[JIRA] Created: (JSCIENCE-3) Error in multiplication of two Polynomials

["sbrisard (JIRA)" <jira-no-reply@kenai.com>]

Error in multiplication of two Polynomials
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                 Key: JSCIENCE-3
                 URL: http://kenai.com/jira/browse/JSCIENCE-3
             Project: jscience
          Issue Type: Bug
         Environment: Any
            Reporter: sbrisard
         Attachments: DemoBug.java

Multiplication of two polynomials sometimes gives the wrong answer (see 
example attached). This is due to an error in the code for Polynomial.times. 
The output of the example is given below
p = [1]a² + [2]ab + [1]b²
q = [1]a5 + [-5]a4b + [10]a³b²
p.times(q) = [1]a7 + [-3]a6b + [11]a5b² + [15]a4b³ + [10]a³b4
q.times(p) = [1]a7 + [-3]a6b + [1]a5b² + [15]a4b³ + [10]a³b4

p.times(q) is wrong, while q.times(p) is correct. During calculation of 
p.times(q), the coefficient of a5b2 goes to 0 = 10+(-10). It should then 
either be *set* to zero in the _termToCoef entry set, or be removed from this 
entry set, until it is again non-zero in further iterations. I chose the 
second option (removal), and the correct code looks like this

    public Polynomial<R> times(Polynomial<R> that) {
        Polynomial<R> result = Polynomial.newInstance();
        R zero = null;
        for (Map.Entry<Term, R> entry1 : this._termToCoef.entrySet()) {
            Term t1 = entry1.getKey();
            R c1 = entry1.getValue();
            for (Map.Entry<Term, R> entry2 : that._termToCoef.entrySet()) {
                Term t2 = entry2.getKey();
                R c2 = entry2.getValue();
                Term t = t1.times(t2);
                R c = c1.times(c2);
                R prev = result.getCoefficient(t);
                R coef = (prev != null) ? prev.plus(c) : c;
                if (isZero(coef)) {
                    zero = coef;
                    result._termToCoef.remove(t); // NOTE : Added this line
                } else {
                    result._termToCoef.put(t, coef);
                }
            }
        }
        if (result._termToCoef.size() == 0)
            return Constant.valueOf(zero);
        return result;
    }


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