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Simplify the intersection #415 asks for, and correct two tests from #666 (#415, #424, #263) #677

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Merged
Happypig375 merged 1 commit into from
Aug 4, 2026
Merged

Simplify the intersection #415 asks for, and correct two tests from #666 (#415, #424, #263) #677

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26 changes: 16 additions & 10 deletions Sources/AngouriMath/Core/Entity/Omni/Sets/SetOperators.Intersection.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -30,15 +30,21 @@ internal static Set IntersectIntervalAndInterval(Interval A, Interval B)
{
if (A.Left == B.Left && A.Right == B.Right)
return new Interval(A.Left, A.LeftClosed && B.LeftClosed, A.Right, A.RightClosed && B.RightClosed);
if (A.Left is not Real aLeft ||
A.Right is not Real aRight ||
B.Left is not Real bLeft ||
B.Right is not Real bRight)
// Compared by what the endpoints are worth, not by whether they are written as
// bare numbers. (sqrt(33) - 3) / 6 is a Divf and never a Real, so an interval
// written with one was given up on -- which is
// https://github.com/asc-community/AngouriMath/issues/415. The bounds of the result
// are taken from the original expressions, so the answer keeps them exact
// rather than turning them into a hundred decimal places.
if (A.Left.Evaled is not Real aLeft ||
A.Right.Evaled is not Real aRight ||
B.Left.Evaled is not Real bLeft ||
B.Right.Evaled is not Real bRight)
return A.Intersect(B);
if (aLeft == bRight)
return A.LeftClosed && B.RightClosed ? new FiniteSet(aLeft) : Empty;
return A.LeftClosed && B.RightClosed ? new FiniteSet(A.Left) : Empty;
if (bLeft == aRight)
return A.RightClosed && B.LeftClosed ? new FiniteSet(bLeft) : Empty;
return A.RightClosed && B.LeftClosed ? new FiniteSet(B.Left) : Empty;
if (aLeft >= aRight)
return B;
if (bLeft >= bRight)
Expand All @@ -49,12 +55,12 @@ B.Left is not Real bLeft ||
return Empty;
var (left, leftClosed) =
aLeft == bLeft ?
(aLeft, A.LeftClosed && B.LeftClosed) :
(bLeft < aLeft ? (aLeft, A.LeftClosed) : (bLeft, B.LeftClosed));
(A.Left, A.LeftClosed && B.LeftClosed) :
(bLeft < aLeft ? (A.Left, A.LeftClosed) : (B.Left, B.LeftClosed));
var (right, rightClosed) =
aRight == bRight ?
(aRight, A.RightClosed && B.RightClosed) :
(bRight > aRight ? (aRight, A.RightClosed) : (bRight, B.RightClosed));
(A.Right, A.RightClosed && B.RightClosed) :
(bRight > aRight ? (A.Right, A.RightClosed) : (B.Right, B.RightClosed));
return new Interval(left, leftClosed, right, rightClosed);
}

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8 changes: 8 additions & 0 deletions Sources/AngouriMath/Functions/Simplification/Patterns/Patterns.Sets.cs
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Expand Up @@ -18,6 +18,14 @@ internal static partial class Patterns
internal static Entity SetOperatorRules(Entity x) => x switch
{
Intersectionf(var any1, var any1a) when any1 == any1a => any1,

// A /\ (B \/ C) = (A /\ B) \/ (A /\ C). Without this, an intersection whose
// other side is a union is left as written however simple each piece is, which
// is half of https://github.com/asc-community/AngouriMath/issues/415.
Intersectionf(Set setA, Unionf(Set setB, Set setC)) =>
setA.Intersect(setB).Unite(setA.Intersect(setC)),
Intersectionf(Unionf(Set setB, Set setC), Set setA) =>
setB.Intersect(setA).Unite(setC.Intersect(setA)),
Unionf(var any1, var any1a) when any1 == any1a => any1,
SetMinusf(var any1, var any1a) when any1 == any1a => Empty,
ConditionalSet(var var1, Inf(var var1a, var set)) when var1 == var1a => set,
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45 changes: 31 additions & 14 deletions Sources/Tests/UnitTests/Common/AlreadyFixedIssuesTest.cs
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Expand Up @@ -44,12 +44,15 @@ private static T Terminates<T>(System.Func<T> work, string what)
[Fact]
public void Issue263_InnerSimplifyTerminates() =>
Terminates(() => Issue263Quotient.ToEntity().InnerSimplified,
"InnerSimplify of the #263 quotient");
"InnerSimplify of the quotient from https://github.com/asc-community/AngouriMath/issues/263");

// The limit is what the quotient was written for, so its value is asserted rather
// than only that it comes back. Reported on the issue, this is 15*14/2 * 3^13.
[Fact]
public void Issue263_LimitTerminates() =>
Terminates(() => Issue263Quotient.ToEntity().Limit("x", 3, ApproachFrom.Left),
"the #263 limit");
public void Issue263_LimitIsComputed() =>
Assert.Equal(Entity.Number.Integer.Create(167403915),
Terminates(() => Issue263Quotient.ToEntity().Limit("x", 3, ApproachFrom.Left).Simplify(),
"the limit from https://github.com/asc-community/AngouriMath/issues/263"));

// https://github.com/asc-community/AngouriMath/issues/347
// Taking a limit of a boolean expression overflowed the stack. It is still not
Expand All @@ -66,23 +69,37 @@ public void Issue362_CoefficientsAreCollected() =>
Assert.Equal("(-2) * d * t", "(-1/2d-3/2d)t".ToEntity().Simplify().Stringize());

// https://github.com/asc-community/AngouriMath/issues/424
// Piecewise was to become compileable.
// Piecewise was to become compileable. These are piecewise() nodes: the earlier
// version of this test used `provided`, which is a Providedf and a different node
// altogether, so it was not testing the issue at all.
[Theory]
[InlineData("5 provided x = 3", 3.0, 5.0)]
[InlineData("x provided true", 7.0, 7.0)]
[InlineData("2 * x provided x > 0", 4.0, 8.0)]
[InlineData("piecewise(2 * x provided x > 0, -x provided true)", 3.0, 6.0)]
[InlineData("piecewise(2 * x provided x > 0, -x provided true)", -4.0, 4.0)]
[InlineData("piecewise(1 provided x > 10, 2 provided x > 5, 3 provided true)", 12.0, 1.0)]
[InlineData("piecewise(1 provided x > 10, 2 provided x > 5, 3 provided true)", 7.0, 2.0)]
[InlineData("piecewise(1 provided x > 10, 2 provided x > 5, 3 provided true)", 1.0, 3.0)]
public void Issue424_PiecewiseCompiles(string expression, double argument, double expected) =>
Assert.Equal(expected, expression.ToEntity().Compile<double, double>("x")(argument), 9);

// https://github.com/asc-community/AngouriMath/issues/415
// Intersections and unions of intervals were to be simplified.
// The example in the issue's screenshot, which is what it asks for. It needed two
// things: an intersection has to distribute over a union, and endpoints have to be
// compared by what they are worth rather than by whether they are written as bare
// numbers -- (sqrt(33) - 3) / 6 is a division and never a Real.
[Fact]
public void Issue415_IntervalsIntersect() =>
Assert.Equal(@"[3; 5]".ToEntity(), @"[1; 5] /\ [3; 8]".ToEntity().Simplify());
public void Issue415_TheScreenshottedExample() =>
Assert.Equal(@"(-1; (sqrt(33) - 3) / 6)".ToEntity().Simplify(),
@"(-1; 1) /\ (((-(sqrt(33) + 3) / 6; (sqrt(33) - 3) / 6) \/ (1; +oo)))"
.ToEntity().Simplify());

[Fact]
public void Issue415_IntervalsUnite() =>
Assert.Equal(@"[1; 8]".ToEntity(), @"[1; 5] \/ [3; 8]".ToEntity().Simplify());
[Theory]
[InlineData(@"[1; 5] /\ [3; 8]", "[3; 5]")]
[InlineData(@"[1; 5] \/ [3; 8]", "[1; 8]")]
[InlineData(@"(-1; 1) /\ ((0; 3) \/ (5; 7))", "(0; 1)")]
[InlineData(@"(-1; 1) /\ (-2; sqrt(2) / 4)", "(-1; sqrt(2) / 4)")]
[InlineData(@"(-1; 1) /\ (1; +oo)", "{ }")]
public void Issue415_IntervalsSimplify(string input, string expected) =>
Assert.Equal(expected.ToEntity().Simplify(), input.ToEntity().Simplify());

// https://github.com/asc-community/AngouriMath/issues/550
// The reporter's small system did not solve. The 25x26 one from the same report
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