/// <summary>
/// x+0 = x, x-0 = x, x*0=0
/// </summary>
/// <param name="obj"></param>
/// <param name="rootTerm"></param>
/// <returns></returns>
public static object ApplyZero(this object obj, Term rootTerm)
{
var term = obj as Term;
if (term == null)
{
return(obj);
}
Term localTerm = term.DepthFirstSearch(rootTerm);
#region Apply Zero Law
var list = localTerm.Args as List <object>;
if (ContainZero(list))
{
if (localTerm.Op.Method.Name.Equals("Multiply"))
{
string kc = AlgebraRule.RuleConcept(AlgebraRule.AlgebraRuleType.Identity);
string rule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Identity);
String appliedRule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Identity,
localTerm, null);
rootTerm.GenerateTrace(localTerm, 0, kc, rule, appliedRule);
return(0);
}
if (localTerm.Op.Method.Name.Equals("Add"))
{
string kc = AlgebraRule.RuleConcept(AlgebraRule.AlgebraRuleType.Identity);
var cloneTerm = localTerm.Clone();
var cloneLst = cloneTerm.Args as List <object>;
Debug.Assert(cloneLst != null);
RemoveZero(ref cloneLst);
//generate trace rule
string rule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Identity);
string appliedRule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Identity,
localTerm, null);
rootTerm.GenerateTrace(localTerm, cloneTerm, kc, rule, appliedRule);
localTerm = cloneTerm;
}
}
#endregion
return(localTerm);
}
/// <summary>
/// x+(y+z) == (x+y)+zm, x(yz) == (xy)z
/// </summary>
/// <param name="term"></param>
/// <param name="gTerm"></param>
/// <returns></returns>
public static object ApplyAssociative(this object obj, Term rootTerm)
{
//(a+1)+1 -> a+(1+1)
//a*3*3 -> a*(3*3)
var term = obj as Term;
if (term == null)
{
return(obj);
}
Term localTerm = term.DepthFirstSearch(rootTerm);
var list = localTerm.Args as List <object>;
if (list == null)
{
throw new Exception("Cannot be null");
}
if (list.Count < 2)
{
return(localTerm);
}
object obj1, obj2;
if (SatisfyAssociativeCondition(term, list[0], list[1], out obj1, out obj2))
{
var cloneTerm = localTerm.Clone();
var cloneLst = cloneTerm.Args as List <object>;
Debug.Assert(cloneLst != null);
cloneLst[0] = obj1;
cloneLst[1] = obj2;
//generate trace rule
string kc = AlgebraRule.RuleConcept(AlgebraRule.AlgebraRuleType.Associative);
string rule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Associative);
String appliedRule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Associative,
list[0], list[1]);
rootTerm.GenerateTrace(localTerm, cloneTerm, kc, rule, appliedRule);
localTerm = cloneTerm;
}
Term gTerm;
if (SatisfyAssociativeCondition2(localTerm, out gTerm))
{
//generate trace rule
string kc = AlgebraRule.RuleConcept(AlgebraRule.AlgebraRuleType.Associative);
string rule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Associative);
String appliedRule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Associative,
list[0], list[1]);
rootTerm.GenerateTrace(localTerm, gTerm, kc, rule, appliedRule);
localTerm = gTerm;
}
return(localTerm);
}
/// <summary>
/// Commutative Law
/// Algorithm: Bubble Sort
/// </summary>
/// <param name="term"></param>
/// <param name="obj"></param>
/// <param name="rootTerm"></param>
public static object ApplyCommutative(this object obj, Term rootTerm)
{
var term = obj as Term;
if (term == null)
{
return(obj);
}
//3+x -> x+3
//x*3 -> 3*x
//x+a -> x+a
//x*a -> x*a
//3*a*3 -> a*3*3
//(x+1)*a -> a*(x+1)
//1+(1+a) -> (a+1)+1
Term localTerm = term.DepthFirstSearch(rootTerm);
#region Apply Commutative Law: Bubble Sort
bool madeChanges;
do
{
var list = localTerm.Args as List <object>;
if (list == null)
{
throw new Exception("Cannot be null");
}
int itemCount = list.Count;
madeChanges = false;
itemCount--;
for (var i = 0; i < itemCount; i++)
{
list = localTerm.Args as List <object>;
Debug.Assert(list != null);
if (SatisfyCommutativeCondition(localTerm, list[i], list[i + 1]))
{
var cloneTerm = localTerm.Clone();
var cloneLst = cloneTerm.Args as List <object>;
Debug.Assert(cloneLst != null);
object tempObj = cloneLst[i];
cloneLst[i] = cloneLst[i + 1];
cloneLst[i + 1] = tempObj;
madeChanges = true;
//generate trace rule
string kc = AlgebraRule.RuleConcept(AlgebraRule.AlgebraRuleType.Commutative);
string rule = AlgebraRule.Rule(AlgebraRule.AlgebraRuleType.Commutative);
string appliedRule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Commutative,
list[i], list[i + 1]);
rootTerm.GenerateTrace(localTerm, cloneTerm, kc, rule, appliedRule);
localTerm = cloneTerm;
}
}
} while (madeChanges);
#endregion
return(localTerm);
}
public static object ApplyDistributive(this object obj, Term rootTerm)
{
//1*y+1*y -> (1+1)*y
//1*y+2*y -> (1+2)*y
//y+y+y -> (1+1+1)*y
//a*y+y+x -> (a+1)*y+x
//1*y^2+2*y^2 -> (1+2)*y^2
//x^2+x^2+x^2 -> (1+1+1)*x^2
//2*x^2+x^2+y -> (2+1)x^2+y
//3*(x+1) -> 3x+3
//a*(x+1) -> ax+a
//x*(a+1) -> xa + x
//(a+1)*(x+1) -> TODO
var term = obj as Term;
if (term == null)
{
return(obj);
}
Term localTerm = term.DepthFirstSearch(rootTerm);
var list = localTerm.Args as List <object>;
if (list == null)
{
throw new Exception("Cannot be null");
}
if (list.Count < 2)
{
return(localTerm);
}
bool madeChanges;
do
{
list = localTerm.Args as List <object>;
if (list == null)
{
throw new Exception("Cannot be null");
}
int itemCount = list.Count;
madeChanges = false;
itemCount--;
for (var i = 0; i < itemCount; i++)
{
list = localTerm.Args as List <object>;
Debug.Assert(list != null);
itemCount = list.Count;
object obj1;
if (i + 1 >= list.Count)
{
break;
}
if (SatisfyDistributiveCondition(term, list[i], list[i + 1], out obj1))
{
var cloneTerm = localTerm.Clone();
var cloneLst = cloneTerm.Args as List <object>;
Debug.Assert(cloneLst != null);
cloneLst[i] = obj1;
cloneLst.RemoveAt(i + 1);
string kc = AlgebraRule.RuleConcept(AlgebraRule.AlgebraRuleType.Distributive);
//generate trace rule
string rule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Distributive);
string appliedRule = AlgebraRule.Rule(
AlgebraRule.AlgebraRuleType.Distributive,
list[i], list[i + 1]);
if (cloneLst.Count == 1)
{
cloneTerm = cloneLst[0] as Term;
}
rootTerm.GenerateTrace(localTerm, cloneTerm, kc, rule, appliedRule);
localTerm = cloneTerm;
madeChanges = true;
}
}
} while (madeChanges);
return(localTerm);
}