GenPolynomial#quotientRemainder()

[axkr]

Using JAS 2.6.5961

For symbolic expressions the a.multiply(ci) in GenPolynomial#quotientRemainder() could return 0 or a more complicated expression which must be tested for 0.

Example for a complicated 0 expression: (e/Sqrt[-e/d]+d*Sqrt(-e/d))/Sqrt(-e/d)

In this case the while loop in the code below will never stop. Could JAS somehow handle this case? For example with testing for a.isZERO()

        while (!r.isZERO()) {
            ExpVector f = r.leadingExpVector();
            if (f.multipleOf(e)) {
                C a = r.leadingBaseCoefficient();
                ExpVector g = f.subtract(e);
                a = a.multiply(ci);
                q = q.sum(a, g);
                h = S.multiply(a, g);
                r = r.subtract(h);
                assert (!f.equals(r.leadingExpVector())) : "leadingExpVector not descending: " + f;
            } else {
                break;
            }
       }

[axkr]

By changing my IExpr#isZERO() implementation for symbolic expressions this issue seemed to be solved.

[kredel]

To simplify such expressions one should construct an appropriate transcendent and algebraic extension field which is then used as coefficient ring of the polynomials. Otherwise expressions not identical to 0 are not considered to be zero.