001/*
002 * $Id: ElementaryIntegrationLazard.java 5850 2018-06-24 15:39:36Z elbarbary $
003 */
004
005package edu.jas.integrate;
006
007
008import java.util.ArrayList;
009import java.util.List;
010import java.util.Map.Entry;
011import java.util.SortedMap;
012
013import org.apache.log4j.Logger;
014
015import edu.jas.poly.AlgebraicNumber;
016import edu.jas.poly.AlgebraicNumberRing;
017import edu.jas.poly.GenPolynomial;
018import edu.jas.poly.GenPolynomialRing;
019import edu.jas.poly.PolyUtil;
020import edu.jas.structure.GcdRingElem;
021import edu.jas.structure.RingFactory;
022import edu.jas.ufd.GCDFactory;
023import edu.jas.ufd.GreatestCommonDivisorAbstract;
024import edu.jas.ufd.GreatestCommonDivisorSubres;
025import edu.jas.ufd.PolyUfdUtil;
026
027
028/**
029 * Method related to elementary integration. Lazard-Rioboo-Trager integration of
030 * the logarithmic part.
031 * 
032 * @author Youssef Elbarbary
033 * @param <C> coefficient type
034 */
035
036public class ElementaryIntegrationLazard<C extends GcdRingElem<C>> extends ElementaryIntegration<C> {
037
038
039    private static final Logger logger = Logger.getLogger(ElementaryIntegrationLazard.class);
040
041
042    /**
043     * Constructor.
044     */
045    public ElementaryIntegrationLazard(RingFactory<C> br) {
046        super(br);
047    }
048
049
050    /**
051     * Univariate GenPolynomial integration of the logaritmic part, Lazard -
052     * Rioboo - Trager
053     * 
054     * @param A univariate GenPolynomial, deg(A) < deg(P).
055     * @param P univariate irreducible GenPolynomial. // gcd(A,P) == 1 automatic
056     * @return logarithmic part container.
057     */
058    @Override
059    public LogIntegral<C> integrateLogPart(GenPolynomial<C> A, GenPolynomial<C> P) {
060        if (P == null || P.isZERO()) {
061            throw new IllegalArgumentException("P == null or P == 0");
062        }
063        // System.out.println("\nP_base_algeb_part = " + P);
064        GenPolynomialRing<C> pfac = P.ring; // K[x]
065        if (pfac.nvar > 1) {
066            throw new IllegalArgumentException("only for univariate polynomials " + pfac);
067        }
068        if (!pfac.coFac.isField()) {
069            throw new IllegalArgumentException("only for field coefficients " + pfac);
070        }
071        List<C> cfactors = new ArrayList<C>();
072        List<GenPolynomial<C>> cdenom = new ArrayList<GenPolynomial<C>>();
073        List<AlgebraicNumber<C>> afactors = new ArrayList<AlgebraicNumber<C>>();
074        List<GenPolynomial<AlgebraicNumber<C>>> adenom = new ArrayList<GenPolynomial<AlgebraicNumber<C>>>();
075
076        // P linear
077        if (P.degree(0) <= 1) {
078            cfactors.add(A.leadingBaseCoefficient());
079            cdenom.add(P);
080            return new LogIntegral<C>(A, P, cfactors, cdenom, afactors, adenom);
081        }
082
083        // deriviative
084        GenPolynomial<C> Pp = PolyUtil.<C> baseDeriviative(P);
085        // no: Pp = Pp.monic();
086        // System.out.println("\nP = " + P);
087
088        // Q[t]
089        String[] vars = new String[] { "t" };
090        GenPolynomialRing<C> cfac = new GenPolynomialRing<C>(pfac.coFac, 1, pfac.tord, vars);
091        GenPolynomial<C> t = cfac.univariate(0);
092        // System.out.println("t = " + t);
093
094        // Q[x][t]
095        GenPolynomialRing<GenPolynomial<C>> rfac = new GenPolynomialRing<GenPolynomial<C>>(pfac, cfac); // sic
096        // System.out.println("rfac = " + rfac.toScript());
097
098        // transform polynomials to bi-variate polynomial
099        GenPolynomial<GenPolynomial<C>> Ac = PolyUfdUtil.<C> introduceLowerVariable(rfac, A);
100        GenPolynomial<GenPolynomial<C>> Pc = PolyUfdUtil.<C> introduceLowerVariable(rfac, P);
101        GenPolynomial<GenPolynomial<C>> Pcp = PolyUfdUtil.<C> introduceLowerVariable(rfac, Pp);
102
103        // Q[t][x]
104        GenPolynomialRing<GenPolynomial<C>> rfac1 = Pc.ring;
105        // System.out.println("rfac1 = " + rfac1.toScript());
106
107        // A - t P'
108        GenPolynomial<GenPolynomial<C>> tc = rfac1.getONE().multiply(t);
109        // System.out.println("tc = " + tc);
110        GenPolynomial<GenPolynomial<C>> At = Ac.subtract(tc.multiply(Pcp));
111        // System.out.println("A - tP' = " + At);
112
113        GreatestCommonDivisorSubres<C> engine = new GreatestCommonDivisorSubres<C>();
114        // = GCDFactory.<C>getImplementation( cfac.coFac );
115        GreatestCommonDivisorAbstract<AlgebraicNumber<C>> aengine = null;
116
117        // Subresultant von A - t P'
118        List<GenPolynomial<GenPolynomial<C>>> RcList = engine.recursiveUnivariateSubResultantList(Pc,
119                        At); // returning
120        GenPolynomial<GenPolynomial<C>> Rc = RcList.get(RcList.size() - 1); // just getting R
121        //System.out.println("R = " + Rc);
122
123        // SquareFree(R)
124        SortedMap<GenPolynomial<C>, Long> resSquareFree = sqf.squarefreeFactors(Rc.leadingBaseCoefficient());
125        if (logger.isInfoEnabled()) {
126            logger.info("SquareFree(R) = " + resSquareFree);
127        }
128            
129        // First Loop
130        SortedMap<GenPolynomial<C>, Long> sfactors = null;
131        GenPolynomial<AlgebraicNumber<C>> Sa = null;
132        GenPolynomial<GenPolynomial<C>> S = null;
133        GenPolynomial<C> Q = null;
134        for (Entry<GenPolynomial<C>, Long> qi : resSquareFree.entrySet()) {
135            Q = qi.getKey();
136            // System.out.println("\nr(t) = " + r);
137            if (Q.isConstant()) {
138                continue;
139            }
140            if (Q.degreeMin() == 1) {
141                Q = Q.divide(t);
142            }
143            vars = pfac.newVars("z_");
144            pfac = pfac.copy();
145            @SuppressWarnings("unused")
146            String[] unused = pfac.setVars(vars);
147            GenPolynomial<C> qi2 = pfac.copy(Q); // hack to exchange the variables
148            // System.out.println("r(z_) = " + r);
149            AlgebraicNumberRing<C> afac = new AlgebraicNumberRing<C>(qi2);
150            if (logger.isDebugEnabled()) {
151                logger.debug("afac = " + afac.toScript());
152            }
153            AlgebraicNumber<C> a = afac.getGenerator();
154            // no: a = a.negate();
155            // System.out.println("a = " + a);
156
157            // K(alpha)[x]
158            GenPolynomialRing<AlgebraicNumber<C>> pafac = new GenPolynomialRing<AlgebraicNumber<C>>(afac,
159                            Pc.ring);
160
161            // 1Condition 2Condition i = deg(D) + Check condition again!
162            if (qi2.degree() > 0) {
163                if (qi.getValue() == Pc.degree()) {
164                    GenPolynomial<C> sExp = P;
165                    // convert to K(alpha)[x]
166                    Sa = PolyUtil.<C> convertToAlgebraicCoefficients(pafac, sExp);
167                    afactors.add(a);
168                    adenom.add(Sa);
169                    return new LogIntegral<C>(A, P, cfactors, cdenom, afactors, adenom);
170                }
171                int countj = 1;
172                // RcList.remove(RcList.size()-1);
173                for (GenPolynomial<GenPolynomial<C>> Ri : RcList) {
174                    if (qi.getValue() == Ri.degree()) {
175                        S = Ri;
176                        // convert to K(alpha)[x]
177                        Sa = PolyUtil.convertRecursiveToAlgebraicCoefficients(pafac, S);
178                        sfactors = sqf.squarefreeFactors(S.leadingBaseCoefficient());
179                        if (logger.isInfoEnabled()) {
180                            logger.info("SquareFree(S)" + sfactors);
181                        }
182                    }
183                }
184                for (GenPolynomial<C> ai : sfactors.keySet()) {
185                    GenPolynomial<AlgebraicNumber<C>> aiC = PolyUtil.<C> convertToAlgebraicCoefficients(pafac,
186                                    ai);
187                    GenPolynomial<AlgebraicNumber<C>> qiC = PolyUtil.<C> convertToAlgebraicCoefficients(pafac,
188                                    qi2);
189                    if (aengine == null) {
190                        aengine = GCDFactory.<AlgebraicNumber<C>> getImplementation(afac);
191                    }
192                    GenPolynomial<AlgebraicNumber<C>> gcd = aengine.baseGcd(aiC, qiC);
193                    gcd = gcd.power(countj);
194                    Sa = (Sa.divide(gcd));
195                    countj++;
196                    if (Sa.isZERO() || a.isZERO()) {
197                        System.out.println("warning constant Sa ignored");
198                        continue;
199                    }
200                }
201                //System.out.println("S = " + Sa);
202                afactors.add(a);
203                adenom.add(Sa.monic());
204                // adenom.add(Sa.monic());
205            }
206        }
207        return new LogIntegral<C>(A, P, cfactors, cdenom, afactors, adenom);
208    }
209}