Source code

001/*
002 * $Id: ComplexAlgebraicNumber.java 4961 2014-10-17 18:59:39Z kredel $
003 */
004
005package edu.jas.root;
006
007
008import edu.jas.arith.BigDecimal;
009import edu.jas.arith.BigRational;
010import edu.jas.arith.Rational;
011import edu.jas.kern.PrettyPrint;
012import edu.jas.poly.AlgebraicNumber;
013import edu.jas.poly.Complex;
014import edu.jas.poly.ComplexRing;
015import edu.jas.poly.GenPolynomial;
016import edu.jas.structure.GcdRingElem;
017import edu.jas.structure.NotInvertibleException;
018
019
020/**
021 * Complex algebraic number class based on AlgebraicNumber. Objects of this
022 * class are immutable.
023 * @author Heinz Kredel
024 */
025
026public class ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>
027/*extends AlgebraicNumber<C>*/
028implements GcdRingElem<ComplexAlgebraicNumber<C>> {
029
030
031    /**
032     * Representing AlgebraicNumber.
033     */
034    public final AlgebraicNumber<Complex<C>> number;
035
036
037    /**
038     * Ring part of the data structure.
039     */
040    public final ComplexAlgebraicRing<C> ring;
041
042
043    /**
044     * The constructor creates a ComplexAlgebraicNumber object from
045     * ComplexAlgebraicRing modul and a GenPolynomial value.
046     * @param r ring ComplexAlgebraicRing<C>.
047     * @param a value GenPolynomial<C>.
048     */
049    public ComplexAlgebraicNumber(ComplexAlgebraicRing<C> r, GenPolynomial<Complex<C>> a) {
050        number = new AlgebraicNumber<Complex<C>>(r.algebraic, a);
051        ring = r;
052    }
053
054
055    /**
056     * The constructor creates a ComplexAlgebraicNumber object from
057     * ComplexAlgebraicRing modul and a AlgebraicNumber value.
058     * @param r ring ComplexAlgebraicRing<C>.
059     * @param a value AlgebraicNumber<C>.
060     */
061    public ComplexAlgebraicNumber(ComplexAlgebraicRing<C> r, AlgebraicNumber<Complex<C>> a) {
062        number = a;
063        ring = r;
064    }
065
066
067    /**
068     * The constructor creates a ComplexAlgebraicNumber object from a
069     * GenPolynomial object module.
070     * @param r ring ComplexAlgebraicRing<C>.
071     */
072    public ComplexAlgebraicNumber(ComplexAlgebraicRing<C> r) {
073        this(r, r.algebraic.getZERO());
074    }
075
076
077    /**
078     * Get the corresponding element factory.
079     * @return factory for this Element.
080     * @see edu.jas.structure.Element#factory()
081     */
082    public ComplexAlgebraicRing<C> factory() {
083        return ring;
084    }
085
086
087    /**
088     * Copy this.
089     * @see edu.jas.structure.Element#copy()
090     */
091    @Override
092    public ComplexAlgebraicNumber<C> copy() {
093        return new ComplexAlgebraicNumber<C>(ring, number);
094    }
095
096
097    /**
098     * Is ComplexAlgebraicNumber zero.
099     * @return If this is 0 then true is returned, else false.
100     * @see edu.jas.structure.RingElem#isZERO()
101     */
102    public boolean isZERO() {
103        return number.isZERO();
104    }
105
106
107    /**
108     * Is ComplexAlgebraicNumber one.
109     * @return If this is 1 then true is returned, else false.
110     * @see edu.jas.structure.RingElem#isONE()
111     */
112    public boolean isONE() {
113        return number.isONE();
114    }
115
116
117    /**
118     * Is ComplexAlgebraicNumber unit.
119     * @return If this is a unit then true is returned, else false.
120     * @see edu.jas.structure.RingElem#isUnit()
121     */
122    public boolean isUnit() {
123        return number.isUnit();
124    }
125
126
127    /**
128     * Get the String representation as RingElem.
129     * @see java.lang.Object#toString()
130     */
131    @Override
132    public String toString() {
133        if (PrettyPrint.isTrue()) {
134            return "{ " + number.toString() + " }";
135        }
136        return "Complex" + number.toString();
137    }
138
139
140    /**
141     * Get a scripting compatible string representation.
142     * @return script compatible representation for this Element.
143     * @see edu.jas.structure.Element#toScript()
144     */
145    @Override
146    public String toScript() {
147        // Python case
148        return number.toScript();
149    }
150
151
152    /**
153     * Get a scripting compatible string representation of the factory.
154     * @return script compatible representation for this ElemFactory.
155     * @see edu.jas.structure.Element#toScriptFactory()
156     */
157    @Override
158    public String toScriptFactory() {
159        // Python case
160        return factory().toScript();
161    }
162
163
164    /**
165     * ComplexAlgebraicNumber comparison.
166     * @param b ComplexAlgebraicNumber.
167     * @return sign(this-b).
168     */
169    @Override
170    public int compareTo(ComplexAlgebraicNumber<C> b) {
171        int s = 0;
172        if (number.ring != b.number.ring) { // avoid compareTo if possible
173            s = number.ring.modul.compareTo(b.number.ring.modul);
174            System.out.println("s_mod = " + s);
175        }
176        if (s != 0) {
177            return s;
178        }
179        s = number.compareTo(b.number); // TODO
180        //System.out.println("s_real = " + s);
181        return s;
182    }
183
184
185    /**
186     * ComplexAlgebraicNumber comparison.
187     * @param b AlgebraicNumber.
188     * @return polynomial sign(this-b).
189     */
190    public int compareTo(AlgebraicNumber<Complex<C>> b) {
191        int s = number.compareTo(b);
192        //System.out.println("s_algeb = " + s);
193        return s;
194    }
195
196
197    /**
198     * Comparison with any other object.
199     * @see java.lang.Object#equals(java.lang.Object)
200     */
201    @Override
202    @SuppressWarnings("unchecked")
203    public boolean equals(Object b) {
204        if (b == null) {
205            return false;
206        }
207        if (!(b instanceof ComplexAlgebraicNumber)) {
208            return false;
209        }
210        ComplexAlgebraicNumber<C> a = (ComplexAlgebraicNumber<C>) b;
211        if (!ring.equals(a.ring)) {
212            return false;
213        }
214        return number.equals(a.number);
215    }
216
217
218    /**
219     * Hash code for this ComplexAlgebraicNumber.
220     * @see java.lang.Object#hashCode()
221     */
222    @Override
223    public int hashCode() {
224        return 37 * number.val.hashCode() + ring.hashCode();
225    }
226
227
228    /**
229     * ComplexAlgebraicNumber absolute value.
230     * @return the absolute value of this.
231     * @see edu.jas.structure.RingElem#abs()
232     */
233    public ComplexAlgebraicNumber<C> abs() {
234        if (this.signum() < 0) {
235            return new ComplexAlgebraicNumber<C>(ring, number.negate());
236        }
237        return this;
238    }
239
240
241    /**
242     * ComplexAlgebraicNumber summation.
243     * @param S ComplexAlgebraicNumber.
244     * @return this+S.
245     */
246    public ComplexAlgebraicNumber<C> sum(ComplexAlgebraicNumber<C> S) {
247        return new ComplexAlgebraicNumber<C>(ring, number.sum(S.number));
248    }
249
250
251    /**
252     * ComplexAlgebraicNumber summation.
253     * @param c complex polynomial.
254     * @return this+c.
255     */
256    public ComplexAlgebraicNumber<C> sum(GenPolynomial<Complex<C>> c) {
257        return new ComplexAlgebraicNumber<C>(ring, number.sum(c));
258    }
259
260
261    /**
262     * ComplexAlgebraicNumber summation.
263     * @param c algebraic number.
264     * @return this+c.
265     */
266    public ComplexAlgebraicNumber<C> sum(AlgebraicNumber<Complex<C>> c) {
267        return new ComplexAlgebraicNumber<C>(ring, number.sum(c));
268    }
269
270
271    /**
272     * ComplexAlgebraicNumber summation.
273     * @param c coefficient.
274     * @return this+c.
275     */
276    public ComplexAlgebraicNumber<C> sum(Complex<C> c) {
277        return new ComplexAlgebraicNumber<C>(ring, number.sum(c));
278    }
279
280
281    /**
282     * ComplexAlgebraicNumber negate.
283     * @return -this.
284     * @see edu.jas.structure.RingElem#negate()
285     */
286    public ComplexAlgebraicNumber<C> negate() {
287        return new ComplexAlgebraicNumber<C>(ring, number.negate());
288    }
289
290
291    /**
292     * ComplexAlgebraicNumber subtraction.
293     * @param S ComplexAlgebraicNumber.
294     * @return this-S.
295     */
296    public ComplexAlgebraicNumber<C> subtract(ComplexAlgebraicNumber<C> S) {
297        return new ComplexAlgebraicNumber<C>(ring, number.subtract(S.number));
298    }
299
300
301    /**
302     * ComplexAlgebraicNumber division.
303     * @param S ComplexAlgebraicNumber.
304     * @return this/S.
305     */
306    public ComplexAlgebraicNumber<C> divide(ComplexAlgebraicNumber<C> S) {
307        return multiply(S.inverse());
308    }
309
310
311    /**
312     * ComplexAlgebraicNumber inverse.
313     * @see edu.jas.structure.RingElem#inverse()
314     * @throws NotInvertibleException if the element is not invertible.
315     * @return S with S = 1/this if defined.
316     */
317    public ComplexAlgebraicNumber<C> inverse() {
318        return new ComplexAlgebraicNumber<C>(ring, number.inverse());
319    }
320
321
322    /**
323     * ComplexAlgebraicNumber remainder.
324     * @param S ComplexAlgebraicNumber.
325     * @return this - (this/S)*S.
326     */
327    public ComplexAlgebraicNumber<C> remainder(ComplexAlgebraicNumber<C> S) {
328        return new ComplexAlgebraicNumber<C>(ring, number.remainder(S.number));
329    }
330
331
332    /**
333     * Quotient and remainder by division of this by S.
334     * @param S a ComplexAlgebraicNumber
335     * @return [this/S, this - (this/S)*S].
336     */
337    public ComplexAlgebraicNumber<C>[] quotientRemainder(ComplexAlgebraicNumber<C> S) {
338        return new ComplexAlgebraicNumber[] { divide(S), remainder(S) };
339    }
340
341
342    /**
343     * ComplexAlgebraicNumber multiplication.
344     * @param S ComplexAlgebraicNumber.
345     * @return this*S.
346     */
347    public ComplexAlgebraicNumber<C> multiply(ComplexAlgebraicNumber<C> S) {
348        return new ComplexAlgebraicNumber<C>(ring, number.multiply(S.number));
349    }
350
351
352    /**
353     * ComplexAlgebraicNumber multiplication.
354     * @param c coefficient.
355     * @return this*c.
356     */
357    public ComplexAlgebraicNumber<C> multiply(Complex<C> c) {
358        return new ComplexAlgebraicNumber<C>(ring, number.multiply(c));
359    }
360
361
362    /**
363     * ComplexAlgebraicNumber multiplication.
364     * @param c polynomial.
365     * @return this*c.
366     */
367    public ComplexAlgebraicNumber<C> multiply(GenPolynomial<Complex<C>> c) {
368        return new ComplexAlgebraicNumber<C>(ring, number.multiply(c));
369    }
370
371
372    /**
373     * ComplexAlgebraicNumber monic.
374     * @return this with monic value part.
375     */
376    public ComplexAlgebraicNumber<C> monic() {
377        return new ComplexAlgebraicNumber<C>(ring, number.monic());
378    }
379
380
381    /**
382     * ComplexAlgebraicNumber greatest common divisor.
383     * @param S ComplexAlgebraicNumber.
384     * @return gcd(this,S).
385     */
386    public ComplexAlgebraicNumber<C> gcd(ComplexAlgebraicNumber<C> S) {
387        return new ComplexAlgebraicNumber<C>(ring, number.gcd(S.number));
388    }
389
390
391    /**
392     * ComplexAlgebraicNumber extended greatest common divisor.
393     * @param S ComplexAlgebraicNumber.
394     * @return [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).
395     */
396    @SuppressWarnings("unchecked")
397    public ComplexAlgebraicNumber<C>[] egcd(ComplexAlgebraicNumber<C> S) {
398        AlgebraicNumber<Complex<C>>[] aret = number.egcd(S.number);
399        ComplexAlgebraicNumber<C>[] ret = new ComplexAlgebraicNumber[3];
400        ret[0] = new ComplexAlgebraicNumber<C>(ring, aret[0]);
401        ret[1] = new ComplexAlgebraicNumber<C>(ring, aret[1]);
402        ret[2] = new ComplexAlgebraicNumber<C>(ring, aret[2]);
403        return ret;
404    }
405
406
407    /**
408     * ComplexAlgebraicNumber signum.
409     * @see edu.jas.structure.RingElem#signum()
410     * @return signum(this).
411     */
412    public int signum() {
413        try {
414            Rectangle<C> v = ring.engine.invariantRectangle(ring.root, ring.algebraic.modul, number.val);
415            ring.setRoot(v);
416            Complex<C> c = v.getCenter();
417            return c.signum();
418        } catch (InvalidBoundaryException e) { // should not happen
419            e.printStackTrace();
420            throw new RuntimeException(e);
421        }
422    }
423
424
425    /**
426     * ComplexAlgebraicNumber magnitude.
427     * @return |this| as complex rational number.
428     */
429    public Complex<BigRational> magnitude() {
430        try {
431            Rectangle<C> v = ring.engine.invariantMagnitudeRectangle(ring.root, ring.algebraic.modul,
432                            number.val, ring.getEps());
433            ring.setRoot(v);
434            //System.out.println("new v = " + v);
435            Complex<C> ev = ring.engine.complexRectangleMagnitude(v, ring.algebraic.modul, number.val); //, ring.eps);
436            //C re = ev.getRe();
437            //if ( (Object) re instanceof Rational) { // true by type parameter
438            BigRational er = ev.getRe().getRational();
439            BigRational ei = ev.getIm().getRational();
440            ComplexRing<BigRational> cr = new ComplexRing<BigRational>(er.factory());
441            return new Complex<BigRational>(cr, er, ei);
442            //} else {
443            //    throw new RuntimeException("Rational expected, but was " + ev.getClass());
444            //}
445        } catch (InvalidBoundaryException e) { // should not happen
446            e.printStackTrace();
447            throw new RuntimeException(e);
448        }
449    }
450
451
452    /**
453     * ComplexAlgebraicNumber magnitude.
454     * @return |this| as complex big decimal.
455     */
456    public Complex<BigDecimal> decimalMagnitude() {
457        Complex<BigRational> cr = magnitude();
458        ComplexRing<BigDecimal> dr = new ComplexRing<BigDecimal>(BigDecimal.ZERO);
459        return new Complex<BigDecimal>(dr, new BigDecimal(cr.getRe()), new BigDecimal(cr.getIm()));
460    }
461
462}