/// <summary>
/// x[n] の式を生成します。
/// </summary>
private void MainEquation()
{
Rational f = 1;
string var = string.Format("f[{0}]", ORDER - 1);
string exp = var;
for (int i = 1; i < ORDER; i++)
{
f /= (i + 1);
var = "h" + var + "'";
exp += "+" + f.ToString() + " " + var;
}
e_f = Expression.EasyParse(exp);
}
//===========================================================
// 計算
//===========================================================
/// <summary>
/// 式を生成します。
/// </summary>
private void InitializeEquations()
{
string exp = "-f[{0}]+f[{1}]";
Rational f = 1;
string var = "f[{1}]";
for (int i = 1; i < ORDER; i++)
{
f /= i;
var = "h" + var + "'";
exp += "+" + f.ToString() + " " + var;
}
for (int i = ORDER - 2; i >= 0; i--)
{
equations[i] = Expression.EasyParse(string.Format(exp, i + 1, i));
}
}
/// <summary>
/// 式を f[n-1]^(m) で表し直します。
/// </summary>
private void UpdatePastDifferentials()
{
build.Append("<ul>\r\n");
string var = "f[{0}]";
for (int n = 1; n < ORDER; n++)
{
var = "h" + var + "'";
// 代入する式の書式文字列を生成
Rational f2 = 1;
string var2 = var;
string exp2 = var;
for (int m = 1; m < ORDER - n; m++)
{
f2 /= -m;
var2 = "h" + var2 + "'";
exp2 += "+" + f2.ToString() + " " + var2;
}
// 式を表示
for (int i = 0; i <= ORDER - 2; i++)
{
string varname = string.Format(var, i);
Expression x = Expression.EasyParse(string.Format(exp2, i + 1));
for (int j = 0; j < equations.Length; j++)
{
equations[j] = equations[j].Substitute(varname, x);
}
//----------
build.Append("<li>");
build.Append(Expression.EasyParse(varname).ToHtml(true));
build.Append(" ＝ ");
build.Append(x.ToHtml(true));
build.Append(" ＋ O(h<sup>" + ORDER.ToString() + "</sup>)</li>\r\n");
}
}
build.Append("</ul>\r\n");
}