public static Pow[] GetNarrowPowers(this Rational r, Rational[] narrows = null)
{
if (narrows == null)
{
narrows = NarrowUtils.GetDefault(r.GetInvolvedPowerCount());
}
int len = r.GetInvolvedPowerCount();
if (len > narrows.Length)
{
return(null);
}
Pow[] res = new Pow[len];
r = r.Clone();
for (int i = len - 1; i >= 0; --i)
{
Pow e = r.GetPrimePower(i);
res[i] = e;
if (e != 0)
{
r /= narrows[i].Power(e);
}
}
return(res);
}
public static string FormatNarrowPowers(this Rational r, Rational[] narrows = null)
{
if (narrows == null)
{
narrows = NarrowUtils.GetDefault(r.GetInvolvedPowerCount());
}
Pow[] pows = GetNarrowPowers(r, narrows);
if (pows == null)
{
return(null); //!!! where invalid narrowPrimes from?
}
return(Powers.ToString(pows, "|}"));
}
public int[] FindCoordinates(Rational vector)
{
int len = vector.GetInvolvedPowerCount();
if (len > height)
{
return(null);
}
//if (width < basisSize + len) throw new Exception("");
int[] pows = vector.GetPrimePowers();
int[] v = new int[height];
Array.Copy(pows, 0, v, 0, len);
//
int[] result = new int[basisSize];
for (int row = 0; row < height; ++row)
{
//
int col = leadCols[row];
int lead = col == -1 ? 0 : m[col, ro[row]];
//
int b = 0;
for (int i = 0; i < height; ++i)
{
b += v[i] * m[basisSize + i, ro[row]];
}
//
if (lead == 0)
{
if (b != 0)
{
return(null);
}
}
else
{
if (b % lead != 0)
{
return(null); // non-integer coordinate
}
result[col] = b / lead;
}
}
return(result);
}
public RationalX[] FindRationalCoordinates(Rational vector)
{
//!!! seems fails if vector == 1/1
int len = vector.GetInvolvedPowerCount();
if (len > height)
{
return(null);
}
//if (width < basisSize + len) throw new Exception("");
int[] pows = vector.GetPrimePowers();
int[] v = new int[height];
Array.Copy(pows, 0, v, 0, len);
//
RationalX[] result = new RationalX[basisSize];
for (int row = 0; row < height; ++row)
{
//
int col = leadCols[row];
int lead = col == -1 ? 0 : m[col, ro[row]];
//
int b = 0;
for (int i = 0; i < height; ++i)
{
b += v[i] * m[basisSize + i, ro[row]];
}
//
if (lead == 0)
{
if (b != 0)
{
return(null); // no solution
}
}
else
{
result[col] = new RationalX(b, lead);
}
}
return(result);
}
