//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;
}