- * @param a multivariate polynomial
- * @param x variable to factor in
- * @return factored polynomial */
-ex sqrfree(const ex &a, const symbol &x)
-{
- int i = 1;
- ex res = _ex1();
- ex b = a.diff(x);
- ex c = univariate_gcd(a, b, x);
- ex w;
- if (c.is_equal(_ex1())) {
- w = a;
- } else {
- w = quo(a, c, x);
- ex y = quo(b, c, x);
- ex z = y - w.diff(x);
- while (!z.is_zero()) {
- ex g = univariate_gcd(w, z, x);
- res *= power(g, i);
- w = quo(w, g, x);
- y = quo(z, g, x);
- z = y - w.diff(x);
- i++;
+ * @param a rational function over Z[x], treated as univariate polynomial
+ * in x
+ * @param x variable to factor in
+ * @return decomposed rational function */
+ex sqrfree_parfrac(const ex & a, const symbol & x)
+{
+ // Find numerator and denominator
+ ex nd = numer_denom(a);
+ ex numer = nd.op(0), denom = nd.op(1);
+//clog << "numer = " << numer << ", denom = " << denom << endl;
+
+ // Convert N(x)/D(x) -> Q(x) + R(x)/D(x), so degree(R) < degree(D)
+ ex red_poly = quo(numer, denom, x), red_numer = rem(numer, denom, x).expand();
+//clog << "red_poly = " << red_poly << ", red_numer = " << red_numer << endl;
+
+ // Factorize denominator and compute cofactors
+ exvector yun = sqrfree_yun(denom, x);
+//clog << "yun factors: " << exprseq(yun) << endl;
+ unsigned num_yun = yun.size();
+ exvector factor; factor.reserve(num_yun);
+ exvector cofac; cofac.reserve(num_yun);
+ for (unsigned i=0; i<num_yun; i++) {
+ if (!yun[i].is_equal(_ex1())) {
+ for (unsigned j=0; j<=i; j++) {
+ factor.push_back(pow(yun[i], j+1));
+ ex prod = _ex1();
+ for (unsigned k=0; k<num_yun; k++) {
+ if (k == i)
+ prod *= pow(yun[k], i-j);
+ else
+ prod *= pow(yun[k], k+1);
+ }
+ cofac.push_back(prod.expand());
+ }