Source code

001/*
002 * $Id$
003 */
004
005package edu.jas.ufd;
006
007
008import java.util.Map;
009import java.util.SortedMap;
010import java.util.TreeMap;
011
012import org.apache.logging.log4j.LogManager;
013import org.apache.logging.log4j.Logger;
014
015import edu.jas.poly.ExpVector;
016import edu.jas.poly.GenPolynomial;
017import edu.jas.poly.GenPolynomialRing;
018import edu.jas.poly.Monomial;
019import edu.jas.poly.PolyUtil;
020import edu.jas.structure.GcdRingElem;
021import edu.jas.structure.RingFactory;
022
023
024/**
025 * Squarefree decomposition for infinite coefficient fields of characteristic p.
026 * @author Heinz Kredel
027 */
028
029public class SquarefreeInfiniteFieldCharP<C extends GcdRingElem<C>>
030                extends SquarefreeFieldCharP<Quotient<C>> {
031
032
033    private static final Logger logger = LogManager.getLogger(SquarefreeInfiniteFieldCharP.class);
034
035
036    //private static final boolean debug = logger.isDebugEnabled();
037
038
039    /**
040     * Squarefree engine for infinite ring of characteristic p base
041     * coefficients.
042     */
043    protected final SquarefreeAbstract<C> qengine;
044
045
046    /**
047     * Constructor.
048     */
049    @SuppressWarnings("unchecked")
050    public SquarefreeInfiniteFieldCharP(RingFactory<Quotient<C>> fac) {
051        super(fac);
052        // isFinite() predicate now present
053        if (fac.isFinite()) {
054            throw new IllegalArgumentException("fac must be in-finite");
055        }
056        QuotientRing<C> qfac = (QuotientRing<C>) fac;
057        GenPolynomialRing<C> rfac = qfac.ring;
058        qengine = (SquarefreeAbstract) SquarefreeFactory.<C> getImplementation(rfac);
059        //qengine = new SquarefreeFiniteFieldCharP<C>(rfac.coFac);
060        //qengine = new SquarefreeInfiniteRingCharP<C>( rfac.coFac );
061    }
062
063
064    /* --------- quotient char-th roots --------------------- */
065
066
067    /**
068     * Squarefree factors of a Quotient.
069     * @param P Quotient.
070     * @return [p_1 -&gt; e_1, ..., p_k -&gt; e_k] with P = prod_{i=1, ..., k}
071     *         p_i^{e_i} and p_i squarefree and gcd(p_i, p_j) = 1, for i != j.
072     */
073    @Override
074    public SortedMap<Quotient<C>, Long> squarefreeFactors(Quotient<C> P) {
075        if (P == null) {
076            throw new IllegalArgumentException(this.getClass().getName() + " P == null");
077        }
078        SortedMap<Quotient<C>, Long> factors = new TreeMap<Quotient<C>, Long>();
079        if (P.isZERO()) {
080            return factors;
081        }
082        if (P.isONE()) {
083            factors.put(P, 1L);
084            return factors;
085        }
086        GenPolynomial<C> num = P.num;
087        GenPolynomial<C> den = P.den;
088        QuotientRing<C> pfac = P.ring;
089        GenPolynomial<C> one = pfac.ring.getONE();
090        if (!num.isONE()) {
091            SortedMap<GenPolynomial<C>, Long> nfac = qengine.squarefreeFactors(num);
092            //System.out.println("nfac = " + nfac);
093            for (Map.Entry<GenPolynomial<C>, Long> me : nfac.entrySet()) {
094                GenPolynomial<C> nfp = me.getKey();
095                Quotient<C> nf = new Quotient<C>(pfac, nfp);
096                factors.put(nf, me.getValue()); //nfac.get(nfp));
097            }
098        }
099        if (den.isONE()) {
100            if (factors.size() == 0) {
101                factors.put(P, 1L);
102            }
103            return factors;
104        }
105        SortedMap<GenPolynomial<C>, Long> dfac = qengine.squarefreeFactors(den);
106        //System.out.println("dfac = " + dfac);
107        for (Map.Entry<GenPolynomial<C>, Long> me : dfac.entrySet()) {
108            GenPolynomial<C> dfp = me.getKey();
109            Quotient<C> df = new Quotient<C>(pfac, one, dfp);
110            factors.put(df, me.getValue()); //dfac.get(dfp));
111        }
112        if (factors.size() == 0) {
113            factors.put(P, 1L);
114        }
115        return factors;
116    }
117
118
119    /**
120     * Characteristics root of a Quotient.
121     * @param P Quotient.
122     * @return [p -&gt; k] if exists k with e=characteristic(P)*k and P = p**e,
123     *         else null.
124     */
125    public SortedMap<Quotient<C>, Long> rootCharacteristic(Quotient<C> P) {
126        if (P == null) {
127            throw new IllegalArgumentException(this.getClass().getName() + " P == null");
128        }
129        java.math.BigInteger c = P.ring.characteristic();
130        if (c.signum() == 0) {
131            return null;
132        }
133        SortedMap<Quotient<C>, Long> root = new TreeMap<Quotient<C>, Long>();
134        if (P.isZERO()) {
135            return root;
136        }
137        if (P.isONE()) {
138            root.put(P, 1L);
139            return root;
140        }
141        SortedMap<Quotient<C>, Long> sf = squarefreeFactors(P);
142        if (sf.size() == 0) {
143            return null;
144        }
145        logger.info("sf,quot = {}", sf);
146        // better: test if sf.size() == 2 // no, since num and den factors 
147        Long k = null;
148        long cl = c.longValueExact();
149        for (Map.Entry<Quotient<C>, Long> me : sf.entrySet()) {
150            Quotient<C> p = me.getKey();
151            //System.out.println("p = " + p);
152            if (p.isConstant()) { // todo: check for non-constants in coefficients
153                continue;
154            }
155            Long e = me.getValue(); //sf.get(p);
156            long E = e.longValue();
157            long r = E % cl;
158            if (r != 0) {
159                //System.out.println("r = " + r);
160                return null;
161            }
162            if (k == null) {
163                k = e;
164            } else if (k >= e) {
165                k = e;
166            }
167        }
168        if (k == null) {
169            k = 1L; //return null;
170        }
171        // now c divides all exponents of non constant elements
172        for (Map.Entry<Quotient<C>, Long> me : sf.entrySet()) {
173            Quotient<C> q = me.getKey();
174            Long e = me.getValue(); //sf.get(q);
175            //System.out.println("q = " + q + ", e = " + e);
176            if (e >= k) {
177                e = e / cl;
178                //q = q.power(e);
179                root.put(q, e);
180            } else { // constant case
181                root.put(q, e);
182            }
183        }
184        //System.out.println("root = " + root);
185        return root;
186    }
187
188
189    /**
190     * GenPolynomial char-th root main variable.
191     * @param P univariate GenPolynomial with Quotient coefficients.
192     * @return char-th_rootOf(P), or null, if P is no char-th root.
193     */
194    public GenPolynomial<Quotient<C>> rootCharacteristic(GenPolynomial<Quotient<C>> P) {
195        if (P == null || P.isZERO()) {
196            return P;
197        }
198        GenPolynomialRing<Quotient<C>> pfac = P.ring;
199        if (pfac.nvar > 1) {
200            // go to recursion
201            GenPolynomialRing<GenPolynomial<Quotient<C>>> rfac = pfac.recursive(1);
202            GenPolynomial<GenPolynomial<Quotient<C>>> Pr = PolyUtil.<Quotient<C>> recursive(rfac, P);
203            GenPolynomial<GenPolynomial<Quotient<C>>> Prc = recursiveUnivariateRootCharacteristic(Pr);
204            if (Prc == null) {
205                return null;
206            }
207            GenPolynomial<Quotient<C>> D = PolyUtil.<Quotient<C>> distribute(pfac, Prc);
208            return D;
209        }
210        RingFactory<Quotient<C>> rf = pfac.coFac;
211        if (rf.characteristic().signum() != 1) {
212            // basePthRoot not possible
213            throw new IllegalArgumentException(
214                            P.getClass().getName() + " only for ModInteger polynomials " + rf);
215        }
216        long mp = rf.characteristic().longValueExact();
217        GenPolynomial<Quotient<C>> d = pfac.getZERO().copy();
218        for (Monomial<Quotient<C>> m : P) {
219            ExpVector f = m.e;
220            long fl = f.getVal(0);
221            if (fl % mp != 0) {
222                return null;
223            }
224            fl = fl / mp;
225            SortedMap<Quotient<C>, Long> sm = rootCharacteristic(m.c);
226            if (sm == null) {
227                return null;
228            }
229            logger.info("sm,root = {}", sm);
230            Quotient<C> r = rf.getONE();
231            for (Map.Entry<Quotient<C>, Long> me : sm.entrySet()) {
232                Quotient<C> rp = me.getKey();
233                long gl = me.getValue(); // sm.get(rp);
234                if (gl > 1) {
235                    rp = rp.power(gl);
236                }
237                r = r.multiply(rp);
238            }
239            ExpVector e = ExpVector.create(1, 0, fl);
240            d.doPutToMap(e, r);
241        }
242        logger.info("sm,root,d = {}", d);
243        return d;
244    }
245
246
247    /**
248     * GenPolynomial char-th root univariate polynomial.
249     * @param P GenPolynomial.
250     * @return char-th_rootOf(P).
251     */
252    @Override
253    public GenPolynomial<Quotient<C>> baseRootCharacteristic(GenPolynomial<Quotient<C>> P) {
254        if (P == null || P.isZERO()) {
255            return P;
256        }
257        GenPolynomialRing<Quotient<C>> pfac = P.ring;
258        if (pfac.nvar > 1) {
259            // basePthRoot not possible by return type
260            throw new IllegalArgumentException(P.getClass().getName() + " only for univariate polynomials");
261        }
262        RingFactory<Quotient<C>> rf = pfac.coFac;
263        if (rf.characteristic().signum() != 1) {
264            // basePthRoot not possible
265            throw new IllegalArgumentException(P.getClass().getName() + " only for char p > 0 " + rf);
266        }
267        long mp = rf.characteristic().longValueExact();
268        GenPolynomial<Quotient<C>> d = pfac.getZERO().copy();
269        for (Monomial<Quotient<C>> m : P) {
270            //System.out.println("m = " + m);
271            ExpVector f = m.e;
272            long fl = f.getVal(0);
273            if (fl % mp != 0) {
274                return null;
275            }
276            fl = fl / mp;
277            SortedMap<Quotient<C>, Long> sm = rootCharacteristic(m.c);
278            if (sm == null) {
279                return null;
280            }
281            logger.info("sm,base,root = {}", sm);
282            Quotient<C> r = rf.getONE();
283            for (Map.Entry<Quotient<C>, Long> me : sm.entrySet()) {
284                Quotient<C> rp = me.getKey();
285                //System.out.println("rp = " + rp);
286                long gl = me.getValue(); //sm.get(rp);
287                //System.out.println("gl = " + gl);
288                Quotient<C> re = rp;
289                if (gl > 1) {
290                    re = rp.power(gl);
291                }
292                //System.out.println("re = " + re);
293                r = r.multiply(re);
294            }
295            ExpVector e = ExpVector.create(1, 0, fl);
296            d.doPutToMap(e, r);
297        }
298        logger.info("sm,base,d = {}", d);
299        return d;
300    }
301
302
303    /**
304     * GenPolynomial char-th root univariate polynomial with polynomial
305     * coefficients.
306     * @param P recursive univariate GenPolynomial.
307     * @return char-th_rootOf(P), or null if P is no char-th root.
308     */
309    @Override
310    public GenPolynomial<GenPolynomial<Quotient<C>>> recursiveUnivariateRootCharacteristic(
311                    GenPolynomial<GenPolynomial<Quotient<C>>> P) {
312        if (P == null || P.isZERO()) {
313            return P;
314        }
315        GenPolynomialRing<GenPolynomial<Quotient<C>>> pfac = P.ring;
316        if (pfac.nvar > 1) {
317            // basePthRoot not possible by return type
318            throw new IllegalArgumentException(
319                            P.getClass().getName() + " only for univariate recursive polynomials");
320        }
321        RingFactory<GenPolynomial<Quotient<C>>> rf = pfac.coFac;
322        if (rf.characteristic().signum() != 1) {
323            // basePthRoot not possible
324            throw new IllegalArgumentException(P.getClass().getName() + " only for char p > 0 " + rf);
325        }
326        long mp = rf.characteristic().longValueExact();
327        GenPolynomial<GenPolynomial<Quotient<C>>> d = pfac.getZERO().copy();
328        for (Monomial<GenPolynomial<Quotient<C>>> m : P) {
329            ExpVector f = m.e;
330            long fl = f.getVal(0);
331            if (fl % mp != 0) {
332                return null;
333            }
334            fl = fl / mp;
335            GenPolynomial<Quotient<C>> r = rootCharacteristic(m.c);
336            if (r == null) {
337                return null;
338            }
339            ExpVector e = ExpVector.create(1, 0, fl);
340            d.doPutToMap(e, r);
341        }
342        return d;
343    }
344
345}