+
+/** Default implementation of ex::to_rational(). It replaces the object with a
+ * temporary symbol.
+ * @see ex::to_rational */
+ex basic::to_rational(lst &repl_lst) const
+{
+ return replace_with_symbol(*this, repl_lst);
+}
+
+
+/** Implementation of ex::to_rational() for symbols. This returns the unmodified symbol.
+ * @see ex::to_rational */
+ex symbol::to_rational(lst &repl_lst) const
+{
+ return *this;
+}
+
+
+/** Implementation of ex::to_rational() for a numeric. It splits complex numbers
+ * into re+I*im and replaces I and non-rational real numbers with a temporary
+ * symbol.
+ * @see ex::to_rational */
+ex numeric::to_rational(lst &repl_lst) const
+{
+ numeric num = numer();
+ ex numex = num;
+
+ if (num.is_real()) {
+ if (!num.is_integer())
+ numex = replace_with_symbol(numex, repl_lst);
+ } else { // complex
+ numeric re = num.real(), im = num.imag();
+ ex re_ex = re.is_rational() ? re : replace_with_symbol(re, repl_lst);
+ ex im_ex = im.is_rational() ? im : replace_with_symbol(im, repl_lst);
+ numex = re_ex + im_ex * replace_with_symbol(I, repl_lst);
+ }
+ return numex;
+}
+
+
+/** Implementation of ex::to_rational() for powers. It replaces non-integer
+ * powers by temporary symbols.
+ * @see ex::to_rational */
+ex power::to_rational(lst &repl_lst) const
+{
+ if (exponent.info(info_flags::integer))
+ return power(basis.to_rational(repl_lst), exponent);
+ else
+ return replace_with_symbol(*this, repl_lst);
+}
+
+
+/** Rationalization of non-rational functions.
+ * This function converts a general expression to a rational polynomial
+ * by replacing all non-rational subexpressions (like non-rational numbers,
+ * non-integer powers or functions like sin(), cos() etc.) to temporary
+ * symbols. This makes it possible to use functions like gcd() and divide()
+ * on non-rational functions by applying to_rational() on the arguments,
+ * calling the desired function and re-substituting the temporary symbols
+ * in the result. To make the last step possible, all temporary symbols and
+ * their associated expressions are collected in the list specified by the
+ * repl_lst parameter in the form {symbol == expression}, ready to be passed
+ * as an argument to ex::subs().
+ *
+ * @param repl_lst collects a list of all temporary symbols and their replacements
+ * @return rationalized expression */
+ex ex::to_rational(lst &repl_lst) const
+{
+ return bp->to_rational(repl_lst);
+}
+
+