A power of a product with a sum in it is multiplied out as a polynomial

BREAKING-CHANGES.md

@@ -435,6 +435,20 @@ by the linear's coefficients, `(b d + 2c d x)^9`, which ran past a minute
 | `"(b + 2*c*x)^9/(a + b*x + c*x^2)^3".ToEntity().Integrate("x")` | past a minute; 76,153 characters on the unreleased master | 607 characters |
 | `"(b*d + 2*c*d*x)^9/(a + b*x + c*x^2)^3".ToEntity().Integrate("x")` | past a minute | 611 characters |
 
+### A square of a symbolic quadratic beside two linears is answered within the budget
+
+**Answers where there were none in time.** `1/((d + k x)(f + g x)(a + b x + c x^2)^2)` was declined by
+2.5.0, and on the unreleased master it did not return in 300 seconds. The norm of the other factors
+modulo the quadratic is a power of a product with a sum in it, and it was multiplied out term by term;
+it is multiplied out as a polynomial in the symbols now. `1/((d + k x)^3 (a + b x + c x^2)^2)` gives the
+same answer as on the unreleased master, in 1.4 seconds rather than 30
+([#718](https://github.com/asc-community/AngouriMath/issues/718)).
+
+| Input | Was (2.5.0) | Now |
+|---|---|---|
+| `"1/((d + k*x)*(f + g*x)*(a + b*x + c*x^2)^2)".ToEntity().Integrate("x")` | `integral(...)` | 24,143 characters |
+| `"1/((d + k*x)^3*(a + b*x + c*x^2)^2)".ToEntity().Integrate("x")` | `integral(...)` | 9,593 characters |
+
 ### A trinomial the numerator holds is divided out of a power of it
 
 **A shorter answer, where 2.5.0 had none.** `(d + g x + f x^2)(a + b x^2 + c x^4)/(a + b x^2 + c x^4)^4`, written

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

@@ -674,8 +674,11 @@ internal static Entity InLowestTermsOverTheSymbols(Entity constant)
         private static Entity ExpandedOverTheSymbols(Entity expr)
         {
             // Only where there is a product to multiply out: a sum or a quotient of sums already
-            // written term by term keeps the spelling every other step reads it in.
-            if (!expr.Nodes.Any(node => node is Powf(Sumf or Minusf, Integer { EInteger: var power }) && power.CompareTo(EInteger.One) > 0
+            // written term by term keeps the spelling every other step reads it in. A power of a
+            // product with a sum in it is one: the norm a repeated quadratic's inverse takes
+            // beside `(d + e x)^3` is `(S c)^2` for a sum `S` of 28 terms, and its expansion
+            // took 27 of the 29 seconds of `1/((d + e x)^3 (a + b x + c x^2)^2)`.
+            if (!expr.Nodes.Any(node => node is Powf(var @base, Integer { EInteger: var power }) && power.CompareTo(EInteger.One) > 0 && @base.Nodes.Any(n => n is Sumf or Minusf)
                     || node is Mulf(var left, var right) && left.Nodes.Any(n => n is Sumf or Minusf) && right.Nodes.Any(n => n is Sumf or Minusf)))
                 return expr.Expand();
             var variables = expr.Vars.OrderBy(v => v.Name, System.StringComparer.Ordinal).ToList();

Sources/Tests/UnitTests/Calculus/SymbolicFactorsPartialFractionsTest.cs

@@ -321,13 +321,17 @@ public void APolynomialOverALinearBesideARadicalIsReduced(string integrand)
         /// iteration. <c>1/((a + b x)^2 (c + d x)^(3/2))</c> is, under <c>u = sqrt(c + d x)</c>,
         /// <c>1/(u^2 (K + u^2)^2)</c> with a symbolic <c>K</c>, and went to the Hermite reduction
         /// for a hundred kilobytes in thirty seconds; it is eight kilobytes in half a second now.
+        /// Beside a cube of a linear, the norm of the other factors' residue is a power of a
+        /// product with a sum in it, which is multiplied out as a polynomial: expanded term by
+        /// term it took 27 of the 29 seconds of <c>1/((d + e x)^3 (a + b x + c x^2)^2)</c>.
         /// </summary>
         [Theory]
         [InlineData("1/((a + b*x)^2*(c + d*x)^(3/2))", 10000)]
         [InlineData("1/(x^2*(a + b*x^2)^2)", 4000)]
         [InlineData("1/(x^3*(a + b*x + c*x^2)^2)", 10000)]
         [InlineData("x/((a + b*x)*(c + x^2)^2)", 4000)]
         [InlineData("(A + B*x)/((a + b*x)*(1 + x^2)^3)", 4000)]
+        [InlineData("1/((d + B*x)^3*(a + b*x + c*x^2)^2)", 12000)]
         public void ARepeatedSymbolicQuadraticBesideALinear(string integrand, int atMost)
         {
             DifferentiatesBack(integrand, "x", ("a", 1.7), ("b", 2.3), ("c", 0.4), ("d", 1.1), ("A", 0.5), ("B", 1.3));