// check/series_expansion.cpp

/* Series expansion test (Laurent and Taylor series). */

#include "ginac.h"

static symbol x("x");

static unsigned check_series(const ex &e, const ex &point, const ex &d)
{
	ex es = e.series(x, point, 8);
	ex ep = static_cast<series *>(es.bp)->convert_to_poly();
	if ((ep - d).compare(exZERO()) != 0) {
		clog << "series expansion of " << e << " at " << point
             << " erroneously returned " << ep << " (instead of " << d
             << ")" << endl;
		(ep-d).printtree(clog);
		return 1;
	}
	return 0;
}

// Series expansion
static unsigned series1(void)
{
	unsigned result = 0;
	ex e, d;

	e = sin(x);
	d = x - pow(x, 3) / 6 + pow(x, 5) / 120 - pow(x, 7) / 5040 + Order(pow(x, 8));
	result += check_series(e, exZERO(), d);

	e = cos(x);
	d = 1 - pow(x, 2) / 2 + pow(x, 4) / 24 - pow(x, 6) / 720 + Order(pow(x, 8));
	result += check_series(e, exZERO(), d);

	e = exp(x);
	d = 1 + x + pow(x, 2) / 2 + pow(x, 3) / 6 + pow(x, 4) / 24 + pow(x, 5) / 120 + pow(x, 6) / 720 + pow(x, 7) / 5040 + Order(pow(x, 8));
	result += check_series(e, exZERO(), d);

	e = pow(1 - x, -1);
	d = 1 + x + pow(x, 2) + pow(x, 3) + pow(x, 4) + pow(x, 5) + pow(x, 6) + pow(x, 7) + Order(pow(x, 8));
	result += check_series(e, exZERO(), d);

	e = x + pow(x, -1);
	d = x + pow(x, -1);
	result += check_series(e, exZERO(), d);

	e = x + pow(x, -1);
	d = 2 + pow(x-1, 2) - pow(x-1, 3) + pow(x-1, 4) - pow(x-1, 5) + pow(x-1, 6) - pow(x-1, 7) + Order(pow(x-1, 8));
	result += check_series(e, exONE(), d);

	e = pow(x + pow(x, 3), -1);
	d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + Order(pow(x, 7));
	result += check_series(e, exZERO(), d);

	e = pow(pow(x, 2) + pow(x, 4), -1);
	d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + Order(pow(x, 6));
	result += check_series(e, exZERO(), d);

	e = pow(sin(x), -2);
	d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + Order(pow(x, 5));
	result += check_series(e, exZERO(), d);

	e = sin(x) / cos(x);
	d = x + pow(x, 3) / 3 + pow(x, 5) * 2/15 + pow(x, 7) * 17/315 + Order(pow(x, 8));
	result += check_series(e, exZERO(), d);

	e = cos(x) / sin(x);
	d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 + Order(pow(x, 6));
	result += check_series(e, exZERO(), d);

	e = pow(numeric(2), x);
	ex t = log(ex(2)) * x;
	d = 1 + t + pow(t, 2) / 2 + pow(t, 3) / 6 + pow(t, 4) / 24 + pow(t, 5) / 120 + pow(t, 6) / 720 + pow(t, 7) / 5040 + Order(pow(x, 8));
	result += check_series(e, exZERO(), d.expand());

	e = pow(Pi, x);
	t = log(Pi) * x;
	d = 1 + t + pow(t, 2) / 2 + pow(t, 3) / 6 + pow(t, 4) / 24 + pow(t, 5) / 120 + pow(t, 6) / 720 + pow(t, 7) / 5040 + Order(pow(x, 8));
	result += check_series(e, exZERO(), d.expand());

	return result;
}

// Series addition
static unsigned series2(void)
{
	unsigned result = 0;
	ex e, d;

	e = pow(sin(x), -1).series(x, exZERO(), 8) + pow(sin(-x), -1).series(x, exZERO(), 12);
	d = Order(pow(x, 6));
	result += check_series(e, exZERO(), d);

	return result;
}

// Series multiplication
static unsigned series3(void)
{
	unsigned result = 0;
	ex e, d;

	e = sin(x).series(x, exZERO(), 8) * pow(sin(x), -1).series(x, exZERO(), 12);
	d = 1 + Order(pow(x, 7));
	result += check_series(e, exZERO(), d);

	return result;
}

unsigned series_expansion(void)
{
	unsigned result = 0;

	cout << "checking series expansion..." << flush;
	clog << "---------series expansion:" << endl;

	result += series1();
	result += series2();
	result += series3();

	if (!result) {
		cout << " passed ";
		clog << "(no output)" << endl;
	} else {
		cout << " failed ";
	}
	return result;
}