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Kronecker symbols

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This commit is contained in:
Alex Dyachenko 2014-05-02 15:30:30 -04:00
parent 6ea5c7b08a
commit cb5954df40
2 changed files with 70 additions and 0 deletions
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15
mpir.net/mpir.net-tests/HugeIntTests/NumberTheoretic.cs
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@ -182,5 +182,20 @@ namespace MPIR.Tests.HugeIntTests
Assert.AreEqual(-1, HugeInt.Legendre(a, p));
}
}
[TestMethod]
public void Kronecker()
{
using (var a = new HugeInt("9288562863495827364985273645298367452"))
using (var b = new HugeInt("29927402397991286489627837734179186385188296382227"))
{
Assert.AreEqual(-1, HugeInt.Kronecker(a, b));
Assert.AreEqual(0, HugeInt.Kronecker(a, 2));
Assert.AreEqual(-1, HugeInt.Kronecker(b, 2));
Assert.AreEqual(-1, HugeInt.Kronecker(2, b));
Assert.AreEqual(-1, HugeInt.Kronecker(b, 2UL));
Assert.AreEqual(-1, HugeInt.Kronecker(2UL, b));
}
}
}
}

55
mpir.net/mpir.net/HugeInt.h
View File

@ -2139,6 +2139,61 @@ namespace MPIR
/// <returns>The Legendre symbol (-1, 0, or 1). Return is undefined unless <paramref name="b"/> is an odd prime.</returns>
static int Legendre(HugeInt^ a, HugeInt^ b) { return mpz_legendre(a->_value, b->_value); }
/// <summary>
/// Calculates the Jacobi symbol (<paramref name="a"/>/<paramref name="b"/>) with the Kronecker extension
/// (<paramref name="a"/>/2) = (2/<paramref name="a"/>) when a odd, or (<paramref name="a"/>/2) = 0 when a even.
/// <para>When <paramref name="b"/> is odd the Jacobi symbol and Kronecker symbol are identical, so the various Kronecker overloads
/// can be used for mixed precision Jacobi symbols too.
/// </para></summary>
/// <param name="a">First source value for the Kronecker symbol</param>
/// <param name="b">Second source value for the Kronecker symbol</param>
/// <returns>The Kronecker symbol (-1, 0, or 1).</returns>
static int Kronecker(HugeInt^ a, HugeInt^ b) { return mpz_kronecker(a->_value, b->_value); }
/// <summary>
/// Calculates the Jacobi symbol (<paramref name="a"/>/<paramref name="b"/>) with the Kronecker extension
/// (<paramref name="a"/>/2) = (2/<paramref name="a"/>) when a odd, or (<paramref name="a"/>/2) = 0 when a even.
/// <para>When <paramref name="b"/> is odd the Jacobi symbol and Kronecker symbol are identical, so the various Kronecker overloads
/// can be used for mixed precision Jacobi symbols too.
/// </para></summary>
/// <param name="a">First source value for the Kronecker symbol</param>
/// <param name="b">Second source value for the Kronecker symbol</param>
/// <returns>The Kronecker symbol (-1, 0, or 1).</returns>
static int Kronecker(HugeInt^ a, mpir_ui b) { return mpz_kronecker_ui(a->_value, b); }
/// <summary>
/// Calculates the Jacobi symbol (<paramref name="a"/>/<paramref name="b"/>) with the Kronecker extension
/// (<paramref name="a"/>/2) = (2/<paramref name="a"/>) when a odd, or (<paramref name="a"/>/2) = 0 when a even.
/// <para>When <paramref name="b"/> is odd the Jacobi symbol and Kronecker symbol are identical, so the various Kronecker overloads
/// can be used for mixed precision Jacobi symbols too.
/// </para></summary>
/// <param name="a">First source value for the Kronecker symbol</param>
/// <param name="b">Second source value for the Kronecker symbol</param>
/// <returns>The Kronecker symbol (-1, 0, or 1).</returns>
static int Kronecker(HugeInt^ a, mpir_si b) { return mpz_kronecker_si(a->_value, b); }
/// <summary>
/// Calculates the Jacobi symbol (<paramref name="a"/>/<paramref name="b"/>) with the Kronecker extension
/// (<paramref name="a"/>/2) = (2/<paramref name="a"/>) when a odd, or (<paramref name="a"/>/2) = 0 when a even.
/// <para>When <paramref name="b"/> is odd the Jacobi symbol and Kronecker symbol are identical, so the various Kronecker overloads
/// can be used for mixed precision Jacobi symbols too.
/// </para></summary>
/// <param name="a">First source value for the Kronecker symbol</param>
/// <param name="b">Second source value for the Kronecker symbol</param>
/// <returns>The Kronecker symbol (-1, 0, or 1).</returns>
static int Kronecker(mpir_ui a, HugeInt^ b) { return mpz_ui_kronecker(a, b->_value); }
/// <summary>
/// Calculates the Jacobi symbol (<paramref name="a"/>/<paramref name="b"/>) with the Kronecker extension
/// (<paramref name="a"/>/2) = (2/<paramref name="a"/>) when a odd, or (<paramref name="a"/>/2) = 0 when a even.
/// <para>When <paramref name="b"/> is odd the Jacobi symbol and Kronecker symbol are identical, so the various Kronecker overloads
/// can be used for mixed precision Jacobi symbols too.
/// </para></summary>
/// <param name="a">First source value for the Kronecker symbol</param>
/// <param name="b">Second source value for the Kronecker symbol</param>
/// <returns>The Kronecker symbol (-1, 0, or 1).</returns>
static int Kronecker(mpir_si a, HugeInt^ b) { return mpz_si_kronecker(a, b->_value); }
#pragma endregion
};