IsolateVariable

Symbolism/IsolateVariable.cs

@@ -0,0 +1,73 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+
+using Symbolism.CoefficientGpe;
+using Symbolism.AlgebraicExpand;
+
+namespace Symbolism.IsolateVariable
+{
+    public static class Extensions
+    {
+        public static MathObject IsolateVariable(this Equation eq, Symbol sym)
+        {
+            if (eq.b.Has(sym)) return IsolateVariable(new Equation(eq.a - eq.b, 0), sym);
+
+            if (eq.a == sym) return eq;
+
+            if (eq.a.AlgebraicExpand().DegreeGpe(new List<MathObject>() { sym }) == 2)
+            {
+                var a = eq.a.AlgebraicExpand().CoefficientGpe(sym, 2);
+                var b = eq.a.AlgebraicExpand().CoefficientGpe(sym, 1);
+                var c = eq.a.AlgebraicExpand().CoefficientGpe(sym, 0);
+
+                //return
+                //    sym == (-b - (((b ^ 2) - 4 * a * c) ^ (new Integer(1) / 2))) / (2 * a);
+
+                return
+                    new Or(
+                        sym == (-b + (((b ^ 2) - 4 * a * c) ^ (new Integer(1) / 2))) / (2 * a),
+                        sym == (-b - (((b ^ 2) - 4 * a * c) ^ (new Integer(1) / 2))) / (2 * a)
+                        ).Simplify();
+            }
+
+
+
+            if (eq.a is Sum)
+            {
+                var items = ((Sum)eq.a).elts.FindAll(elt => elt.FreeOf(sym));
+
+                //return IsolateVariable(
+                //    new Equation(
+                //        eq.a - new Sum() { elts = items }.Simplify(),
+                //        eq.b - new Sum() { elts = items }.Simplify()),
+                //    sym);
+
+                var new_a = eq.a; items.ForEach(elt => new_a = new_a - elt);
+                var new_b = eq.b; items.ForEach(elt => new_b = new_b - elt);
+
+                return IsolateVariable(new Equation(new_a, new_b), sym);
+
+                //return IsolateVariable(
+                //    new Equation(
+                //        eq.a + new Sum() { elts = items.ConvertAll(elt => elt * -1) }.Simplify(),
+                //        eq.b - new Sum() { elts = items }.Simplify()),
+                //    sym);
+            }
+
+            if (eq.a is Product)
+            {
+                var items = ((Product)eq.a).elts.FindAll(elt => elt.FreeOf(sym));
+
+                return IsolateVariable(
+                    new Equation(
+                        eq.a / new Product() { elts = items }.Simplify(),
+                        eq.b / new Product() { elts = items }.Simplify()),
+                    sym);
+            }
+
+            throw new Exception();
+        }
+    }
+}

Symbolism/Symbolism.csproj

@@ -50,6 +50,7 @@
     <Compile Include="CoefficientGpe.cs" />
     <Compile Include="ExpandPower.cs" />
     <Compile Include="ExpandProduct.cs" />
+    <Compile Include="IsolateVariable.cs" />
     <Compile Include="Symbolism.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
   </ItemGroup>

Tests/Tests.cs

@@ -23,6 +23,7 @@
 
 using Symbolism.CoefficientGpe;
 using Symbolism.AlgebraicExpand;
+using Symbolism.IsolateVariable;
 
 namespace Tests
 {
@@ -284,6 +285,12 @@ static void Main(string[] args)
 
                 #endregion
 
+                #region IsolateVariable
+
+                Assert((0 == x - y).IsolateVariable(x).Equals(x == y), "(0 == x - y).IsolateVariable(x).Equals(x == y)");
+
+                #endregion
+
             }
 
             #region PSE 5E Example 4.3