public static List<EdgeAggregator> Instantiate(GroundedClause c)
{
annotation.active = EngineUIBridge.JustificationSwitch.SEGMENT_ADDITION_AXIOM;
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
InMiddle im = c as InMiddle;
if (im == null) return newGrounded;
Segment s1 = new Segment(im.segment.Point1, im.point);
Segment s2 = new Segment(im.point, im.segment.Point2);
Addition sum = new Addition(s1, s2);
GeometricSegmentEquation eq = new GeometricSegmentEquation(sum, im.segment);
eq.MakeAxiomatic();
// For hypergraph
List<GroundedClause> antecedent = Utilities.MakeList<GroundedClause>(im);
newGrounded.Add(new EdgeAggregator(antecedent, eq, annotation));
return newGrounded;
}
public static List<EdgeAggregator> InstantiateMidpointTheorem(GroundedClause original, Midpoint midpt)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Construct 2AM
Multiplication product1 = new Multiplication(new NumericValue(2), new Segment(midpt.point, midpt.segment.Point1));
// Construct 2BM
Multiplication product2 = new Multiplication(new NumericValue(2), new Segment(midpt.point, midpt.segment.Point2));
// 2X = AB
GeometricSegmentEquation newEq1 = new GeometricSegmentEquation(product1, midpt.segment);
GeometricSegmentEquation newEq2 = new GeometricSegmentEquation(product2, midpt.segment);
// For hypergraph
List<GroundedClause> antecedent = Utilities.MakeList<GroundedClause>(original);
newGrounded.Add(new EdgeAggregator(antecedent, newEq1, annotation));
newGrounded.Add(new EdgeAggregator(antecedent, newEq2, annotation));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateToTheorem(Trapezoid trapezoid, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// If median has not been checked, check now
if (!trapezoid.IsMedianChecked()) trapezoid.FindMedian();
// Generate only if the median is valid (exists in the original figure)
if (!trapezoid.IsMedianValid()) return newGrounded;
Addition sum = new Addition(trapezoid.baseSegment, trapezoid.oppBaseSegment);
Multiplication product = new Multiplication(new NumericValue(2), trapezoid.median);
GeometricSegmentEquation gseq = new GeometricSegmentEquation(product, sum);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
newGrounded.Add(new EdgeAggregator(antecedent, gseq, annotation));
return newGrounded;
}
//private static readonly string NAME = "Simplification";
//
// Given an equation, simplify algebraically using the following notions:
// A + A = B -> 2A = B
// A + B = B + C -> A = C
// A + B = 2B + C -> A = B + C
//
public static Equation Simplify(Equation original)
{
// Do we have an equation?
if (original == null) throw new ArgumentException();
// Is the equation 0 = 0? This should be allowed at it indicates a tautology
if (original.lhs.Equals(new NumericValue(0)) && original.rhs.Equals(new NumericValue(0)))
{
throw new ArgumentException("Should not have an equation that is 0 = 0: " + original.ToString());
}
//
// Ideally, flattening would:
// Remove all subtractions -> adding a negative instead
// Distribute subtraction or multiplication over addition
//
// Flatten the equation so that each side is a sum of atomic expressions
Equation copyEq = (Equation)original.DeepCopy();
FlatEquation flattened = new FlatEquation(copyEq.lhs.CollectTerms(), copyEq.rhs.CollectTerms());
//Debug.WriteLine("Equation prior to simplification: " + flattened.ToString());
// Combine terms only on each side (do not cross =)
FlatEquation combined = CombineLikeTerms(flattened);
//Debug.WriteLine("Equation after like terms combined on both sides: " + combined);
// Combine terms across the equal sign
FlatEquation across = CombineLikeTermsAcrossEqual(combined);
//Debug.WriteLine("Equation after simplifying both sides: " + across);
FlatEquation constSimplify = SimplifyForMultipliersAndConstants(across);
//
// Inflate the equation
//
Equation inflated = null;
GroundedClause singleLeftExp = InflateEntireSide(constSimplify.lhsExps);
GroundedClause singleRightExp = InflateEntireSide(constSimplify.rhsExps);
if (original is AlgebraicSegmentEquation)
{
inflated = new AlgebraicSegmentEquation(singleLeftExp, singleRightExp);
}
else if (original is GeometricSegmentEquation)
{
inflated = new GeometricSegmentEquation(singleLeftExp, singleRightExp);
}
else if (original is AlgebraicAngleEquation)
{
inflated = new AlgebraicAngleEquation(singleLeftExp, singleRightExp);
}
else if (original is GeometricAngleEquation)
{
inflated = new GeometricAngleEquation(singleLeftExp, singleRightExp);
}
else if (original is AlgebraicArcEquation)
{
inflated = new AlgebraicArcEquation(singleLeftExp, singleRightExp);
}
else if (original is GeometricArcEquation)
{
inflated = new GeometricArcEquation(singleLeftExp, singleRightExp);
}
else if (original is AlgebraicAngleArcEquation)
{
inflated = new AlgebraicAngleArcEquation(singleLeftExp, singleRightExp);
}
else if (original is GeometricAngleArcEquation)
{
inflated = new GeometricAngleArcEquation(singleLeftExp, singleRightExp);
}
// If simplifying didn't do anything, return the original equation
if (inflated.Equals(original))
{
return original;
}
//
// 0 = 0 should not be allowable.
//
if (inflated.lhs.Equals(new NumericValue(0)) && inflated.rhs.Equals(new NumericValue(0)))
{
return null;
}
return inflated;
}
