- if (b.is_zero())
- throw(std::overflow_error("prem: division by zero"));
- if (is_ex_exactly_of_type(a, numeric)) {
- if (is_ex_exactly_of_type(b, numeric))
- return _ex0();
- else
- return b;
- }
- if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)))
- throw(std::invalid_argument("prem: arguments must be polynomials over the rationals"));
-
- // Polynomial long division
- ex r = a.expand();
- ex eb = b.expand();
- int rdeg = r.degree(x);
- int bdeg = eb.degree(x);
- ex blcoeff;
- if (bdeg <= rdeg) {
- blcoeff = eb.coeff(x, bdeg);
- if (bdeg == 0)
- eb = _ex0();
- else
- eb -= blcoeff * power(x, bdeg);
- } else
- blcoeff = _ex1();
-
- int delta = rdeg - bdeg + 1, i = 0;
- while (rdeg >= bdeg && !r.is_zero()) {
- ex rlcoeff = r.coeff(x, rdeg);
- ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand();
- if (rdeg == 0)
- r = _ex0();
- else
- r -= rlcoeff * power(x, rdeg);
- r = (blcoeff * r).expand() - term;
- rdeg = r.degree(x);
- i++;
- }
- return power(blcoeff, delta - i) * r;
+ if (b.is_zero())
+ throw(std::overflow_error("prem: division by zero"));
+ if (is_ex_exactly_of_type(a, numeric)) {
+ if (is_ex_exactly_of_type(b, numeric))
+ return _ex0();
+ else
+ return b;
+ }
+ if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)))
+ throw(std::invalid_argument("prem: arguments must be polynomials over the rationals"));
+
+ // Polynomial long division
+ ex r = a.expand();
+ ex eb = b.expand();
+ int rdeg = r.degree(x);
+ int bdeg = eb.degree(x);
+ ex blcoeff;
+ if (bdeg <= rdeg) {
+ blcoeff = eb.coeff(x, bdeg);
+ if (bdeg == 0)
+ eb = _ex0();
+ else
+ eb -= blcoeff * power(x, bdeg);
+ } else
+ blcoeff = _ex1();
+
+ int delta = rdeg - bdeg + 1, i = 0;
+ while (rdeg >= bdeg && !r.is_zero()) {
+ ex rlcoeff = r.coeff(x, rdeg);
+ ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand();
+ if (rdeg == 0)
+ r = _ex0();
+ else
+ r -= rlcoeff * power(x, rdeg);
+ r = (blcoeff * r).expand() - term;
+ rdeg = r.degree(x);
+ i++;
+ }
+ return power(blcoeff, delta - i) * r;
+}
+
+
+/** Sparse pseudo-remainder of polynomials a(x) and b(x) in Z[x].
+ *
+ * @param a first polynomial in x (dividend)
+ * @param b second polynomial in x (divisor)
+ * @param x a and b are polynomials in x
+ * @param check_args check whether a and b are polynomials with rational
+ * coefficients (defaults to "true")
+ * @return sparse pseudo-remainder of a(x) and b(x) in Z[x] */
+
+ex sprem(const ex &a, const ex &b, const symbol &x, bool check_args)
+{
+ if (b.is_zero())
+ throw(std::overflow_error("prem: division by zero"));
+ if (is_ex_exactly_of_type(a, numeric)) {
+ if (is_ex_exactly_of_type(b, numeric))
+ return _ex0();
+ else
+ return b;
+ }
+ if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)))
+ throw(std::invalid_argument("prem: arguments must be polynomials over the rationals"));
+
+ // Polynomial long division
+ ex r = a.expand();
+ ex eb = b.expand();
+ int rdeg = r.degree(x);
+ int bdeg = eb.degree(x);
+ ex blcoeff;
+ if (bdeg <= rdeg) {
+ blcoeff = eb.coeff(x, bdeg);
+ if (bdeg == 0)
+ eb = _ex0();
+ else
+ eb -= blcoeff * power(x, bdeg);
+ } else
+ blcoeff = _ex1();
+
+ while (rdeg >= bdeg && !r.is_zero()) {
+ ex rlcoeff = r.coeff(x, rdeg);
+ ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand();
+ if (rdeg == 0)
+ r = _ex0();
+ else
+ r -= rlcoeff * power(x, rdeg);
+ r = (blcoeff * r).expand() - term;
+ rdeg = r.degree(x);
+ }
+ return r;