public static List <EdgeAggregator> Instantiate(GroundedClause c) { annotation.active = EngineUIBridge.JustificationSwitch.ARC_ADDITION_AXIOM; List <EdgeAggregator> newGrounded = new List <EdgeAggregator>(); ArcInMiddle im = c as ArcInMiddle; if (im == null) { return(newGrounded); } Addition sum = null; // Temporarily assume that the two arcs formed by the intersection are both minor arcs MinorArc a1 = new MinorArc(im.arc.theCircle, im.arc.endpoint1, im.point); MinorArc a2 = new MinorArc(im.arc.theCircle, im.point, im.arc.endpoint2); // If the intersected arc is a minor arc, this will always be true. // If the intersected arc is a major arc, this might be true. Other case is one minor arc and one major arc. if (Arc.BetweenMajor(im.point, im.arc)) { // Check if both arcs are genuinely minor arcs. // If the other endpoint falls in the new arc, then the major arc should be used instead if (Arc.BetweenMinor(im.arc.endpoint2, a1)) { MajorArc majorArc = new MajorArc(im.arc.theCircle, im.arc.endpoint1, im.point); sum = new Addition(majorArc, a2); } else if (Arc.BetweenMinor(im.arc.endpoint1, a2)) { MajorArc majorArc = new MajorArc(im.arc.theCircle, im.point, im.arc.endpoint2); sum = new Addition(a1, majorArc); } } if (sum == null) { sum = new Addition(a1, a2); } GeometricArcEquation eq = new GeometricArcEquation(sum, im.arc); eq.MakeAxiomatic(); // For hypergraph List <GroundedClause> antecedent = Utilities.MakeList <GroundedClause>(im); newGrounded.Add(new EdgeAggregator(antecedent, eq, 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); }