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            return true;
        return false;
    }
    
    Polynomial = function Polynomial(a)
    {
        if (new.target)
            throw TypeError("not a constructor");
        if (a instanceof Polynomial) {
            return a;
        } else if (Array.isArray(a)) {
            if (a.length == 0)
                a = [ 0 ];
            Object.setPrototypeOf(a, Polynomial.prototype);
            return a.trim();
        } else if (polynomial_is_scalar(a)) {
            a = [a];
            Object.setPrototypeOf(a, Polynomial.prototype);
            return a;
        } else {
            throw TypeError("invalid type");
        }
    }

    function number_need_paren(c)
    {
        return !(Integer.isInteger(c) ||
                 Float.isFloat(c) ||
                 c instanceof Fraction ||
                 (c instanceof Complex && c.re == 0));
    }

    /* string for c*X^i */
    function monomial_toString(c, i)
    {
        var str1;
        if (i == 0) {
            str1 = c.toString();
        } else {
            if (c == 1) {
                str1 = "";
            } else if (c == -1) {
                str1 = "-";
            } else {
                if (number_need_paren(c)) {
                    str1 = "(" + c + ")";
                } else {
                    str1 = String(c);
                }
                str1 += "*";
            }
            str1 += "X";
            if (i != 1) {
                str1 += "^" + i;
            }
        }
        return str1;
    }

    /* find one complex root of 'p' starting from z at precision eps using
       at most max_it iterations. Return null if could not find root. */
    function poly_root_laguerre1(p, z, max_it)
    {
        var p1, p2, i, z0, z1, z2, d, t0, t1, d1, d2, e, el, zl;

        d = p.deg();
        if (d == 1) {
            /* monomial case */
            return -p[0] / p[1];
        }
        /* trivial zero */
        if (p[0] == 0)
            return 0.0;
        
        p1 = p.deriv();
        p2 = p1.deriv();
        el = 0.0;
        zl = 0.0;
        for(i = 0; i < max_it; i++) {
            z0 = p.apply(z);
            if (z0 == 0)
                return z; /* simple exit case */

            /* Ward stopping criteria */
            e = abs(z - zl);
//            print("e", i, e);
            if (i >= 2 && e >= el) {
                if (abs(zl) < 1e-4) {
                    if (e < 1e-7)
                        return zl;
                } else {
                    if (e < abs(zl) * 1e-3)
                        return zl;
                }
            }
            el = e;
            zl = z;
            
            z1 = p1.apply(z);
            z2 = p2.apply(z);
            t0 = (d - 1) * z1;
            t0 = t0 * t0;
            t1 = d * (d - 1) * z0 * z2;
            t0 = sqrt(t0 - t1);
            d1 = z1 + t0;
            d2 = z1 - t0;
            if (norm2(d2) > norm2(d1))
                d1 = d2;
            if (d1 == 0) 
                return null;
            z = z - d * z0 / d1;
        }
        return null;
    }

    function poly_roots(p)
    {
        var d, i, roots, j, z, eps;
        var start_points = [ 0.1, -1.4, 1.7 ];

        if (!(p instanceof Polynomial))