); 
571     end
572 end

    # File examples/jas.rb
595 def zero()
596     return RingElem.new( @elem.factory().getZERO() );
597 end

    # File examples/jas.rb
609 def zero?()
610     return @elem.isZERO();
611 end