Route the gcd and lowest-terms calls added since #2003 through GreatestCommonDivisors (#2006)

#2003 put the library's 177 gcd and lowest-terms call sites through
GreatestCommonDivisors, whose results are PeterO's and whose large-operand
case is about 800 times faster. Seventeen sites written since, in
PartialFractions, IndefiniteIntegralSolver and RothsteinTrager, called
EInteger.Gcd and ERational.ToLowestTerms directly again.

On the 35 rows the PRs that wrote them moved, the answers and allocation are
identical: the operands those rows see are small. The change keeps the
contract in one place for the operands that are not.

Part of #233.


Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

Co-authored-by: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

Author: Rafael-SOWNet

Sources/AngouriMath/Functions/Algebra/Polynomials/PartialFractions.cs

@@ -1170,10 +1170,10 @@ private static (Entity P, Entity Q)[]? OverTheGaussianRoots(
                 || Read(2) is not { } leading || leading.IsZero || Read(1) is not { } linear || Read(0) is not { } free)
                 return null;
             // M = x^2 + s x + t = (x - ρ)^2 + σ^2.
-            var s = linear.Divide(leading).ToLowestTerms();
-            var t = free.Divide(leading).ToLowestTerms();
-            var rho = s.Negate().Divide(ERational.FromInt32(2)).ToLowestTerms();
-            var sigmaSquared = t.Subtract(rho.Multiply(rho)).ToLowestTerms();
+            var s = linear.Divide(leading).InLowestTerms();
+            var t = free.Divide(leading).InLowestTerms();
+            var rho = s.Negate().Divide(ERational.FromInt32(2)).InLowestTerms();
+            var sigmaSquared = t.Subtract(rho.Multiply(rho)).InLowestTerms();
             if (sigmaSquared.Sign <= 0)
                 return null;
             var (sigmaAbove, sigmaBelow) = (sigmaSquared.Numerator.Sqrt(), sigmaSquared.Denominator.Sqrt());
@@ -1296,8 +1296,8 @@ bool TakeIn(Entity side, bool above)
                         next[m].Im.Add(binomial[m].Im.Multiply(rho.Negate())).Add(binomial[m].Re.Multiply(sigma)));
                 }
                 binomial = next;
-                real[j] = binomial.Select(c => c.Re.ToLowestTerms()).ToArray();
-                imaginary[j] = binomial.Select(c => c.Im.ToLowestTerms()).ToArray();
+                real[j] = binomial.Select(c => c.Re.InLowestTerms()).ToArray();
+                imaginary[j] = binomial.Select(c => c.Im.InLowestTerms()).ToArray();
             }
 
             // The digits in powers of M: c_j (x - r)^(-j) and its conjugate are 2 Re(c_j (x - r̄)^j)/M^j,
@@ -1343,7 +1343,7 @@ private static ERational Power(ERational value, int exponent)
         {
             var result = ERational.One;
             for (var k = 0; k < exponent; k++)
-                result = result.Multiply(value).ToLowestTerms();
+                result = result.Multiply(value).InLowestTerms();
             return result;
         }
 
@@ -1364,8 +1364,8 @@ private static ERational Power(ERational value, int exponent)
                 {
                     var coefficient = remainder[k];
                     quotient[k - 2] = coefficient;
-                    remainder[k - 1] = remainder[k - 1].Subtract(coefficient.Multiply(s)).ToLowestTerms();
-                    remainder[k - 2] = remainder[k - 2].Subtract(coefficient.Multiply(t)).ToLowestTerms();
+                    remainder[k - 1] = remainder[k - 1].Subtract(coefficient.Multiply(s)).InLowestTerms();
+                    remainder[k - 2] = remainder[k - 2].Subtract(coefficient.Multiply(t)).InLowestTerms();
                 }
                 digits.Add((remainder[0], remainder.Length > 1 ? remainder[1] : ERational.Zero));
                 current = quotient;

Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs

@@ -1089,7 +1089,7 @@ static bool APowerOfAQuotientOfLinearsVanishingAtPlusOrMinusOne(Entity inU, Vari
             var kappa = Functions.PartialFractions.Bare((a2 / (qs * ss)).Simplify());
             if (!VanishesIdentically(b2 - kappa * (ps * ss + qs * rs)) || !VanishesIdentically(c2 - kappa * ps * rs) || VanishesIdentically(c2))
                 return null;
-            var half = quadraticPower.Negate().Subtract(ERational.FromInt32(1).Divide(ERational.FromInt32(2))).ToLowestTerms();
+            var half = quadraticPower.Negate().Subtract(ERational.FromInt32(1).Divide(ERational.FromInt32(2))).InLowestTerms();
             if (!half.Denominator.Equals(EInteger.One) || !half.Numerator.CanFitInInt32() || half.Numerator.Abs().CompareTo(EInteger.FromInt32(12)) > 0)
                 return null;
             var bigK = half.Numerator.ToInt32Checked();
@@ -1178,9 +1178,9 @@ static bool APowerOfAQuotientOfLinearsVanishingAtPlusOrMinusOne(Entity inU, Vari
             }
             // L the largest exponent every one is a whole multiple of: the first times g/d, with d the
             // denominators' least common multiple and g the numerators' greatest common divisor over it.
-            var denominator = ratios.Aggregate(EInteger.One, (lcm, r) => lcm * r.Denominator / lcm.Gcd(r.Denominator));
+            var denominator = ratios.Aggregate(EInteger.One, (lcm, r) => lcm * r.Denominator / lcm.GreatestCommonDivisor(r.Denominator));
             var wholes = ratios.Select(r => r.Numerator * (denominator / r.Denominator)).ToList();
-            var divisor = wholes.Aggregate(EInteger.Zero, (gcd, n) => gcd.Gcd(n.Abs()));
+            var divisor = wholes.Aggregate(EInteger.Zero, (gcd, n) => gcd.GreatestCommonDivisor(n.Abs()));
             if (divisor.IsZero)
                 return null;
             var unit = Number.Rational.Create(divisor, denominator);
@@ -1279,7 +1279,7 @@ static bool AFactorAboveAQuadratic(List<KeyValuePair<EInteger, Entity>> terms, b
                         if (coefficient.Evaled is not Number.Rational rational || !power.CanFitInInt32() || power.ToInt32Checked() > 2 * IntegerPolynomial.MaxDegree)
                             return false;
                         rationals[halved ? power.ToInt32Checked() / 2 : power.ToInt32Checked()] = rational.ERational;
-                        denominator = denominator * rational.ERational.Denominator / denominator.Gcd(rational.ERational.Denominator);
+                        denominator = denominator * rational.ERational.Denominator / denominator.GreatestCommonDivisor(rational.ERational.Denominator);
                     }
                     var whole = new EInteger[rationals.Keys.Max() + 1];
                     for (var k = 0; k < whole.Length; k++)
@@ -18220,7 +18220,7 @@ private static bool IsAFunctionToRaise(Entity factor, Entity.Variable x)
                 var (exponent, coefficient) = (ERational.Zero, term);
                 if (term.ContainsNode(x) && !TryReadAMonomial(term, x, out exponent, out coefficient))
                     return null;
-                read.Add((coefficient, exponent.ToLowestTerms()));
+                read.Add((coefficient, exponent.InLowestTerms()));
             }
             if (read.Count < 2)
                 return null;
@@ -18232,7 +18232,7 @@ private static bool IsAFunctionToRaise(Entity factor, Entity.Variable x)
                 var (degree, coefficient) = (ERational.Zero, term);
                 if (term.ContainsNode(x) && !TryReadAMonomial(term, x, out degree, out coefficient))
                     return null;
-                degree = degree.ToLowestTerms();
+                degree = degree.InLowestTerms();
                 inB[degree] = inB.TryGetValue(degree, out var was) ? was + coefficient : coefficient;
             }
             var degrees = inB.Keys.Where(degree => !degree.IsZero).OrderBy(degree => degree).ToList();
@@ -18259,7 +18259,7 @@ private static bool IsAFunctionToRaise(Entity factor, Entity.Variable x)
             var inU = new Dictionary<int, Entity>();
             foreach (var (coefficient, exponent) in read)
             {
-                var scaled = exponent.Multiply(ERational.FromInt32(k)).Add(ERational.FromInt32(k - 1)).ToLowestTerms();
+                var scaled = exponent.Multiply(ERational.FromInt32(k)).Add(ERational.FromInt32(k - 1)).InLowestTerms();
                 if (!scaled.Denominator.Equals(EInteger.One) || !scaled.Numerator.CanFitInInt32())
                     return null;
                 var e = scaled.Numerator.ToInt32Unchecked();

Sources/AngouriMath/Functions/Continuous/Integration/RothsteinTrager.cs

@@ -370,7 +370,7 @@ internal static bool WantsASumOverRootsAlone(Entity numerator, Entity denominato
         private static bool InAPowerOfAShift(IntegerPolynomial poly)
         {
             var n = poly.Degree;
-            var shift = ERational.Create(poly[n - 1], poly[n].Multiply(EInteger.FromInt32(n))).ToLowestTerms();
+            var shift = ERational.Create(poly[n - 1], poly[n].Multiply(EInteger.FromInt32(n))).InLowestTerms();
             // Horner in y - s: g = g (y - s) + a_i, from the leading coefficient down.
             var g = new ERational[n + 1];
             for (var i = 0; i <= n; i++)