/*
* given m=2, k=3, y=3x+2
*/
public static void FromSlopeInterceptToLineSlopeIntercept(EqGoal slopeGoal, EqGoal interceptGoal, LineSymbol ls)
{
//1. Substitute slope and intercept properties into the line slope-intercept form y=mx+b.
////////////////////////////////////////////////////////
var ts0 = new TraceStep(null, slopeGoal, GeometryScaffold.KC_LineSlopeForm, PlottingRule.PlottingStrategy, PlottingRule.Plot(slopeGoal));
var ts1 = new TraceStep(null, interceptGoal, GeometryScaffold.KC_LineInterceptForm, PlottingRule.PlottingStrategy, PlottingRule.Plot(interceptGoal));
ls._innerLoop.Add(ts0);
var abstractLs = new Line(ls.Shape.Label, slopeGoal.Lhs, interceptGoal.Lhs);
var abstractLss = new LineSymbol(abstractLs);
var internalLs = new Line(ls.Shape.Label, ls.SymSlope, interceptGoal.Lhs);
var internalLss = new LineSymbol(internalLs);
var traceStep1 = new TraceStep(abstractLss, internalLss, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy, SubstitutionRule.ApplySubstitute(abstractLss, slopeGoal));
ls._innerLoop.Add(traceStep1);
ls._innerLoop.Add(ts1);
/*
* var rule = "Substitute given property to line slope-intercept form.";
* var appliedRule1 = string.Format("Substitute slope={0} into y=mx+b", ls.SymSlope);
* var appliedRule2= string.Format("Substitute intercept={0} into y=mx+b", ls.SymIntercept);*/
var traceStep2 = new TraceStep(internalLss, ls, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy, SubstitutionRule.ApplySubstitute(internalLss, interceptGoal));
ls._innerLoop.Add(traceStep2);
string strategy = "Substitute slope and intercept properties into the line slope-intercept form y = mx + b.";
ls.GenerateATrace(strategy);
}
public static void FromPointPointToLine(PointSymbol ps1, PointSymbol ps2, LineSymbol ls)
{
var m = new Var("m");
var k = new Var("k");
var x = new Var("x");
var y = new Var("y");
var term = new Term(Expression.Multiply, new List <object>()
{
m, x
});
var term1 = new Term(Expression.Add, new List <object>()
{
term, k
});
var eqPattern = new Equation(y, term1);
var term2 = new Term(Expression.Multiply, new List <object>()
{
m, ps1.SymXCoordinate
});
var term22 = new Term(Expression.Add, new List <object>()
{
term2, k
});
var eqPattern1 = new Equation(ps1.SymYCoordinate, term22);
var term3 = new Term(Expression.Multiply, new List <object>()
{
m, ps2.SymXCoordinate
});
var term33 = new Term(Expression.Add, new List <object>()
{
term3, k
});
var eqPattern2 = new Equation(ps2.SymYCoordinate, term33);
string strategy = "Generate a line by substituting two given points into the line slope-intercept form y=mx+k.";
var ts0 = new TraceStep(eqPattern, eqPattern1, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy,
SubstitutionRule.ApplySubstitute(eqPattern, ps1));
var ts1 = new TraceStep(eqPattern, eqPattern2, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy,
SubstitutionRule.ApplySubstitute(eqPattern, ps2));
string kc = GeometryScaffold.KC_LineSlopeForm;
var ts2 = new TraceStep(null, ls, kc, "calculate m and k through the above two linear equations.",
"calculate m and k through linear equation and retrieve y=mx+k line form.");
ls._innerLoop.Add(ts0);
ls._innerLoop.Add(ts1);
ls._innerLoop.Add(ts2);
ls.GenerateATrace(strategy);
}
public static void FromLineSlopeIntercetpToLineGeneralForm(LineSymbol ls)
{
var line = ls.Shape as Line;
Debug.Assert(line != null);
Debug.Assert(ls.OutputType == LineType.GeneralForm);
string step1metaRule = "Given the line slope-intercept from y=mx+b, move y term to the right side of equation.";
string step1AppliedRule = String.Format("Move y to the right side of equation");
string kc = GeometryScaffold.KC_LinePatternsTransform;
var ts = new TraceStep(ls.SlopeInterceptForm, ls.GeneralForm, kc, step1metaRule, step1AppliedRule);
string strategy = strategy_si_general;
ls._innerLoop.Add(ts);
ls.GenerateATrace(strategy);
}
/// <summary>
/// Trace from Line General Form to Slope-Intercept Form
/// ax+by+c=0 => y=mx+b
/// </summary>
/// <param name="target"></param>
/// <returns></returns>
public static void FromLineGeneralFormToSlopeIntercept(LineSymbol ls)
{
string strategy = "Given a general form line ax+by+c=0, the slope-intercept form of it is y = -(a/b)x-c/b.";
var line = ls.Shape as Line;
Debug.Assert(line != null);
var newLS = new LineSymbol(line);
newLS.OutputType = LineType.SlopeIntercept;
var x = new Var("x");
var y = new Var("y");
var xTerm = new Term(Expression.Multiply, new List <object>()
{
line.A, x
});
var yTerm = new Term(Expression.Multiply, new List <object>()
{
line.B, y
});
var oldEqLeft = new Term(Expression.Add, new List <object>()
{
xTerm, yTerm, line.C
});
var oldEq = new Equation(oldEqLeft, 0);
var invertXTerm = new Term(Expression.Multiply, new List <object>()
{
-1, xTerm
});
var intertZ = new Term(Expression.Multiply, new List <object>()
{
-1, line.C
});
var internalRight = new Term(Expression.Add, new List <object>()
{
invertXTerm, intertZ
});
var internalEq = new Equation(yTerm, internalRight);
var finalXTerm = new Term(Expression.Multiply, new List <object>()
{
line.Slope, x
});
var finalRight = new Term(Expression.Add, new List <object>()
{
finalXTerm, line.Intercept
});
var lastEq = new Equation(yTerm, finalRight);
string step1metaRule = "Given the line general form ax+by+c=0, move x term and Constant term to the right side of equation.";
string step1AppliedRule = String.Format("Move {0}x and {1} to right side of equation.", ls.SymA, ls.SymC);
string kc = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
var ts0 = new TraceStep(null, internalEq, kc, step1metaRule, step1AppliedRule);
ls._innerLoop.Add(ts0);
string appliedRule = string.Format("divide coefficient b in both side of equation.");
kc = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Inverse);
var ts1 = new TraceStep(null, lastEq, kc, AlgebraRule.AlgebraicStrategy, appliedRule);
ls._innerLoop.Add(ts1);
ls.GenerateATrace(strategy);
}
public static void FromPointSlopeToLine(PointSymbol ps, EqGoal goal, LineSymbol ls)
{
string strategy = "Substitute point and slope property into line form.";
// 1. Substitute slope property into the line slope-intercept form.
// 2. Calculate the line intercept by substituting the point into line pattern.
//////////////////////////////////////////////////////////////////////
string strategy1 = "Substitute slope property into the line slope-intercept form.";
var m = new Var("m");
var k = new Var("k");
var x = new Var("x");
var y = new Var("y");
var term = new Term(Expression.Multiply, new List <object>()
{
m, x
});
var term1 = new Term(Expression.Add, new List <object>()
{
term, k
});
var eqPattern = new Equation(y, term1);
var term2 = new Term(Expression.Multiply, new List <object>()
{
goal.Rhs, x
});
var term3 = new Term(Expression.Add, new List <object>()
{
term2, k
});
var eqInternal1 = new Equation(y, term3);
var appliedRule1 = SubstitutionRule.ApplySubstitute(eqPattern, goal);
var ts0 = new TraceStep(eqPattern, eqInternal1, SubstitutionRule.SubstituteKC(), strategy1, appliedRule1);
ls._innerLoop.Add(ts0);
//////////////////////////////////////////////////////////////////////
var point = ps.Shape as Point;
Debug.Assert(point != null);
string strategy2 = "Calculate the line intercept by substituting the point into line pattern.";
var term4 = new Term(Expression.Multiply, new List <object>()
{
goal.Rhs, point.XCoordinate
});
var term5 = new Term(Expression.Add, new List <object>()
{
term4, k
});
var eqinternal2 = new Equation(point.YCoordinate, term5);
object obj;
bool result = eqinternal2.IsEqGoal(out obj);
var eqGoal = obj as EqGoal;
Debug.Assert(eqGoal != null);
var gTuple = eqGoal.Traces[0];
var gLst = gTuple.Item2 as List <TraceStep>;
Debug.Assert(gLst != null);
ls._innerLoop.AddRange(gLst);
var appliedRule2 = SubstitutionRule.ApplySubstitute(eqInternal1, ps);
var ts = new TraceStep(eqInternal1, ls, SubstitutionRule.SubstituteKC(), strategy2, appliedRule2);
ls._innerLoop.Add(ts);
ls.GenerateATrace(strategy);
}
public static void LineSlopeIntercepToGraph(LineSymbol ls)
{
string strategy = strategy_graphing;
//Plotting shapes
//1. plotting Y-Intercept
//2. plotting X-Intercept
//3. plotting the line
//////////////////////////////////////////////////////////////
// Step 1:
var pt = new Point(0, ls.SymIntercept);
var ptSym = new PointSymbol(pt);
var ts0 = new TraceStep(null, ptSym, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym));
ls._innerLoop.Add(ts0);
//////////////////////////////////////////////////////////////
// Step 2:
var line = ls.Shape as Line;
Debug.Assert(line != null);
Equation eq;
if (line.B == null)
{
}
else
{
var x = new Var("x");
//step 2.1
var term = new Term(Expression.Multiply, new List <object>()
{
line.Slope, x
});
var term1 = new Term(Expression.Add, new List <object>()
{
term, line.Intercept
});
eq = new Equation(term1, 0);
object obj;
EqGoal gGoal = null;
bool result = eq.IsEqGoal(out obj);
if (result)
{
gGoal = obj as EqGoal;
}
if (gGoal != null)
{
double dX;
LogicSharp.IsDouble(gGoal.Rhs, out dX);
var pt1 = new Point(dX, 0);
var ptSym1 = new PointSymbol(pt1);
var ts1 = new TraceStep(null, ptSym1, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym1));
ls._innerLoop.Add(ts1);
}
}
/////////////////////////////////////////////////////////////////
const string step1MetaRule = "Given the line slope-intercept form y=mx+b, plot the line by passing points (0,b) and (-b/m,0).";
string step1AppliedRule = String.Format("Plotting the line passing through (0,{0}) and ({1},0) ", ls.SymIntercept, ls.SymC);
//var ts = new TraceStep(null, ls.SlopeInterceptForm, step1MetaRule, step1AppliedRule);
string kc = GeometryScaffold.KC_LineGraphing;
var ts = new TraceStep(null, ls, kc, step1MetaRule, step1AppliedRule);
ls._innerLoop.Add(ts);
//////////////////////////////////////////////////////////////////
ls.GenerateATrace(strategy);
}
/// <summary>
/// Trace from Line General Form to Slope-Intercept Form
/// ax+by+c=0 => y=mx+b
/// </summary>
/// <param name="target"></param>
/// <returns></returns>
public static void FromLineGeneralFormToSlopeIntercept(LineSymbol ls)
{
string strategy = "Given a general form line ax+by+c=0, the slope-intercept form of it is y = -(a/b)x-c/b.";
var line = ls.Shape as Line;
Debug.Assert(line != null);
var newLS = new LineSymbol(line);
newLS.OutputType = LineType.SlopeIntercept;
var x = new Var("x");
var y = new Var("y");
var xTerm = new Term(Expression.Multiply, new List<object>() { line.A, x });
var yTerm = new Term(Expression.Multiply, new List<object>() { line.B, y });
var oldEqLeft = new Term(Expression.Add, new List<object>() { xTerm, yTerm, line.C });
var oldEq = new Equation(oldEqLeft, 0);
var invertXTerm = new Term(Expression.Multiply, new List<object>() { -1, xTerm });
var intertZ = new Term(Expression.Multiply, new List<object>() { -1, line.C });
var internalRight = new Term(Expression.Add, new List<object>() { invertXTerm, intertZ });
var internalEq = new Equation(yTerm, internalRight);
var finalXTerm = new Term(Expression.Multiply, new List<object>() { line.Slope, x });
var finalRight = new Term(Expression.Add, new List<object>() { finalXTerm, line.Intercept });
var lastEq = new Equation(yTerm, finalRight);
string step1metaRule = "Given the line general form ax+by+c=0, move x term and Constant term to the right side of equation.";
string step1AppliedRule = String.Format("Move {0}x and {1} to right side of equation.", ls.SymA, ls.SymC);
string kc = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
var ts0 = new TraceStep(null, internalEq, kc, step1metaRule, step1AppliedRule);
ls._innerLoop.Add(ts0);
string appliedRule = string.Format("divide coefficient b in both side of equation.");
kc = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Inverse);
var ts1 = new TraceStep(null, lastEq, kc, AlgebraRule.AlgebraicStrategy, appliedRule);
ls._innerLoop.Add(ts1);
ls.GenerateATrace(strategy);
}
public static void FromPointSlopeToLine(PointSymbol ps, EqGoal goal, LineSymbol ls)
{
string strategy = "Substitute point and slope property into line form.";
// 1. Substitute slope property into the line slope-intercept form.
// 2. Calculate the line intercept by substituting the point into line pattern.
//////////////////////////////////////////////////////////////////////
string strategy1 = "Substitute slope property into the line slope-intercept form.";
var m = new Var("m");
var k = new Var("k");
var x = new Var("x");
var y = new Var("y");
var term = new Term(Expression.Multiply, new List<object>() {m, x});
var term1 = new Term(Expression.Add, new List<object>() {term, k});
var eqPattern = new Equation(y, term1);
var term2 = new Term(Expression.Multiply, new List<object>() {goal.Rhs,x});
var term3 = new Term(Expression.Add, new List<object>() {term2, k});
var eqInternal1 = new Equation(y, term3);
var appliedRule1 = SubstitutionRule.ApplySubstitute(eqPattern, goal);
var ts0 = new TraceStep(eqPattern, eqInternal1, SubstitutionRule.SubstituteKC(), strategy1, appliedRule1);
ls._innerLoop.Add(ts0);
//////////////////////////////////////////////////////////////////////
var point = ps.Shape as Point;
Debug.Assert(point != null);
string strategy2 = "Calculate the line intercept by substituting the point into line pattern.";
var term4 = new Term(Expression.Multiply, new List<object>() { goal.Rhs, point.XCoordinate});
var term5 = new Term(Expression.Add, new List<object>() {term4, k});
var eqinternal2 = new Equation(point.YCoordinate, term5);
object obj;
bool result = eqinternal2.IsEqGoal(out obj);
var eqGoal = obj as EqGoal;
Debug.Assert(eqGoal != null);
var gTuple = eqGoal.Traces[0];
var gLst = gTuple.Item2 as List<TraceStep>;
Debug.Assert(gLst != null);
ls._innerLoop.AddRange(gLst);
var appliedRule2 = SubstitutionRule.ApplySubstitute(eqInternal1, ps);
var ts = new TraceStep(eqInternal1, ls, SubstitutionRule.SubstituteKC(), strategy2, appliedRule2);
ls._innerLoop.Add(ts);
ls.GenerateATrace(strategy);
}
public static void FromPointPointToLine(PointSymbol ps1, PointSymbol ps2, LineSymbol ls)
{
var m = new Var("m");
var k = new Var("k");
var x = new Var("x");
var y = new Var("y");
var term = new Term(Expression.Multiply, new List<object>() { m, x });
var term1 = new Term(Expression.Add, new List<object>() { term, k });
var eqPattern = new Equation(y, term1);
var term2 = new Term(Expression.Multiply, new List<object>() {m, ps1.SymXCoordinate});
var term22 = new Term(Expression.Add, new List<object>() {term2, k});
var eqPattern1 = new Equation(ps1.SymYCoordinate, term22);
var term3 = new Term(Expression.Multiply, new List<object>() {m, ps2.SymXCoordinate});
var term33 = new Term(Expression.Add, new List<object>() { term3, k });
var eqPattern2 = new Equation(ps2.SymYCoordinate, term33);
string strategy = "Generate a line by substituting two given points into the line slope-intercept form y=mx+k.";
var ts0 = new TraceStep(eqPattern, eqPattern1, SubstitutionRule.SubstituteKC(),SubstitutionRule.SubstitutionStrategy,
SubstitutionRule.ApplySubstitute(eqPattern, ps1));
var ts1 = new TraceStep(eqPattern, eqPattern2, SubstitutionRule.SubstituteKC(),SubstitutionRule.SubstitutionStrategy,
SubstitutionRule.ApplySubstitute(eqPattern, ps2));
string kc = GeometryScaffold.KC_LineSlopeForm;
var ts2 = new TraceStep(null, ls, kc, "calculate m and k through the above two linear equations.",
"calculate m and k through linear equation and retrieve y=mx+k line form.");
ls._innerLoop.Add(ts0);
ls._innerLoop.Add(ts1);
ls._innerLoop.Add(ts2);
ls.GenerateATrace(strategy);
}
/*
* given m=2, k=3, y=3x+2
*/
public static void FromSlopeInterceptToLineSlopeIntercept(EqGoal slopeGoal, EqGoal interceptGoal, LineSymbol ls)
{
//1. Substitute slope and intercept properties into the line slope-intercept form y=mx+b.
////////////////////////////////////////////////////////
var ts0 = new TraceStep(null, slopeGoal, GeometryScaffold.KC_LineSlopeForm, PlottingRule.PlottingStrategy, PlottingRule.Plot(slopeGoal));
var ts1 = new TraceStep(null, interceptGoal, GeometryScaffold.KC_LineInterceptForm, PlottingRule.PlottingStrategy, PlottingRule.Plot(interceptGoal));
ls._innerLoop.Add(ts0);
var abstractLs = new Line(ls.Shape.Label, slopeGoal.Lhs, interceptGoal.Lhs);
var abstractLss = new LineSymbol(abstractLs);
var internalLs = new Line(ls.Shape.Label, ls.SymSlope, interceptGoal.Lhs);
var internalLss = new LineSymbol(internalLs);
var traceStep1 = new TraceStep(abstractLss, internalLss, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy, SubstitutionRule.ApplySubstitute(abstractLss, slopeGoal));
ls._innerLoop.Add(traceStep1);
ls._innerLoop.Add(ts1);
/*
var rule = "Substitute given property to line slope-intercept form.";
var appliedRule1 = string.Format("Substitute slope={0} into y=mx+b", ls.SymSlope);
var appliedRule2= string.Format("Substitute intercept={0} into y=mx+b", ls.SymIntercept);*/
var traceStep2 = new TraceStep(internalLss, ls, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy, SubstitutionRule.ApplySubstitute(internalLss, interceptGoal));
ls._innerLoop.Add(traceStep2);
string strategy = "Substitute slope and intercept properties into the line slope-intercept form y = mx + b.";
ls.GenerateATrace(strategy);
}
public static void LineSlopeIntercepToGraph(LineSymbol ls)
{
string strategy = strategy_graphing;
//Plotting shapes
//1. plotting Y-Intercept
//2. plotting X-Intercept
//3. plotting the line
//////////////////////////////////////////////////////////////
// Step 1:
var pt = new Point(0, ls.SymIntercept);
var ptSym = new PointSymbol(pt);
var ts0 = new TraceStep(null, ptSym, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym));
ls._innerLoop.Add(ts0);
//////////////////////////////////////////////////////////////
// Step 2:
var line = ls.Shape as Line;
Debug.Assert(line != null);
Equation eq;
if (line.B == null)
{
}
else
{
var x = new Var("x");
//step 2.1
var term = new Term(Expression.Multiply, new List<object>() { line.Slope, x });
var term1 = new Term(Expression.Add, new List<object>() { term, line.Intercept });
eq = new Equation(term1, 0);
object obj;
EqGoal gGoal = null;
bool result = eq.IsEqGoal(out obj);
if (result)
{
gGoal = obj as EqGoal;
}
if (gGoal != null)
{
double dX;
LogicSharp.IsDouble(gGoal.Rhs, out dX);
var pt1 = new Point(dX, 0);
var ptSym1 = new PointSymbol(pt1);
var ts1 = new TraceStep(null, ptSym1, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym1));
ls._innerLoop.Add(ts1);
}
}
/////////////////////////////////////////////////////////////////
const string step1MetaRule = "Given the line slope-intercept form y=mx+b, plot the line by passing points (0,b) and (-b/m,0).";
string step1AppliedRule = String.Format("Plotting the line passing through (0,{0}) and ({1},0) ", ls.SymIntercept, ls.SymC);
//var ts = new TraceStep(null, ls.SlopeInterceptForm, step1MetaRule, step1AppliedRule);
string kc = GeometryScaffold.KC_LineGraphing;
var ts = new TraceStep(null, ls, kc, step1MetaRule, step1AppliedRule);
ls._innerLoop.Add(ts);
//////////////////////////////////////////////////////////////////
ls.GenerateATrace(strategy);
}
public static void FromLineSlopeIntercetpToLineGeneralForm(LineSymbol ls)
{
var line = ls.Shape as Line;
Debug.Assert(line != null);
Debug.Assert(ls.OutputType == LineType.GeneralForm);
string step1metaRule = "Given the line slope-intercept from y=mx+b, move y term to the right side of equation.";
string step1AppliedRule = String.Format("Move y to the right side of equation");
string kc = GeometryScaffold.KC_LinePatternsTransform;
var ts = new TraceStep(ls.SlopeInterceptForm, ls.GeneralForm, kc, step1metaRule, step1AppliedRule);
string strategy = strategy_si_general;
ls._innerLoop.Add(ts);
ls.GenerateATrace(strategy);
}
