#include "function.h"
#include "ex.h"
+#include "lst.h"
#include "archive.h"
#include "inifcns.h"
#include "utils.h"
{
ex result;
- if (serial==function_index_Order) {
+ if (serial == function_index_Order) {
// Order Term function only differentiates the argument
return Order(seq[0].diff(s));
+ } else if (serial == function_index_Derivative) {
+ // Inert derivative performs chain rule on the first argument only, and
+ // adds differentiation parameter to list (second argument)
+ GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
+ GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
+ ex fcn = seq[0];
+ ex arg_diff;
+ for (unsigned i=0; i!=fcn.nops(); i++) {
+ arg_diff = fcn.op(i).diff(s);
+ if (!arg_diff.is_zero()) {
+ lst new_lst = ex_to_lst(seq[1]);
+ new_lst.append(i);
+ result += arg_diff * Derivative(fcn, new_lst);
+ }
+ }
} else {
// Chain rule
ex arg_diff;
GINAC_ASSERT(serial<registered_functions().size());
if (registered_functions()[serial].derivative_f==0) {
- return Derivative(*this, diff_param);
+ return Derivative(*this, lst(diff_param));
}
switch (registered_functions()[serial].nparams) {
// the following lines have been generated for max. ${maxargs} parameters
REGISTER_FUNCTION(Order, eval_func(Order_eval).
series_func(Order_series));
-//////////
-// Inert differentiation
-//////////
-
-static ex Diff_eval(const ex & f, const ex & x)
-{
- return Diff(f, x).hold();
-}
-
-static ex Diff_deriv(const ex & f, const ex & x, unsigned deriv_param)
-{
- GINAC_ASSERT(deriv_param == 0 || deriv_param == 1);
- if (deriv_param == 1)
- return Diff(Diff(f, x), x);
- else
- return _ex0();
-}
-
-REGISTER_FUNCTION(Diff, eval_func(Diff_eval).
- derivative_func(Diff_deriv));
-
//////////
// Inert partial differentiation operator
//////////
-static ex Derivative_eval(const ex & f, const ex & n)
+static ex Derivative_eval(const ex & f, const ex & l)
{
- if (is_ex_exactly_of_type(n, numeric) && ex_to_numeric(n).is_nonneg_integer()) {
- unsigned i = ex_to_numeric(n).to_int();
- if (is_ex_exactly_of_type(f, function)) {
- if (i < f.nops() && is_ex_exactly_of_type(f.op(i), symbol))
- return Diff(f, f.op(i));
- }
+ if (!is_ex_exactly_of_type(f, function)) {
+ throw(std::invalid_argument("Derivative(): 1st argument must be a function"));
}
- return Derivative(f, n).hold();
+ if (!is_ex_exactly_of_type(l, lst)) {
+ throw(std::invalid_argument("Derivative(): 2nd argument must be a list"));
+ }
+ return Derivative(f, l).hold();
}
REGISTER_FUNCTION(Derivative, eval_func(Derivative_eval));
/** Order term function (for truncated power series). */
DECLARE_FUNCTION_1P(Order)
-/** Inert differentiation. */
-DECLARE_FUNCTION_2P(Diff)
-
/** Inert partial differentiation operator. */
DECLARE_FUNCTION_2P(Derivative)