public ModMatrix invert()
{
ModMatrix mm = new ModMatrix(this);
ModMatrix mi = new ModMatrix(dimension, modulus);
BigInteger g = 0, tmp, inv;
for (int y = 0; y < dimension; y++)
{
// find row with invertible leading value
int yy;
for (yy = y; yy < dimension; yy++)
{
g = mm[y, yy].GCD(modulus);
if (g == 1)
{
break;
}
}
if (g != 1)
{
return(null);
}
// swap rows y and yy
for (int x = 0; x < dimension; x++)
{
tmp = mm[x, y]; mm[x, y] = mm[x, yy]; mm[x, yy] = tmp;
tmp = mi[x, y]; mi[x, y] = mi[x, yy]; mi[x, yy] = tmp;
}
// normalize rows
inv = BigIntegerHelper.ModInverse(mm[y, y], modulus);
for (int x = 0; x < dimension; x++)
{
mm[x, y] = (mm[x, y] * inv) % modulus;
mi[x, y] = (mi[x, y] * inv) % modulus;
}
for (yy = 0; yy < dimension; yy++)
{
if (yy == y)
{
continue;
}
tmp = (modulus - mm[y, yy]) % modulus;
for (int x = 0; x < dimension; x++)
{
mm[x, yy] = (mm[x, yy] + tmp * mm[x, y]) % modulus;
mi[x, yy] = (mi[x, yy] + tmp * mi[x, y]) % modulus;
}
}
}
return(mi);
}
private static BigInteger Parse(Stack <TOKEN> stack, Priority priority, bool endbracket)
{
if (stack.Count == 0)
{
throw new Exception("Expression Parsing Error.");
}
int minus = 1;
BigInteger v = 0;
TOKEN t = stack.Pop(); //get -, +, integer or bracket
if (t.ttype == TOKEN.Ttype.MINUS)
{
minus = -1;
t = stack.Pop(); //get integer or bracket
}
else if (t.ttype == TOKEN.Ttype.PLUS)
{
minus = 1;
t = stack.Pop(); //get integer or bracket
}
if (t.ttype == TOKEN.Ttype.INTEGER)
{
v = minus * t.integer;
}
else if (t.ttype == TOKEN.Ttype.BRACKETOPEN)
{
v = minus * Parse(stack, Priority.ALL, true);
stack.Pop(); //pop the closing bracket
}
while (stack.Count != 0)
{
switch (stack.Peek().ttype) //next operator
{
case TOKEN.Ttype.PLUS:
if (priority == Priority.MULTDIV || priority == Priority.POW)
{
return(v);
}
stack.Pop();
v = v + Parse(stack, Priority.ADDSUB, endbracket);
break;
case TOKEN.Ttype.MINUS:
if (priority == Priority.MULTDIV || priority == Priority.POW)
{
return(v);
}
stack.Pop();
v = v - Parse(stack, Priority.ADDSUB, endbracket);
break;
case TOKEN.Ttype.MULTIPLY:
if (priority == Priority.POW)
{
return(v);
}
stack.Pop();
v = v * Parse(stack, Priority.MULTDIV, endbracket);
break;
case TOKEN.Ttype.DIVIDE:
if (priority == Priority.POW)
{
return(v);
}
stack.Pop();
v = v / Parse(stack, Priority.MULTDIV, endbracket);
break;
case TOKEN.Ttype.POW:
stack.Pop();
v = BigIntegerHelper.Pow(v, Parse(stack, Priority.POW, endbracket));
break;
case TOKEN.Ttype.BRACKETCLOSE:
if (endbracket)
{
return(v);
}
else
{
throw new Exception("Expression Parsing Error (closing bracket misplaced).");
}
default:
throw new Exception("Expression Parsing Error.");
}
}
if (endbracket)
{
throw new Exception("Expression Parsing Error (closing bracket missing).");
}
return(v);
}