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Take the greatest common divisor of large integers by Euclid rather than PeterO's #2003

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Merged
Rafael-SOWNet merged 1 commit into from
Oct 21, 2026
Merged

Take the greatest common divisor of large integers by Euclid rather than PeterO's #2003

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3 changes: 3 additions & 0 deletions Sources/.editorconfig
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Expand Up @@ -312,6 +312,9 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
[AngouriMath/Functions/NumberTheory/ResidueClasses.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n

[AngouriMath/Functions/NumberTheory/GreatestCommonDivisor.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n

[Tests/UnitTests/Calculus/APowerTimesAFunctionOfItsPowerTest.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n

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2 changes: 1 addition & 1 deletion Sources/AngouriMath/Convenience/MathS.Polynomials.cs
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Expand Up @@ -448,7 +448,7 @@ private static bool SameAsOne(MultivariatePolynomial poly)
var denominator = EInteger.One;
foreach (var coefficient in rational)
denominator = coefficient.Denominator
.Divide(coefficient.Denominator.Gcd(denominator)).Multiply(denominator);
.Divide(coefficient.Denominator.GreatestCommonDivisor(denominator)).Multiply(denominator);
var whole = new EInteger[rational.Length];
for (var i = 0; i < whole.Length; i++)
whole[i] = rational[i].Numerator.Multiply(denominator.Divide(rational[i].Denominator));
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2 changes: 1 addition & 1 deletion Sources/AngouriMath/Convenience/MathS.cs
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Expand Up @@ -192,7 +192,7 @@ public static class NumberTheory
/// </code>
/// </example>
public static Integer GreatestCommonDivisor(Integer a, Integer b)
=> a.EInteger.Gcd(b.EInteger);
=> a.EInteger.GreatestCommonDivisor(b.EInteger);

}

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8 changes: 4 additions & 4 deletions Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.Rational.Definition.cs
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Expand Up @@ -127,11 +127,11 @@ public static Rational Create(ERational value)
+ $"use {nameof(Real)}.{nameof(Real.Create)} instead");

if (!MathS.Settings.DowncastingEnabled)
return new Rational(value.ToLowestTerms());
return new Rational(value.InLowestTerms());

// Call ToLowestTerms() through new RationalNumber first
// Call InLowestTerms() through new RationalNumber first
// before determining whether the denominator equals one
var @return = new Rational(value.ToLowestTerms());
var @return = new Rational(value.InLowestTerms());
if (@return.ERational.Denominator.Equals(1))
return Integer.Create(@return.ERational.Numerator);
else
Expand Down Expand Up @@ -208,7 +208,7 @@ public static Rational Create(ERational value)
var rat = FindRationalExactly(inv, iterCount - 1);
if (rat is null)
return null;
return new Rational((intPart * sign + sign / rat.ERational).ToLowestTerms());
return new Rational((intPart * sign + sign / rat.ERational).InLowestTerms());
}
}

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4 changes: 2 additions & 2 deletions Sources/AngouriMath/Functions/Algebra/Groebner/Fglm.cs
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Expand Up @@ -174,9 +174,9 @@ internal static class Fglm
continue;
var factor = vector[pivot].Divide(rowVectors[row][pivot]);
for (var i = 0; i < vector.Length; i++)
vector[i] = vector[i].Subtract(factor.Multiply(rowVectors[row][i])).ToLowestTerms();
vector[i] = vector[i].Subtract(factor.Multiply(rowVectors[row][i])).InLowestTerms();
for (var i = 0; i < rowCombinations[row].Length && i < combination.Length; i++)
combination[i] = combination[i].Add(factor.Multiply(rowCombinations[row][i])).ToLowestTerms();
combination[i] = combination[i].Add(factor.Multiply(rowCombinations[row][i])).InLowestTerms();
}

var pivotAt = -1;
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2 changes: 1 addition & 1 deletion Sources/AngouriMath/Functions/Algebra/Groebner/MultivariatePolynomial.Groebner.cs
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Expand Up @@ -41,7 +41,7 @@ internal static MultivariatePolynomial Term(int variableCount, ulong monomial, E
{
var built = new Dictionary<ulong, ERational>();
if (!coefficient.IsZero)
built[monomial] = coefficient.ToLowestTerms();
built[monomial] = coefficient.InLowestTerms();
return new(variableCount, built);
}

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2 changes: 1 addition & 1 deletion Sources/AngouriMath/Functions/Algebra/Polynomials/BivariateHenselFactorization.cs
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Expand Up @@ -628,6 +628,6 @@ private static RationalPolynomial Derivative(RationalPolynomial poly)

private static EInteger Lcm(EInteger left, EInteger right)
=> left.IsZero || right.IsZero ? EInteger.One
: left.Divide(left.Gcd(right)).Multiply(right);
: left.Divide(left.GreatestCommonDivisor(right)).Multiply(right);
}
}
4 changes: 2 additions & 2 deletions Sources/AngouriMath/Functions/Algebra/Polynomials/EvaluationHomomorphism.cs
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Expand Up @@ -185,12 +185,12 @@ private static bool NextPoint(int[] point, int attempt, int count)
if (Evaluate(pair.Value, others, point, depth + 1) is not { } inner)
return null;
total = total.Add(inner.Multiply(ERational.Create(at.Pow(pair.Key), EInteger.One)))
.ToLowestTerms();
.InLowestTerms();
}
return total;
}

private static EInteger Lcm(EInteger left, EInteger right)
=> left.Divide(left.Gcd(right)).Multiply(right);
=> left.Divide(left.GreatestCommonDivisor(right)).Multiply(right);
}
}
4 changes: 2 additions & 2 deletions Sources/AngouriMath/Functions/Algebra/Polynomials/IntegerPolynomial.cs
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Expand Up @@ -194,7 +194,7 @@ internal EInteger Content()
{
var content = EInteger.Zero;
foreach (var coefficient in coefficients)
content = content.Gcd(coefficient);
content = content.GreatestCommonDivisor(coefficient);
return content;
}

Expand Down Expand Up @@ -276,7 +276,7 @@ internal static IntegerPolynomial Gcd(IntegerPolynomial left, IntegerPolynomial
if (right.IsZero)
return left.PrimitivePart().ScaleBy(left.Content());

var contentGcd = left.Content().Gcd(right.Content());
var contentGcd = left.Content().GreatestCommonDivisor(right.Content());
var a = left.PrimitivePart();
var b = right.PrimitivePart();
if (a.Degree < b.Degree)
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4 changes: 2 additions & 2 deletions Sources/AngouriMath/Functions/Algebra/Polynomials/IversonSum.cs
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Expand Up @@ -390,7 +390,7 @@ private static (EInteger Residue, EInteger Modulus)? Residue(Entity divisor, Ent
return null;
// s k + e = 0 mod m: solvable where g = gcd(s, m) divides e, and then k is one class
// modulo m / g, found by trying its members.
var g = s.EInteger.Gcd(m);
var g = s.EInteger.GreatestCommonDivisor(m);
if (!e.EInteger.Remainder(g).IsZero)
return (EInteger.Zero, EInteger.Zero);
var classModulus = m.Divide(g);
Expand All @@ -408,7 +408,7 @@ private static (EInteger Residue, EInteger Modulus)? Residue(Entity divisor, Ent
/// </summary>
private static (EInteger Residue, EInteger Modulus)? Combined(EInteger r1, EInteger m1, EInteger r2, EInteger m2)
{
var combined = m1.Divide(m1.Gcd(m2)).Multiply(m2);
var combined = m1.Divide(m1.GreatestCommonDivisor(m2)).Multiply(m2);
if (combined.CompareTo(EInteger.FromInt32(MaxModulus)) > 0)
return null;
for (var t = r1; t.CompareTo(combined) < 0; t = t.Add(m1))
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2 changes: 1 addition & 1 deletion Sources/AngouriMath/Functions/Algebra/Polynomials/KroneckerFactorization.cs
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Expand Up @@ -221,7 +221,7 @@ bool Peel(MultivariatePolynomial rest, int depth, int at)
}

private static EInteger Lcm(EInteger left, EInteger right)
=> left.Divide(left.Gcd(right)).Multiply(right);
=> left.Divide(left.GreatestCommonDivisor(right)).Multiply(right);

/// <summary>
/// Reading each exponent back as one digit of the numeral — or <see langword="null"/>
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22 changes: 11 additions & 11 deletions Sources/AngouriMath/Functions/Algebra/Polynomials/MultivariatePolynomial.cs
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Expand Up @@ -105,7 +105,7 @@ internal static MultivariatePolynomial Constant(int variableCount, ERational val
{
var terms = new Dictionary<ulong, ERational>();
if (!value.IsZero)
terms[0] = value.ToLowestTerms();
terms[0] = value.InLowestTerms();
return new(variableCount, terms);
}

Expand Down Expand Up @@ -177,7 +177,7 @@ private static void Accumulate(Dictionary<ulong, ERational> into, ulong monomial
into[monomial] = value;
return;
}
var sum = existing.Add(value).ToLowestTerms();
var sum = existing.Add(value).InLowestTerms();
if (sum.IsZero)
into.Remove(monomial);
else
Expand All @@ -194,7 +194,7 @@ private static void Accumulate(Dictionary<ulong, ERational> into, ulong monomial
{
if (!TryMultiplyMonomials(left.Key, right.Key, VariableCount, out var monomial))
return null;
Accumulate(result, monomial, left.Value.Multiply(right.Value).ToLowestTerms());
Accumulate(result, monomial, left.Value.Multiply(right.Value).InLowestTerms());
if (result.Count > maxTerms)
return null;
}
Expand Down Expand Up @@ -231,7 +231,7 @@ internal MultivariatePolynomial ScaleBy(ERational factor)
return Zero(VariableCount);
var result = new Dictionary<ulong, ERational>(terms.Count);
foreach (var term in terms)
result[term.Key] = term.Value.Multiply(factor).ToLowestTerms();
result[term.Key] = term.Value.Multiply(factor).InLowestTerms();
return new(VariableCount, result);
}

Expand Down Expand Up @@ -324,7 +324,7 @@ internal MultivariatePolynomial DerivativeIn(int variable)
if (power == 0)
continue;
Accumulate(result, Without(term.Key, variable) | Pack(variable, power - 1),
term.Value.Multiply(ERational.FromInt32(power)).ToLowestTerms());
term.Value.Multiply(ERational.FromInt32(power)).InLowestTerms());
}
return new(VariableCount, result);
}
Expand All @@ -347,7 +347,7 @@ internal MultivariatePolynomial DerivativeIn(int variable)
return this;
if (IsConstant)
{
var value = ConstantValue.ToLowestTerms();
var value = ConstantValue.InLowestTerms();
if (value.Sign < 0)
return null;
var (above, below) = (value.Numerator.Sqrt(), value.Denominator.Sqrt());
Expand Down Expand Up @@ -443,7 +443,7 @@ internal MultivariatePolynomial LeadingCoefficientIn(int variable)
// no later step can make it one -- so this is a "no" and not a "gave up".
if (!TryDivideMonomials(lead, divisorLead, VariableCount, out var monomial))
return null;
var value = rest.terms[lead].Divide(divisorValue).ToLowestTerms();
var value = rest.terms[lead].Divide(divisorValue).InLowestTerms();
quotient[monomial] = value;
if (divisor.MultiplyByTerm(monomial, value) is not { } product)
{
Expand All @@ -468,7 +468,7 @@ internal MultivariatePolynomial LeadingCoefficientIn(int variable)
{
if (!TryMultiplyMonomials(term.Key, monomial, VariableCount, out var product))
return null;
result[product] = term.Value.Multiply(value).ToLowestTerms();
result[product] = term.Value.Multiply(value).InLowestTerms();
}
return new(VariableCount, result);
}
Expand Down Expand Up @@ -526,7 +526,7 @@ internal MultivariatePolynomial Normalized(out ERational scale)
denominators = Lcm(denominators, term.Value.Denominator);
var numerators = EInteger.Zero;
foreach (var term in terms)
numerators = numerators.Gcd(
numerators = numerators.GreatestCommonDivisor(
term.Value.Numerator.Multiply(denominators.Divide(term.Value.Denominator)));
if (numerators.IsZero)
return this;
Expand All @@ -536,7 +536,7 @@ internal MultivariatePolynomial Normalized(out ERational scale)
return ScaleBy(scale);
}

private static EInteger Lcm(EInteger a, EInteger b) => a.Divide(a.Gcd(b)).Multiply(b);
private static EInteger Lcm(EInteger a, EInteger b) => a.Divide(a.GreatestCommonDivisor(b)).Multiply(b);

internal bool SameAs(MultivariatePolynomial other)
{
Expand Down Expand Up @@ -606,7 +606,7 @@ internal bool SameAs(MultivariatePolynomial other)
var inverse = ERational.One.Divide(parsed.ConstantValue);
var result = ERational.One;
for (var i = 0; i < -power; i++)
result = result.Multiply(inverse).ToLowestTerms();
result = result.Multiply(inverse).InLowestTerms();
return Constant(variables.Count, result);
}

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20 changes: 10 additions & 10 deletions Sources/AngouriMath/Functions/Algebra/Polynomials/PartialFractions.cs
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Expand Up @@ -1849,13 +1849,13 @@ private static bool TrySolveByLifting(ERational[][] augmented, int rows, int wid
var common = EInteger.One;
for (var column = 0; column <= width; column++)
{
var reduced = augmented[row][column].ToLowestTerms();
var reduced = augmented[row][column].InLowestTerms();
augmented[row][column] = reduced;
common = common.Multiply(reduced.Denominator).Divide(common.Gcd(reduced.Denominator));
common = common.Multiply(reduced.Denominator).Divide(common.GreatestCommonDivisor(reduced.Denominator));
}
a[row] = new EInteger[width + 1];
for (var column = 0; column <= width; column++)
a[row][column] = augmented[row][column].Multiply(ERational.FromEInteger(common)).ToLowestTerms().Numerator;
a[row][column] = augmented[row][column].Multiply(ERational.FromEInteger(common)).InLowestTerms().Numerator;
}
var prime = EInteger.FromInt64(LiftingPrime);
static long Mod(EInteger value, EInteger prime)
Expand Down Expand Up @@ -2032,7 +2032,7 @@ static long Inverse(long value)
var sum = ERational.Zero;
for (var j = 0; j < rank; j++)
sum = sum.Add(solution[j].Multiply(ERational.FromEInteger(s[i][j])));
holds = sum.Subtract(ERational.FromEInteger(t[i])).ToLowestTerms().IsZero;
holds = sum.Subtract(ERational.FromEInteger(t[i])).InLowestTerms().IsZero;
}
if (holds)
break;
Expand All @@ -2047,14 +2047,14 @@ static long Inverse(long value)
var sum = ERational.Zero;
for (var j = 0; j < rank; j++)
sum = sum.Add(solution[j].Multiply(ERational.FromEInteger(a[row][pivotColumns[j]])));
if (!sum.Subtract(ERational.FromEInteger(a[row][width])).ToLowestTerms().IsZero)
if (!sum.Subtract(ERational.FromEInteger(a[row][width])).InLowestTerms().IsZero)
return false;
}
values = new Entity[width];
for (var column = 0; column < width; column++)
values[column] = Integer.Zero;
for (var j = 0; j < rank; j++)
values[pivotColumns[j]] = Rational.Create(solution[j].ToLowestTerms());
values[pivotColumns[j]] = Rational.Create(solution[j].InLowestTerms());
return true;
}

Expand All @@ -2079,7 +2079,7 @@ private static bool TryReconstructRational(EInteger u, EInteger m, out ERational
}
if (t1.IsZero || t1.Abs().CompareTo(bound) > 0)
return false;
value = ERational.Create(t1.Sign < 0 ? r1.Negate() : r1, t1.Abs()).ToLowestTerms();
value = ERational.Create(t1.Sign < 0 ? r1.Negate() : r1, t1.Abs()).InLowestTerms();
return true;
}

Expand Down Expand Up @@ -2132,7 +2132,7 @@ private static bool TrySolveOverRationals(Entity[][] matrix, Entity[] rhs, [NotN
// that is not grows with every row it is used against.
var pivotValue = augmented[rank][column];
for (var k = 0; k <= width; k++)
augmented[rank][k] = augmented[rank][k].Divide(pivotValue).ToLowestTerms();
augmented[rank][k] = augmented[rank][k].Divide(pivotValue).InLowestTerms();
for (var row = 0; row < rows; row++)
{
if (row == rank)
Expand All @@ -2141,7 +2141,7 @@ private static bool TrySolveOverRationals(Entity[][] matrix, Entity[] rhs, [NotN
if (factor.IsZero)
continue;
for (var k = 0; k <= width; k++)
augmented[row][k] = augmented[row][k].Subtract(factor.Multiply(augmented[rank][k])).ToLowestTerms();
augmented[row][k] = augmented[row][k].Subtract(factor.Multiply(augmented[rank][k])).InLowestTerms();
}
pivotColumnOfRow[rank] = column;
rank++;
Expand All @@ -2153,7 +2153,7 @@ private static bool TrySolveOverRationals(Entity[][] matrix, Entity[] rhs, [NotN
for (var column = 0; column < width; column++)
values[column] = Integer.Zero;
for (var row = 0; row < rank; row++)
values[pivotColumnOfRow[row]] = Rational.Create(augmented[row][width].ToLowestTerms());
values[pivotColumnOfRow[row]] = Rational.Create(augmented[row][width].InLowestTerms());
return true;
}

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2 changes: 1 addition & 1 deletion Sources/AngouriMath/Functions/Algebra/Polynomials/PolynomialFactoring.cs
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Expand Up @@ -414,7 +414,7 @@ private static IEnumerable<ERational> RationalRootCandidates(ERational[] coeffic
return candidates.Distinct();
}

private static EInteger Lcm(EInteger a, EInteger b) => a.Divide(a.Gcd(b)).Multiply(b);
private static EInteger Lcm(EInteger a, EInteger b) => a.Divide(a.GreatestCommonDivisor(b)).Multiply(b);

private static IEnumerable<EInteger> Divisors(EInteger n)
{
Expand Down
4 changes: 2 additions & 2 deletions Sources/AngouriMath/Functions/Algebra/Polynomials/PolynomialFactorization.cs
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Expand Up @@ -222,7 +222,7 @@ internal static bool IsWorthFactoringToSolve(Entity expr, Variable x)
if (FactorPrimitive(primitive) is not { } parts)
return null;

return new Factorization(ERational.Create(content, denominator).ToLowestTerms(), parts);
return new Factorization(ERational.Create(content, denominator).InLowestTerms(), parts);
}

/// <summary>
Expand Down Expand Up @@ -577,7 +577,7 @@ private static bool NextCombination(int[] indices, int poolCount)
return true;
}

private static EInteger Lcm(EInteger a, EInteger b) => a.Divide(a.Gcd(b)).Multiply(b);
private static EInteger Lcm(EInteger a, EInteger b) => a.Divide(a.GreatestCommonDivisor(b)).Multiply(b);

/// <summary>A polynomial written as a rational constant times powers of irreducibles.</summary>
internal readonly struct Factorization
Expand Down
2 changes: 1 addition & 1 deletion Sources/AngouriMath/Functions/Algebra/Polynomials/RationalFunction.cs
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Expand Up @@ -135,7 +135,7 @@ internal static bool TryCanonicalize(Entity expr, [NotNullWhen(true)] out Entity
return false;
if (leading.CompareTo(ERational.One) != 0)
{
var inverse = ERational.One.Divide(leading).ToLowestTerms();
var inverse = ERational.One.Divide(leading).InLowestTerms();
numerator = numerator.ScaleBy(inverse);
denominator = denominator.ScaleBy(inverse);
}
Expand Down
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