/// <summary>
/// Converts the symbolic variable into a state of separate simle terms with different denominators
/// </summary>
/// <param name="sv"></param>
/// <returns></returns>
public static SymbolicVariable[] SeparateWithDifferentDenominators(SymbolicVariable sv)
{
List <SymbolicVariable> SeparatedVariabls = new List <SymbolicVariable>();
for (int i = 0; i < sv.TermsCount; i++)
{
SymbolicVariable ordered;
SymbolicVariable.ReOrderNegativeSymbols(sv[i], out ordered);
SeparatedVariabls.Add(ordered);
}
foreach (var eTerm in sv.ExtraTerms)
{
for (int i = 0; i < eTerm.Term.TermsCount; i++)
{
SymbolicVariable ordered;
SymbolicVariable.ReOrderNegativeSymbols(eTerm.Term[i], out ordered);
if (eTerm.Negative)
{
ordered = SymbolicVariable.Multiply(SymbolicVariable.NegativeOne, ordered);
}
SeparatedVariabls.Add(ordered);
}
}
return(SeparatedVariabls.ToArray());
}
/// <summary>
/// Raise to specified power.
/// </summary>
/// <param name="power"></param>
/// <returns></returns>
public SymbolicVariable Power(int power)
{
if (power == 0)
{
return(SymbolicVariable._One);
}
SymbolicVariable total = this.Clone();
int pw = Math.Abs(power);
while (pw > 1)
{
if (this.IsFunction && this.FunctionName.Equals("Sqrt", StringComparison.OrdinalIgnoreCase))
{
//
var parameterpower = power * 0.5;
total = this.FunctionParameters[0].Power(parameterpower);
pw = 0; // to end the loop
}
else
{
total = SymbolicVariable.Multiply(total, this);
pw--;
}
}
if (power < 0)
{
total = SymbolicVariable.Divide(SymbolicVariable._One, total);
}
return(total);
}
/// <summary>
/// Substitute variable with another variable
/// </summary>
/// <param name="variable"></param>
/// <param name="value"></param>
/// <returns></returns>
public SymbolicVariable Substitute(string variable, SymbolicVariable value)
{
var s = this.ToString();
var ss = s.Replace(variable, "(" + value.ToString() + ")");
return(Parse(ss));
}
/// <summary>
/// Solve for the variable and gets the whole expression for that variable
/// </summary>
/// <param name="variable"></param>
/// <returns></returns>
public SymbolicVariable Solve(string variable)
{
// "5*t1+3/t2" ==> 5*t1 = -3/t2 ==> t1 = (-3/t2)*5
if (_ExtraTerms != null && _ExtraTerms.Count > 0)
{
throw new SymbolicException("can't solve expression with extra terms that hold terms with different denominator");
}
// Algorithm:
// search for the term with variable in it
// don't accept more than one term
// don't accept terms with power other than 1
// solve
SymbolicVariable ExtractedTerm = null;
SymbolicVariable RestTerm = this.Clone();
// extract the needed term
if (this.Symbol.Equals(variable, StringComparison.OrdinalIgnoreCase))
{
ExtractedTerm = this.Clone();
ExtractedTerm._AddedTerms = null;
RestTerm.Coeffecient = 0;
AdjustZeroCoeffecientTerms(ref RestTerm); // this will adjust the internal structure of symbolic variabl
}
else
{
foreach (var t in RestTerm.AddedTerms)
{
if (t.Value.Symbol.Equals(variable, StringComparison.OrdinalIgnoreCase))
{
ExtractedTerm = t.Value.Clone();
t.Value.Coeffecient = 0;
break;
}
}
AdjustZeroCoeffecientTerms(ref RestTerm);
}
if (ExtractedTerm == null)
{
throw new SymbolicException("the variable (" + variable + ") of solving not found");
}
if (ExtractedTerm.SymbolPower != 1)
{
throw new SymbolicException("Variables with higher powers is not solvable for now");
}
RestTerm = RestTerm * SymbolicVariable.NegativeOne; // this will transfer the rest value from left to right
// now we have extracted term as 3*x [Extracted Term] = 5*y [Rest Term]
SymbolicVariable result = RestTerm / ExtractedTerm.Coeffecient;
return(result);
}
public static SymbolicVariable Abs(this SymbolicVariable sv)
{
if (sv.IsNegative)
{
return(sv * SymbolicVariable.NegativeOne);
}
else
{
return(sv.Clone());
}
}
/// <summary>
/// Multiply hybrid variable by symbolic variable, and returns the value into symbolic variable.
/// because hybrid variable is either number of symbolic.
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns><see cref="SymbolicVariable"/></returns>
internal static SymbolicVariable Multiply(HybridVariable a, SymbolicVariable b)
{
if (a.SymbolicVariable != null)
{
return(Multiply(a.SymbolicVariable, b));
}
else
{
return(Multiply(new SymbolicVariable(a.NumericalVariable.ToString(CultureInfo.InvariantCulture)), b));
}
}
/// <summary>
/// Trys to simplify the expression with trigonemtric rules.
/// </summary>
/// <param name="sv"></param>
/// <returns></returns>
public static SymbolicVariable TrigSimplify(SymbolicVariable sv)
{
if (sv.ExtraTerms.Count > 0)
{
return(sv.Clone()); //prevent simplification in case of extra terms
}
var factorized = FactorWithCommonFactor(sv);
SymbolicVariable total = SymbolicVariable.Zero.Clone();
// facorized expressions contain their terms in the multiplied symbols
for (int i = 0; i < factorized.TermsCount; i++)
{
// go through each term
var term = factorized[i];
for (int fui = 0; fui < term.FusedSymbols.Count; fui++)
{
var ss = term.GetFusedTerm(fui);
var sp = ss;
if (!ss.IsOneTerm)
{
if (ss.CanBeFactored())
{
sp = TrigSimplify(ss);
}
else
{
sp = PartialTrigSimplify(ss);
}
if (sp.IsOne) // if equals 1 then remove it
{
// remove this fused symbol from the structure
term._FusedSymbols.Remove(term.GetFusedKey(fui));
}
else
{
// replace with the new value in the fused symbols.
term._FusedSymbols.Add(sp.ToString(), term._FusedSymbols[term.GetFusedKey(fui)]);
term._FusedSymbols.Remove(term.GetFusedKey(fui));
}
}
}
total = total + term;
}
// so begin in the factorized
var tsimp = PartialTrigSimplify(total);
return(tsimp);
}
/// <summary>
/// Reorders the negative symbols and gets them into DividedTerm object.
/// for example 4*x^-2*y^6*u^-4 will get u^4*x^2 and 5/a will get a
/// works only in single term doesn't include extra terms
/// </summary>
/// <param name="sVariable">source symbolic variable (processed in one term only)</param>
/// <param name="reOrderedVariable"></param>
/// <returns></returns>
public static SymbolicVariable ReOrderNegativeSymbols(SymbolicVariable sVariable, out SymbolicVariable reOrderedVariable)
{
SymbolicVariable denominator = SymbolicVariable.One.Clone();
reOrderedVariable = sVariable.Clone();
if (sVariable.SymbolPower < 0)
{
// transfer symbols into the divided term
denominator.SymbolPower = Math.Abs(sVariable.SymbolPower);
denominator.Symbol = sVariable.Symbol;
if (sVariable._SymbolPowerTerm != null) //include the symbol power term also but invert its sign
{
denominator._SymbolPowerTerm = SymbolicVariable.Multiply(SymbolicVariable.NegativeOne, sVariable._SymbolPowerTerm);
}
// fix the reordered variable by removing this symbol information because it will appear later
// in the divided term.
reOrderedVariable.SymbolPower = 0;
reOrderedVariable._SymbolPowerTerm = null;
reOrderedVariable.Symbol = string.Empty;
}
foreach (var fs in sVariable.FusedSymbols)
{
if (fs.Value.IsNegative)
{
var siv = new SymbolicVariable(fs.Key);
if (fs.Value.SymbolicVariable != null)
{
siv._SymbolPowerTerm =
SymbolicVariable.Multiply(SymbolicVariable.NegativeOne, fs.Value.SymbolicVariable);
}
else
{
siv.SymbolPower = Math.Abs(fs.Value.NumericalVariable);
}
denominator = SymbolicVariable.Multiply(denominator, siv); // accumulate negative power symbols here
// remove this fused symbol from reOrdered variable
reOrderedVariable.FusedSymbols.Remove(fs.Key);
}
}
reOrderedVariable.DividedTerm = SymbolicVariable.Multiply(reOrderedVariable.DividedTerm, denominator);
return(denominator);
}
/// <summary>
/// Converts the symbolic variable into a state of separate simple terms with different denominators
/// </summary>
/// <param name="sv"></param>
/// <returns></returns>
public static SymbolicVariable[] SeparateWithDifferentDenominators(SymbolicVariable sv)
{
List <SymbolicVariable> SeparatedVariabls = new List <SymbolicVariable>();
var svclone = sv.Clone(true);
var divisor = svclone._DividedTerm;
svclone._DividedTerm = SymbolicVariable.One;
for (int i = 0; i < svclone.TermsCount; i++)
{
SymbolicVariable ordered;
SymbolicVariable.ReOrderNegativeSymbols(svclone[i], out ordered);
ordered._DividedTerm = SymbolicVariable.Multiply(divisor, ordered._DividedTerm);
SeparatedVariabls.Add(ordered);
}
var extraTerms = sv.ExtraTerms;
foreach (var eTerm in extraTerms)
{
/*
* for (int i = 0; i < eTerm.Term.TermsCount; i++)
* {
* SymbolicVariable ordered;
* SymbolicVariable.ReOrderNegativeSymbols(eTerm.Term[i], out ordered);
*
* if (eTerm.Negative)
* {
* ordered = SymbolicVariable.Multiply(SymbolicVariable.NegativeOne, ordered);
* }
*
* SeparatedVariabls.Add(ordered);
* }
*/
SeparatedVariabls.AddRange(SeparateWithDifferentDenominators(eTerm.Term));
}
return(SeparatedVariabls.ToArray());
}
public SymbolicVariable Power(double power)
{
if (Math.Floor(power) == power)
{
return(Power((int)power));
}
SymbolicVariable p = this.Clone();
if (p.IsOneTerm)
{
// raise the coeffecient and symbol
if (!string.IsNullOrEmpty(p.Symbol))
{
p.SymbolPower = power;
}
p.Coeffecient = Math.Pow(p.Coeffecient, power);
}
else
{
if (power == 0.5)
{
// return sqrt function of the multi term
return(new SymbolicVariable("Sqrt(" + p.ToString() + ")"));
}
else if (power > 0 && power < 1)
{
// I don't have solution for this now
throw new SymbolicException("I don't have solution for this type of power " + p.ToString() + "^ (" + power.ToString() + ")");
}
else
{
// multi term that we can't raise it to the double
return(p.RaiseToSymbolicPower(new SymbolicVariable(power.ToString())));
}
}
return(p);
}
/// <summary>
/// Works on expressions of extra terms to get an expression unified in denominator
/// </summary>
/// <param name="sv"></param>
/// <returns></returns>
public static SymbolicVariable UnifyDenominators(SymbolicVariable sv)
{
var terms = SeparateWithDifferentDenominators(sv);
SymbolicVariable OrderedVariable = SymbolicVariable.Zero;
foreach (var exTerm in terms)
{
var proTerm = exTerm.Clone();
if (exTerm._DividedTerm.ExtraTerms.Count > 0)
{
// the denominator needs to be unified also
var unif = UnifyDenominators(exTerm._DividedTerm);
proTerm._DividedTerm = unif.Numerator;
proTerm = SymbolicVariable.Multiply(proTerm, unif.Denominator);
}
// multipy the OrderedVariable divided term in the target extra term
var exNumerator = SymbolicVariable.Multiply(OrderedVariable.DividedTerm, proTerm.Numerator);
var exDenominator = SymbolicVariable.Multiply(OrderedVariable.DividedTerm, proTerm.Denominator);
var OrdNumerator = SymbolicVariable.Multiply(proTerm.Denominator, OrderedVariable.Numerator);
OrderedVariable = SymbolicVariable.Add(OrdNumerator, exNumerator);
OrderedVariable._DividedTerm = exDenominator;
}
return(OrderedVariable);
}
/// <summary>
/// Works on expressions of extra terms to get an expression unified in denominator
/// </summary>
/// <param name="sv"></param>
/// <returns></returns>
public static SymbolicVariable UnifyDenominators(SymbolicVariable sv)
{
var terms = SeparateWithDifferentDenominators(sv);
SymbolicVariable OrderedVariable = SymbolicVariable.Zero;
foreach (var exTerm in terms)
{
// multipy the OrderedVariable divided term in the target extra term
var exNumerator = SymbolicVariable.Multiply(OrderedVariable.DividedTerm, exTerm.Numerator);
var exDenominator = SymbolicVariable.Multiply(OrderedVariable.DividedTerm, exTerm.Denominator);
var OrdNumerator = SymbolicVariable.Multiply(exTerm.Denominator, OrderedVariable.Numerator);
OrderedVariable = SymbolicVariable.Add(OrdNumerator, exNumerator);
OrderedVariable._DividedTerm = exDenominator;
}
return(OrderedVariable);
}
public static SymbolicVariable Simplify(SymbolicVariable sv)
{
return(UnifyDenominators(sv));
}
/// <summary>
/// Simplify Trigonometric Functions
/// </summary>
/// <param name="sv"></param>
public static SymbolicVariable PartialTrigSimplify(SymbolicVariable sv)
{
// please refer to TrigSimplification.txt for the algorithm
Dictionary <string, ParameterSquareTrig> PSTS = new Dictionary <string, ParameterSquareTrig>();
Func <string, ParameterSquareTrig> PST = (nm) =>
{
ParameterSquareTrig p;
if (!PSTS.TryGetValue(nm, out p))
{
p = new ParameterSquareTrig {
Parameter = nm
};
PSTS.Add(nm, p);
return(p);
}
else
{
return(p);
}
};
Action <SymbolicVariable> Loop2 = (termPart) =>
{
// first test the term then test its fused variables
var TermsToBeTested = termPart.GetMultipliedTerms();
foreach (var term in TermsToBeTested)
{
if (term.IsFunction && term._SymbolPower == 2 && term.RawFunctionParameters.Length == 1)
{
if (term.FunctionName.Equals("Sin", StringComparison.OrdinalIgnoreCase))
{
PST(term.RawFunctionParameters[0]).Sin_2_Count++;
}
else if (term.FunctionName.Equals("Cos", StringComparison.OrdinalIgnoreCase))
{
PST(term.RawFunctionParameters[0]).Cos_2_Count++;
}
else
{
// not Trigonometric function
}
}
}
};
Loop2(sv);
if (sv._AddedTerms != null)
{
foreach (var term in sv._AddedTerms.Values)
{
Loop2(term);
}
}
// coduct the third operation .. final calulcation
SymbolicVariable SimplifiedResult = sv.Clone();
foreach (var pst in PSTS.Values)
{
while (pst.Cos_2_Count > 0 && pst.Sin_2_Count > 0)
{
var tttt = SymbolicVariable.Add(SimplifiedResult, pst.NegativeSimplifyValue);
SimplifiedResult = tttt;
pst.Cos_2_Count--;
pst.Sin_2_Count--;
}
}
return(SimplifiedResult);
}
private static SymbolicVariable ArithExpression(SymbolicExpressionOperator eop, out short skip)
{
SymbolicVariable left = eop.SymbolicExpression;
string op = eop.Operation;
SymbolicVariable right = eop.Next.SymbolicExpression;
skip = 1;
if (op == "|")
{
int p = (int)right.SymbolPower;
string rp = right.Symbol;
SymbolicVariable v = left;
while (p > 0)
{
v = v.Differentiate(rp);
p--;
}
return(v);
}
if (op == "^")
{
// This will be right associative operator
// which means if more than one power appeared like this 3^2^4 then it will be processed like this 3^(2^4)
if (eop.Next.Next != null)
{
if (eop.Next.Operation == "^")
{
short iskip;
var powerResult = SymbolicVariable.SymbolicPower(
left
, ArithExpression(eop.Next, out iskip)
);
skip += iskip;
return(powerResult);
}
else
{
return(SymbolicVariable.SymbolicPower(left, right));
}
}
else
{
return(SymbolicVariable.SymbolicPower(left, right));
}
}
if (op == "*")
{
return(SymbolicVariable.Multiply(left, right));
}
if (op == "/")
{
return(SymbolicVariable.Divide(left, right));
}
if (op == "+")
{
return(SymbolicVariable.Add(left, right));
}
if (op == "-")
{
return(SymbolicVariable.Subtract(left, right));
}
throw new NotSupportedException("Not Supported Operator '" + op + "'");
}
public static SymbolicVariable operator -(SymbolicVariable a, SymbolicVariable b)
{
return(SymbolicVariable.Subtract(a, b));
}
/// <summary>
/// Factor the expression.
/// </summary>
/// <param name="sv"></param>
/// <returns></returns>
public static SymbolicVariable FactorWithCommonFactor(SymbolicVariable sv)
{
var map = sv.GetCommonFactorsMap();
// get all keys sorted by number of elements
var keys = (from mk in map
orderby mk.Value.Count descending
where mk.Key.Equals(One) == false && mk.Value.Count > 1 && mk.Key.IsCoeffecientOnly == false
select mk.Key).ToArray();
if (keys.Length == 0)
{
return(sv.Clone());
}
// ignore the 1 key
// imagine a*x+a*y result is a*(x+y)
SymbolicVariable result = SymbolicVariable.One.Clone();
var term_key = keys[0]; // the biggest values count as shown above in the query statement
var term_indices = map[term_key];
List <SymbolicVariable> Common_Factors_Keys = new List <SymbolicVariable>();
Common_Factors_Keys.Add(term_key);
// find the other keys that has the same indices like this key
for (int i = 1; i < keys.Length; i++)
{
var target_indices = map[keys[i]];
if (target_indices.Count == term_indices.Count)
{
// compare indices toghether
foreach (var idc in term_indices)
{
if (!target_indices.Contains(idc))
{
continue;
}
}
// reaching this line indicates that the two arrays contains the same indices
// so we save this key as another common factor for the expression
Common_Factors_Keys.Add(keys[i]);
}
if (target_indices.Count < term_indices.Count)
{
break; // the array is ordered from higher count to low count so there is no point in comparing more results .. break the loop
}
}
//Common_Factors_Keys now contains the factors that I will work on it.
SymbolicVariable common_multipliers = SymbolicVariable.Zero.Clone();
SymbolicVariable rest_multipliers = SymbolicVariable.Zero.Clone();
for (int i = 0; i < sv.TermsCount; i++)
{
if (term_indices.Contains(i))
{
// remove the common factor and add the result into the common_multipliers
var term = sv[i].Clone();
foreach (SymbolicVariable ke in Common_Factors_Keys)
{
term = SymbolicVariable.Divide(term, ke); // divide by factor to remove it from the term.
/*
* if (term.Symbol == ke.Symbol)
* {
* term.SymbolPower = 0;
* AdjustZeroPowerTerms(term);
* }
* else
* {
* // remove from the fused symbols
* term._FusedSymbols.Remove(ke.ToString());
* }
*/
}
common_multipliers += term;
}
else
{
// doesn't contain the variable we want to remove so we store the term into the rest of the expressions to be added at the end of this procedure
rest_multipliers += sv[i].Clone();
}
}
// at last alter the symbolic variable instant so that it contains the new shape
foreach (var ke in Common_Factors_Keys)
{
result = result * ke;
}
result.FusedSymbols.Add(common_multipliers.ToString(), new HybridVariable {
NumericalVariable = 1.0
});
result = result + rest_multipliers;
return(result);
}
/// <summary>
/// Subtracts symbolic variable b from symbolic variable a
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static SymbolicVariable Subtract(SymbolicVariable a, SymbolicVariable b)
{
if (a == null || b == null)
{
return(null);
}
if (!a.DividedTerm.Equals(b.DividedTerm))
{
SymbolicVariable a_b = a.Clone();
bool econsumed = false;
if (a_b.ExtraTerms.Count > 0)
{
// find if in extra terms there is an equality of b into it
for (int iet = 0; iet < a_b.ExtraTerms.Count; iet++)
{
if (a_b.ExtraTerms[iet].Term.DividedTerm.Equals(b.DividedTerm))
{
a_b.ExtraTerms[iet].Term = Subtract(a_b.ExtraTerms[iet].Term, b);
econsumed = true;
break;
}
}
}
if (!econsumed)
{
// add in the extra terms
var negative_b = b.Clone();
a_b.ExtraTerms.Add(new ExtraTerm {
Term = negative_b, Negative = true
});
}
AdjustZeroCoeffecientTerms(ref a_b);
return(a_b);
}
SymbolicVariable subB = b.Clone();
int sub = -1;
SymbolicVariable sv = a.Clone();
NewPart:
bool consumed = false;
if (a.BaseEquals(subB))
{
if (a.CoeffecientPowerTerm == null && subB.CoeffecientPowerTerm == null)
{
sv.Coeffecient = a.Coeffecient - subB.Coeffecient;
consumed = true;
}
else if (a.CoeffecientPowerTerm != null && subB.CoeffecientPowerTerm != null)
{
if (a.CoeffecientPowerTerm.Equals(subB.CoeffecientPowerTerm))
{
var cr = a.Coeffecient - subB.Coeffecient;
if (cr == 0)
{
sv.Coeffecient = cr;
consumed = true;
}
}
}
else
{
// nothing
}
}
//so the equality doesn't exits or this instance have other terms also
// there are two cases now
// 1- the symbolic can be added to one of the existing terms (which will be perfect)
// 2- there are no compatible term so we have to add it to the addedvariables of this instance.
foreach (var av in a.AddedTerms)
{
if (av.Value.BaseEquals(subB))
{
var iv = a.AddedTerms[av.Key].Clone();
if (iv.CoeffecientPowerTerm == null && subB.CoeffecientPowerTerm == null)
{
iv.Coeffecient = iv.Coeffecient - subB.Coeffecient;
sv.AddedTerms[av.Key] = iv;
consumed = true;
}
else if (iv.CoeffecientPowerTerm != null && subB.CoeffecientPowerTerm != null)
{
if (iv.CoeffecientPowerTerm.Equals(subB.CoeffecientPowerTerm))
{
var cr = iv.Coeffecient - subB.Coeffecient;
if (cr == 0)
{
iv.Coeffecient = cr;
sv.AddedTerms[av.Key] = iv;
consumed = true;
}
}
}
else
{
}
}
}
if (!consumed)
{
// add it to the positive variables.
SymbolicVariable pv;
sv.AddedTerms.TryGetValue(subB.WholeValueBaseKey, out pv);
if (pv == null)
{
pv = subB.Clone();
pv.Coeffecient *= -1;
var SubTerms = pv._AddedTerms; // store them for later use.
pv._AddedTerms = null;
pv.DividedTerm = One;
sv.AddedTerms.Add(pv.WholeValueBaseKey, pv);
if (SubTerms != null)
{
//then add the value added terms if exist
foreach (var at in pv.AddedTerms)
{
at.Value.Coeffecient *= -1;
sv.AddedTerms.Add(at.Value.WholeValueBaseKey, at.Value);
}
}
}
else
{
//exist before add it to this variable.
sv.AddedTerms[subB.WholeValueBaseKey] = Subtract(sv.AddedTerms[subB.WholeValueBaseKey], subB);
}
}
if (b.AddedTerms.Count > 0)
{
sub = sub + 1; //increase
if (sub < b.AddedTerms.Count)
{
// there are still terms to be consumed
// this new term is a sub term in b and will be added to all terms of a.
subB = b.AddedTerms.ElementAt(sub).Value;
goto NewPart;
}
}
// reaching here indicates that we didn't sum up the value to any of the target extra terms
// so we need to include extra terms here
if (b._ExtraTerms != null && b._ExtraTerms.Count > 0)
{
// add extra terms of b into sv
foreach (var eb in b._ExtraTerms)
{
var eeb = eb.Clone();
if (eeb.Negative)
{
eeb.Negative = false; // -- == +
}
sv.ExtraTerms.Add(eeb);
}
}
AdjustSpecialFunctions(ref sv);
AdjustZeroPowerTerms(sv);
AdjustZeroCoeffecientTerms(ref sv);
return(sv);
}
/// <summary>
/// Parse expression of variables and make SymbolicVariable
/// </summary>
/// <param name="expr"></param>
/// <returns></returns>
public static SymbolicVariable Parse(string expression)
{
var r = from zr in expression.Split(new string[] { ":=" }, StringSplitOptions.RemoveEmptyEntries)
where string.IsNullOrWhiteSpace(zr) == false
select zr.Trim();
string[] rr = r.ToArray();
string expr = string.Empty;
if (rr.Length == 0)
{
return(null);
}
if (rr.Length > 1)
{
//function
expr = rr[1];
}
else
{
expr = rr[0];
}
char[] separators = { '^', '*', '/', '+', '-', '(', '|' };
char[] seps = { '^', '*', '/', '+', '-', '|' };
expr = expr.Replace(" ", "");
//if (expression.StartsWith("-") ||expression.StartsWith("+")) expression = expression.Insert(1,"1*");
// simple parsing
// obeys the rules of priorities
// Priorities
// ^ Power
// * multiplication
// / division
// + Addition
// - Subtraction
bool NextGroupIsNegativeSign = false;
// Tokenization is done by separating with operators
SymbolicExpressionOperator Root = new SymbolicExpressionOperator();
SymbolicExpressionOperator ep = Root;
StringBuilder TokenBuilder = new StringBuilder();
Stack <int> PLevels = new Stack <int>();
bool Inner = false;
bool FunctionContext = false;
for (int ix = 0; ix < expr.Length; ix++)
{
if (PLevels.Count == 0)
{
// include the normal parsing when we are not in parenthesis group
if (separators.Contains(expr[ix]))
{
if ((expr[ix] == '-' || expr[ix] == '+') && ix == 0)
{
if (expr[ix] == '-')
{
// in case of -x for example ..this will converted into operations
// of -1 * x
ep.SymbolicExpression = SymbolicVariable.NegativeOne;
ep.Operation = "*";
ep.Next = new SymbolicExpressionOperator();
ep = ep.Next; // advance the reference to the next node to make the linked list.
TokenBuilder = new StringBuilder();
}
else
{
// append the normal token
TokenBuilder.Append(expr[ix]);
}
}
else if (ix > 1 &&
char.ToUpper(expr[ix - 1]) == 'E' && char.IsDigit(expr[ix - 2]) &&
(expr[ix] == '-' || expr[ix] == '+'))
{
// case of 3e+2 4e-2 all cases with e in it.
TokenBuilder.Append(expr[ix]);
}
else if (expr[ix] == '(')
{
PLevels.Push(1);
var bb = ix > 0 ? separators.Contains(expr[ix - 1]) : true;
if (!bb)
{
//the previous charachter is normal word which indicates we reached a function
FunctionContext = true;
TokenBuilder.Append(expr[ix]);
}
}
else if (
seps.Contains(expr[ix - 1]) &&
(expr[ix] == '-' || expr[ix] == '+')
)
{
if (expr[ix + 1] == '(')
{
// so this sign is glued to the next parentheisis group
TokenBuilder.Append(expr[ix]);
// now TokenBuilder contains all signs before this
// and we need to preserve the information about next group
// that it has a sign.
string signs = TokenBuilder.ToString();
int nve = signs.ToCharArray().Count(sign => sign == '-');
if ((nve % 2.0) != 0)
{
// negative sign
NextGroupIsNegativeSign = true;
}
TokenBuilder.Clear();
}
else
{
TokenBuilder.Append(expr[ix]);
}
}
else
{
// tokenize when we reach any operator or open '(' parenthesis
if (Inner)
{
ep.SymbolicExpression = Parse(TokenBuilder.ToString());
if (NextGroupIsNegativeSign)
{
ep.SymbolicExpression = SymbolicVariable.Multiply(SymbolicVariable.NegativeOne, ep.SymbolicExpression);
NextGroupIsNegativeSign = false;
}
Inner = false;
}
else
{
ep.SymbolicExpression = new SymbolicVariable(TokenBuilder.ToString());
}
TokenBuilder = new StringBuilder();
ep.Operation = expr[ix].ToString();
ep.Next = new SymbolicExpressionOperator();
ep = ep.Next; // advance the reference to the next node to make the linked list.
}
}
else
{
TokenBuilder.Append(expr[ix]);
}
}
else
{
// we are in group
if (expr[ix] == '(')
{
PLevels.Push(1);
}
if (expr[ix] == ')')
{
PLevels.Pop();
if (PLevels.Count == 0)
{
Inner = true;
if (FunctionContext)
{
TokenBuilder.Append(expr[ix]);
FunctionContext = false;
Inner = false; // because i am taking the function body as a whole in this parse pass.
// then inner parameters of the function will be parsed again
}
}
else
{
TokenBuilder.Append(expr[ix]);
}
}
else
{
TokenBuilder.Append(expr[ix]);
}
}
}
// Last pass that escaped from the loop.
if (Inner)
{
ep.SymbolicExpression = Parse(TokenBuilder.ToString());
if (NextGroupIsNegativeSign)
{
ep.SymbolicExpression = SymbolicVariable.Multiply(SymbolicVariable.NegativeOne, ep.SymbolicExpression);
NextGroupIsNegativeSign = false;
}
Inner = false;
}
else
{
ep.SymbolicExpression = new SymbolicVariable(TokenBuilder.ToString());
}
TokenBuilder = null;
string[] Group = { "^" /* Power for normal product '*' */
};
string[] SymGroup = { "|" /* Derivation operator */ };
string[] Group1 = { "*" /* normal multiplication */,
"/" /* normal division */,
"%" /* modulus */ };
string[] Group2 = { "+", "-" };
/// Operator Groups Ordered by Priorities.
string[][] OperatorGroups = { Group, SymGroup, Group1, Group2 };
foreach (var opg in OperatorGroups)
{
SymbolicExpressionOperator eop = Root;
//Pass for '[op]' and merge it but from top to child :) {forward)
while (eop.Next != null)
{
//if the operator in node found in the opg (current operator group) then execute the logic
if (opg.Count(c => c.Equals(eop.Operation, StringComparison.OrdinalIgnoreCase)) > 0)
{
short skip;
eop.SymbolicExpression = ArithExpression(eop, out skip);
//drop eop.Next
if (eop.Next.Next != null)
{
while (skip > 0)
{
eop.Operation = eop.Next.Operation;
eop.Next = eop.Next.Next;
skip--;
}
}
else
{
//no more nodes exit the loop
eop.Next = null; //last item were processed.
eop.Operation = string.Empty;
}
}
else
{
eop = eop.Next;
}
}
}
if (rr.Length > 1)
{
// there was a function defintion
var fname = rr[0];
Functions[fname] = Root.SymbolicExpression;
}
return(Root.SymbolicExpression);
}
public static SymbolicVariable operator /(int a, SymbolicVariable b)
{
var sv = new SymbolicVariable(a.ToString(CultureInfo.InvariantCulture)) / b;
return(sv);
}
public static SymbolicVariable operator +(SymbolicVariable a, SymbolicVariable b)
{
return(SymbolicVariable.Add(a, b));
}
public static SymbolicVariable Divide(SymbolicVariable a, SymbolicVariable b)
{
if (a == null || b == null)
{
return(null);
}
SymbolicVariable SourceTerm = a.Clone();
// if the divided term is more than on term
// x^2/(y-x) ==>
if (b.AddedTerms.Count > 0 || (b._ExtraTerms != null && b._ExtraTerms.Count > 0))
{
if (a.Equals(b))
{
return(new SymbolicVariable("1"));
}
//multiply divided term by this value
if (!a.IsZero)
{
SourceTerm.DividedTerm = Multiply(SourceTerm.DividedTerm, b);
return(SourceTerm);
}
else
{
return(new SymbolicVariable("0"));
}
}
SymbolicVariable TargetSubTerm = b.Clone();
TargetSubTerm._AddedTerms = null; // remove added variables to prevent its repeated calculations in second passes
TargetSubTerm._ExtraTerms = null;
// or to make sure nothing bad happens {my idiot design :S)
if (a.BaseEquals(TargetSubTerm))
{
#region symbols are equal (I mean 2*x^3 = 2*X^3)
DivideCoeffecients(ref SourceTerm, TargetSubTerm);
if (a.SymbolPowerTerm != null || TargetSubTerm.SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm = a.SymbolPowerTerm - TargetSubTerm.SymbolPowerTerm;
}
else
{
SourceTerm.SymbolPower = SourceTerm.SymbolPower - TargetSubTerm.SymbolPower;
}
//fuse the fused symbols in b into sv
foreach (var bfv in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(bfv.Key))
{
SourceTerm.FusedSymbols[bfv.Key] -= bfv.Value;
}
else
{
SourceTerm.FusedSymbols.Add(bfv.Key, bfv.Value * -1);
}
}
#endregion
}
else
{
#region Symbols are different
if (string.IsNullOrEmpty(SourceTerm.Symbol))
{
#region First Case: Source primary symbol doesn't exist
// the instance have an empty primary variable so we should add it
if (TargetSubTerm._BaseVariable != null)
{
SourceTerm._BaseVariable = TargetSubTerm._BaseVariable;
}
else
{
SourceTerm.Symbol = TargetSubTerm.Symbol;
}
SourceTerm.SymbolPower = -1 * TargetSubTerm.SymbolPower;
if (TargetSubTerm.SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm = -1 * TargetSubTerm.SymbolPowerTerm.Clone();
}
//fuse the fusedvariables in b into sv
foreach (var bfv in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(bfv.Key))
{
SourceTerm.FusedSymbols[bfv.Key] -= bfv.Value;
}
else
{
SourceTerm.FusedSymbols.Add(bfv.Key, bfv.Value * -1);
}
}
#endregion
}
else
{
if (SourceTerm.Symbol.Equals(TargetSubTerm.Symbol, StringComparison.OrdinalIgnoreCase))
{
#region Second Case: Primary symbol in both source and target exist and equal
if (SourceTerm._SymbolPowerTerm != null || TargetSubTerm._SymbolPowerTerm != null)
{
// make sure the object of symbol power term have values if they don't
if (SourceTerm._SymbolPowerTerm == null)
{
// transfer the numerical power into symbolic variable mode
SourceTerm._SymbolPowerTerm = new SymbolicVariable(SourceTerm.SymbolPower.ToString(CultureInfo.InvariantCulture));
// also revert the original symbol power into 1 for validation after this
SourceTerm.SymbolPower = 1;
}
if (TargetSubTerm._SymbolPowerTerm == null)
{
TargetSubTerm._SymbolPowerTerm = new SymbolicVariable(TargetSubTerm.SymbolPower.ToString(CultureInfo.InvariantCulture));
TargetSubTerm.SymbolPower = -1; // the target will always be dominator
}
SourceTerm._SymbolPowerTerm -= TargetSubTerm._SymbolPowerTerm;
if (SourceTerm._SymbolPowerTerm.IsCoeffecientOnly)
{
SourceTerm._SymbolPower = SourceTerm._SymbolPowerTerm.Coeffecient;
SourceTerm._SymbolPowerTerm = null; // remove it because we don't need symbolic when we reach co
}
else
{
// correct the source symbol power (because after division the power may still be positive
if (SourceTerm._SymbolPowerTerm.IsNegative)
{
SourceTerm._SymbolPower = -1;
SourceTerm._SymbolPowerTerm *= NegativeOne;
}
}
}
else
{
SourceTerm.SymbolPower -= TargetSubTerm.SymbolPower;
}
// also subtract the fused variables
foreach (var fv in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(fv.Key))
{
SourceTerm.FusedSymbols[fv.Key] -= fv.Value;
}
else
{
SourceTerm.FusedSymbols.Add(fv.Key, fv.Value * -1);
}
}
#endregion
}
else if (SourceTerm.FusedSymbols.ContainsKey(TargetSubTerm.Symbol))
{
#region Third Case: Target primary symbol exist in source fused variables
if (TargetSubTerm.SymbolPowerTerm != null)
{
SourceTerm.FusedSymbols[TargetSubTerm.Symbol] -= TargetSubTerm.SymbolPowerTerm;
}
else
{
SourceTerm.FusedSymbols[TargetSubTerm.Symbol] -= TargetSubTerm.SymbolPower;
}
// however primary symbol in source still the same so we need to add it to the value in target (if applicable)
// also
// there are still some fused variables in source that weren't altered by the target fused symbols
// go through every symbol in fused symbols and add it to the source fused symbols
foreach (var tfs in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(tfs.Key))
{
// symbol exist so accumulate it
SourceTerm._FusedSymbols[tfs.Key] -= tfs.Value;
}
else
{
// two cases here
// 1 the fused key equal the primary symbol in source
if (SourceTerm.Symbol.Equals(tfs.Key, StringComparison.OrdinalIgnoreCase))
{
if (tfs.Value.SymbolicVariable != null)
{
if (SourceTerm._SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm -= tfs.Value.SymbolicVariable;
}
else
{
// sum the value in the numerical part to the value in symbolic part
SourceTerm._SymbolPowerTerm = new SymbolicVariable(SourceTerm._SymbolPower.ToString(CultureInfo.InvariantCulture)) - tfs.Value.SymbolicVariable;
// reset the value in numerical part
SourceTerm._SymbolPower = -1;
}
if (SourceTerm._SymbolPowerTerm.IsCoeffecientOnly)
{
SourceTerm._SymbolPower = SourceTerm._SymbolPowerTerm.Coeffecient;
SourceTerm._SymbolPowerTerm = null;
}
}
else
{
SourceTerm._SymbolPower -= tfs.Value.NumericalVariable;
}
}
else
{
// 2 no matching at all which needs to add the symbol in target into the fused symbols in source.
SourceTerm.FusedSymbols.Add(tfs.Key, tfs.Value * -1);
}
}
}
#endregion
}
else
{
#region Fourth Case: Target primary symbol doesn't exist in Source Primary Symbol nor Source Fused symbols
// Add Target primary symbol to the fused symbols in source
SourceTerm.FusedSymbols.Add(
TargetSubTerm.Symbol,
new HybridVariable
{
NumericalVariable = -1 * TargetSubTerm.SymbolPower,
SymbolicVariable = TargetSubTerm.SymbolPowerTerm == null ? null : -1 * (SymbolicVariable)TargetSubTerm.SymbolPowerTerm
});
// But the primary symbol of source may exist in the target fused variables.
foreach (var fsv in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(fsv.Key))
{
SourceTerm.FusedSymbols[fsv.Key] -= fsv.Value;
}
else
{
// 1- if symbol is the same as priamry source
if (SourceTerm.Symbol.Equals(fsv.Key, StringComparison.OrdinalIgnoreCase))
{
if (fsv.Value.SymbolicVariable != null)
{
if (SourceTerm._SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm -= fsv.Value.SymbolicVariable;
}
else
{
// sum the value in the numerical part to the value in symbolic part
SourceTerm._SymbolPowerTerm =
new SymbolicVariable(SourceTerm._SymbolPower.ToString(CultureInfo.InvariantCulture)) - fsv.Value.SymbolicVariable;
// reset the value in numerical part
SourceTerm._SymbolPower = -1;
}
}
else
{
if (SourceTerm.SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm -= new SymbolicVariable(fsv.Value.ToString());
}
else
{
SourceTerm._SymbolPower -= fsv.Value.NumericalVariable;
}
}
}
else
{
SourceTerm.FusedSymbols.Add(fsv.Key, fsv.Value * -1);
}
}
}
#endregion
}
}
DivideCoeffecients(ref SourceTerm, TargetSubTerm);
#endregion
}
if (SourceTerm.AddedTerms.Count > 0)
{
Dictionary <string, SymbolicVariable> newAddedVariables = new Dictionary <string, SymbolicVariable>(StringComparer.OrdinalIgnoreCase);
foreach (var vv in SourceTerm.AddedTerms)
{
// get rid of divided term here because I already include it for the source term above
var TSubTerm = TargetSubTerm.Numerator;
var newv = Divide(vv.Value, TSubTerm);
newAddedVariables.Add(newv.WholeValueBaseKey, newv);
}
SourceTerm._AddedTerms = newAddedVariables;
}
// Extra Terms of a
if (SourceTerm.ExtraTerms.Count > 0)
{
List <ExtraTerm> newExtraTerms = new List <ExtraTerm>();
foreach (var et in SourceTerm.ExtraTerms)
{
var eterm = et.Term;
if (et.Negative)
{
eterm = Multiply(NegativeOne, eterm);
}
var newe = Divide(eterm, TargetSubTerm);
newExtraTerms.Add(new ExtraTerm {
Term = newe
});
}
SourceTerm._ExtraTerms = newExtraTerms;
}
int subIndex = 0;
SymbolicVariable total = SourceTerm;
while (subIndex < b.AddedTerms.Count)
{
// we should multiply other parts also
// then add it to the current instance
// there are still terms to be consumed
// this new term is a sub term in b and will be added to all terms of a.
TargetSubTerm = b.AddedTerms.ElementAt(subIndex).Value.Clone();
TargetSubTerm.DividedTerm = b.DividedTerm; // this line is important because I extracted this added term from a bigger term with the same divided term
// and when I did this the extracted term lost its divided term
total = total + Divide(a, TargetSubTerm);
subIndex = subIndex + 1; //increase
}
// for extra terms {terms that has different divided term}
int extraIndex = 0;
while (extraIndex < b.ExtraTerms.Count)
{
var eTerm = b.ExtraTerms[extraIndex];
TargetSubTerm = eTerm.Term;
if (eTerm.Negative)
{
TargetSubTerm = Multiply(NegativeOne, TargetSubTerm);
}
var TargetTermSubTotal = Divide(a, TargetSubTerm);
total = Add(total, TargetTermSubTotal);
extraIndex++;
}
AdjustSpecialFunctions(ref total);
AdjustZeroPowerTerms(total);
AdjustZeroCoeffecientTerms(ref total);
return(total);
}
public static SymbolicVariable operator /(SymbolicVariable a, SymbolicVariable b)
{
return(SymbolicVariable.Divide(a, b));
}
public static SymbolicVariable operator *(SymbolicVariable a, SymbolicVariable b)
{
return(SymbolicVariable.Multiply(a, b));
}
public static SymbolicVariable DiffBFunction(SymbolicVariable fv, string parameter)
{
var pa = fv.GetFunctionParameters()[0];
var ps = SymbolicVariable.Multiply(pa, pa);
var func = fv.FunctionName;
var dpa = pa.Differentiate(parameter);
if (string.Equals(func, "asin", StringComparison.OrdinalIgnoreCase))
{
//asin(x) → 1 / sqrt(1-x^2)
return(SymbolicVariable.Parse(dpa.ToString() + "/sqrt(1-(" + ps.ToString() + "))"));
}
if (string.Equals(func, "acos", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/sqrt(1-(" + ps.ToString() + "))"));
}
if (string.Equals(func, "atan", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse(dpa.ToString() + "/(" + ps.ToString() + "+1)"));
}
if (string.Equals(func, "acot", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(" + ps.ToString() + "+1)"));
}
if (string.Equals(func, "asec", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse(dpa.ToString() + "/(sqrt(1-1/(" + ps.ToString() + "))*" + ps.ToString() + ")"));
}
if (string.Equals(func, "acsc", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(sqrt(1-1/(" + ps.ToString() + "))*" + ps.ToString() + ")"));
}
#region hyperbolic functions
if (string.Equals(func, "asinh", StringComparison.OrdinalIgnoreCase))
{
//asin(x) → 1 / sqrt(x^2+1)
return(SymbolicVariable.Parse(dpa.ToString() + "/sqrt(" + ps.ToString() + "+1)"));
}
if (string.Equals(func, "acosh", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/sqrt(" + ps.ToString() + "-1)"));
}
if (string.Equals(func, "atanh", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse(dpa.ToString() + "/(1-(" + ps.ToString() + "))"));
}
if (string.Equals(func, "acoth", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(" + ps.ToString() + "-1)"));
}
if (string.Equals(func, "asech", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(sqrt(1/" + ps.ToString() + "-1)*" + ps.ToString() + ")"));
}
if (string.Equals(func, "acsch", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(sqrt(1/" + ps.ToString() + "+1)*" + ps.ToString() + ")"));
}
#endregion
throw new SymbolicException(fv.FunctionName + " differentiation not implemented yet");
}
/*
*
* Expression like a*sin(x)+a*cos(x) can be written as follow a*(sin(x)+cos(x))
* i want to know the common factor that can be multiplied in these terms
*
* so the common factor in my case is a variable key in fused terms or whatever
*
* the result should be factor and its existence in indices in the symblic variable added terms
*
* in case of previous example [a..>0,1]
*
* and the result should be the common factor as symbolic variable
* multiplied term
* terms that cannot be factorized .. to be added later
*
*/
/// <summary>
/// Returns a map of occurence of variable name in the terms of the symbolic variable expression
/// </summary>
/// <returns></returns>
public Dictionary <SymbolicVariable, List <int> > GetCommonFactorsMap()
{
// a*sin(x)+a*cos(x) + c
// loop through all terms
// begin with primary term
// see if it exists in added terms in primary or fusedsymbols
// build a dictionary with the existence of this variable
// repeat this for each fused variable
// the dictionary will increase in its data
// once we are done check the dictionary lenghs for each variable .. the one with more existence of 2 or more is what we need
// begin an analysis for the existence indices
// a => 2,5,9
// b => 2,3,4
// then a*b => 2 and etc.
List <SymbolicVariable[]> bo2bo2 = new List <SymbolicVariable[]>();
bo2bo2.Add(this.GetMultipliedTerms());
if (_AddedTerms != null)
{
foreach (var aterm in _AddedTerms)
{
bo2bo2.Add(aterm.Value.GetMultipliedTerms());
}
}
// now i have the matrix of multiplied terms.
/*
* a*sin(x)+a*cos(x) + c
*
* 0 1 2
* -------------------------
* a a c
* sin(x) cos(x)
*
*
* a in columns 0, 1
*
*/
// take each column components and compare to next columns components
Dictionary <SymbolicVariable, List <int> > CommonFactorsMap = new Dictionary <SymbolicVariable, List <int> >();
for (int column = 0; column < bo2bo2.Count; column++)
{
var components = bo2bo2[column];
for (int ix = 0; ix < components.Length; ix++)
{
// get the component.
SymbolicVariable src_component = components[ix];
// once we this component we should write its existence in the list
List <int> indices;
if (!CommonFactorsMap.TryGetValue(src_component, out indices))
{
// new creation of the list
indices = new List <int>();
indices.Add(column);
CommonFactorsMap.Add(src_component, indices);
}
for (int nxc = column + 1; nxc < bo2bo2.Count; nxc++)
{
var targetColumn = bo2bo2[nxc];
// compare it to the next column components
for (int nx_i = 0; nx_i < targetColumn.Length; nx_i++)
{
var trg_nx_compnent = targetColumn[nx_i];
if (src_component.Equals(trg_nx_compnent))
{
// bingo we found a match .. write this information
if (!indices.Contains(nxc))
{
indices.Add(nxc);
}
}
}
}
}
}
return(CommonFactorsMap);
}
/// <summary>
/// get the function derivation like sin => cos
/// </summary>
/// <param name="function"></param>
/// <param name="negative">indicates if the function returned should have negative value or not</param>
/// <returns>string of the differentiated function</returns>
public static string[] DiffFFunction(SymbolicVariable function, out bool negative)
{
string func = function.FunctionName;
if (string.Equals(func, "exp", StringComparison.OrdinalIgnoreCase))
{
negative = false;
return(new string[] { "exp" });
}
if (string.Equals(func, "sin", StringComparison.OrdinalIgnoreCase))
{
negative = false;
return(new string[] { "cos" });
}
if (string.Equals(func, "sinh", StringComparison.OrdinalIgnoreCase))
{
negative = false;
return(new string[] { "cosh" });
}
if (string.Equals(func, "cos", StringComparison.OrdinalIgnoreCase))
{
negative = true;
return(new string[] { "sin" });
}
if (string.Equals(func, "cosh", StringComparison.OrdinalIgnoreCase))
{
negative = false;
return(new string[] { "sinh" });
}
if (string.Equals(func, "tan", StringComparison.OrdinalIgnoreCase))
{
negative = false;
return(new string[] { "sec", "sec" });
}
if (string.Equals(func, "tanh", StringComparison.OrdinalIgnoreCase))
{
negative = false;
return(new string[] { "sech", "sech" });
}
if (string.Equals(func, "sec", StringComparison.OrdinalIgnoreCase))
{
negative = false;
return(new string[] { "sec", "tan" });
}
if (string.Equals(func, "sech", StringComparison.OrdinalIgnoreCase))
{
negative = true;
return(new string[] { "sech", "tanh" });
}
if (string.Equals(func, "csc", StringComparison.OrdinalIgnoreCase))
{
negative = true;
return(new string[] { "csc", "cot" });
}
if (string.Equals(func, "csch", StringComparison.OrdinalIgnoreCase))
{
negative = true;
return(new string[] { "csch", "coth" });
}
if (string.Equals(func, "cot", StringComparison.OrdinalIgnoreCase))
{
negative = true;
return(new string[] { "csc", "csc" });
}
if (string.Equals(func, "coth", StringComparison.OrdinalIgnoreCase))
{
negative = true;
return(new string[] { "csch", "csch" });
}
negative = false;
return(null);
}
/// <summary>
/// Multiply two symbolic variables
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static SymbolicVariable Multiply(SymbolicVariable a, SymbolicVariable b)
{
if (a == null || b == null)
{
return(null);
}
if (a.IsZero)
{
return(new SymbolicVariable("0"));
}
if (b.IsZero)
{
return(new SymbolicVariable("0"));
}
if (a.IsOne)
{
return(b.Clone());
}
if (b.IsOne)
{
return(a.Clone());
}
SymbolicVariable TargetSubTerm = b.Clone();
TargetSubTerm._AddedTerms = null; // remove added variables to prevent its repeated calculations in second passes
TargetSubTerm._ExtraTerms = null; // remove the extra terms also
// or to make sure nothing bad happens {my idiot design :S)
SymbolicVariable SourceTerm = a.Clone();
if (a.BaseEquals(TargetSubTerm))
{
#region Symbols are Equal (I mean 2*x^3 = 2*X^3)
MultiplyCoeffecients(ref SourceTerm, TargetSubTerm);
if (a.SymbolPowerTerm != null || TargetSubTerm.SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm = a.SymbolPowerTerm + TargetSubTerm.SymbolPowerTerm;
}
else
{
SourceTerm.SymbolPower = SourceTerm.SymbolPower + TargetSubTerm.SymbolPower;
}
//fuse the fused variables in b into sv
foreach (var bfv in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(bfv.Key))
{
SourceTerm.FusedSymbols[bfv.Key] += bfv.Value;
}
else
{
SourceTerm.FusedSymbols.Add(bfv.Key, bfv.Value);
}
}
#endregion
}
else
{
#region Symbols are Different
if (string.IsNullOrEmpty(SourceTerm.Symbol))
{
#region First Case: Source primary symbol doesn't exist
// so take the primary symbol from the target into source
// and copy the symbol power to it and symbolic power
//
// the instance have an empty primary variable so we should add it
if (TargetSubTerm._BaseVariable != null)
{
SourceTerm._BaseVariable = TargetSubTerm._BaseVariable;
}
else
{
SourceTerm.Symbol = TargetSubTerm.Symbol;
}
SourceTerm.SymbolPower = TargetSubTerm.SymbolPower;
if (TargetSubTerm.SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm = TargetSubTerm.SymbolPowerTerm.Clone();
}
else
{
SourceTerm._SymbolPowerTerm = null;
}
//fuse the fused variables in target into source
foreach (var fv in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(fv.Key))
{
SourceTerm.FusedSymbols[fv.Key] += fv.Value;
}
else
{
SourceTerm.FusedSymbols.Add(fv.Key, fv.Value);
}
}
#endregion
}
else
{
#region Testing against symbol of targetsubterm
if (SourceTerm.Symbol.Equals(TargetSubTerm.Symbol, StringComparison.OrdinalIgnoreCase))
{
#region Second Case: Primary symbol in both source and target exist and equal
// which means the difference is only in fused variables.
// test for complex power (power that contains other symbolic variable)
if (SourceTerm._SymbolPowerTerm != null || TargetSubTerm._SymbolPowerTerm != null)
{
// make sure the object of symbol power term have values if they don't
if (SourceTerm._SymbolPowerTerm == null)
{
// transfer the numerical power into symbolic variable mode
SourceTerm._SymbolPowerTerm = new SymbolicVariable(SourceTerm.SymbolPower.ToString(CultureInfo.InvariantCulture));
// also revert the original symbol power into 1 for validation after this
SourceTerm.SymbolPower = 1;
}
if (TargetSubTerm._SymbolPowerTerm == null)
{
TargetSubTerm._SymbolPowerTerm = new SymbolicVariable(TargetSubTerm.SymbolPower.ToString(CultureInfo.InvariantCulture));
TargetSubTerm.SymbolPower = 1;
}
// we used symbol power term
SourceTerm._SymbolPowerTerm += TargetSubTerm._SymbolPowerTerm;
}
else
{
SourceTerm.SymbolPower += TargetSubTerm.SymbolPower;
}
// then add the fused variables
foreach (var fv in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(fv.Key))
{
SourceTerm.FusedSymbols[fv.Key] += fv.Value;
}
else
{
SourceTerm.FusedSymbols.Add(fv.Key, fv.Value);
}
}
#endregion
}
else if (SourceTerm.FusedSymbols.ContainsKey(TargetSubTerm.Symbol))
{
#region Third Case: Target primary symbol exist in source fused variables
// fill the source symbol in fused variables from the primary symbol in Target term.
if (TargetSubTerm.SymbolPowerTerm != null)
{
SourceTerm.FusedSymbols[TargetSubTerm.Symbol] +=
new HybridVariable
{
NumericalVariable = TargetSubTerm.SymbolPower,
SymbolicVariable = TargetSubTerm.SymbolPowerTerm
}
}
;
else
{
SourceTerm.FusedSymbols[TargetSubTerm.Symbol] += TargetSubTerm.SymbolPower;
}
// however primary symbol in source still the same so we need to add it to the value in target
// (if exist in fused variables in target)
// also
// there are still some fused variables in source that weren't altered by the target fused symbols
// go through every symbol in fused symbols and add it to the source fused symbols
foreach (var tfs in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(tfs.Key))
{
// symbol exist so accumulate it
SourceTerm._FusedSymbols[tfs.Key] += tfs.Value;
}
else
{
// two cases here
// 1 the fused key equal the primary symbol in source
if (SourceTerm.Symbol.Equals(tfs.Key, StringComparison.OrdinalIgnoreCase))
{
if (tfs.Value.SymbolicVariable != null)
{
if (SourceTerm._SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm += tfs.Value.SymbolicVariable;
}
else
{
// sum the value in the numerical part to the value in symbolic part
SourceTerm._SymbolPowerTerm = new SymbolicVariable(SourceTerm._SymbolPower.ToString(CultureInfo.InvariantCulture)) + tfs.Value.SymbolicVariable;
// reset the value in numerical part
SourceTerm._SymbolPower = 1;
}
}
else
{
SourceTerm._SymbolPower += tfs.Value.NumericalVariable;
}
}
else
{
// 2 no matching at all which needs to add the symbol from target into the fused symbols in source.
SourceTerm.FusedSymbols.Add(tfs.Key, tfs.Value);
}
}
}
#endregion
}
else
{
#region Fourth Case: Target primary symbol doesn't exist in Source Primary Symbol nor Source Fused symbols
// Add Target primary symbol to the fused symbols in source
SourceTerm.FusedSymbols.Add(
TargetSubTerm.Symbol,
new HybridVariable
{
NumericalVariable = TargetSubTerm.SymbolPower,
SymbolicVariable = TargetSubTerm.SymbolPowerTerm == null ? null : TargetSubTerm.SymbolPowerTerm.Clone()
});
// But the primary symbol of source may exist in the target fused variables.
foreach (var fsv in TargetSubTerm.FusedSymbols)
{
if (SourceTerm.FusedSymbols.ContainsKey(fsv.Key))
{
SourceTerm.FusedSymbols[fsv.Key] += fsv.Value;
}
else
{
// 1- if symbol is the same as priamry source
if (SourceTerm.Symbol.Equals(fsv.Key, StringComparison.OrdinalIgnoreCase))
{
if (fsv.Value.SymbolicVariable != null)
{
if (SourceTerm._SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm += fsv.Value.SymbolicVariable;
}
else
{
// sum the value in the numerical part to the value in symbolic part
SourceTerm._SymbolPowerTerm = new SymbolicVariable(SourceTerm._SymbolPower.ToString(CultureInfo.InvariantCulture)) + fsv.Value.SymbolicVariable;
// reset the value in numerical part
SourceTerm._SymbolPower = 1;
}
}
else
{
if (SourceTerm.SymbolPowerTerm != null)
{
SourceTerm._SymbolPowerTerm += new SymbolicVariable(fsv.Value.ToString());
}
else
{
SourceTerm._SymbolPower += fsv.Value.NumericalVariable;
}
}
}
else
{
SourceTerm.FusedSymbols.Add(fsv.Key, fsv.Value);
}
}
}
#endregion
}
#endregion
}
MultiplyCoeffecients(ref SourceTerm, TargetSubTerm);
#endregion
}
if (SourceTerm.DividedTerm.IsOne)
{
SourceTerm.DividedTerm = TargetSubTerm.DividedTerm;
}
else
{
SourceTerm.DividedTerm = Multiply(SourceTerm.DividedTerm, TargetSubTerm.DividedTerm);
}
//here is a code to continue with other parts of a when multiplying them
if (SourceTerm.AddedTerms.Count > 0)
{
Dictionary <string, SymbolicVariable> newAddedVariables = new Dictionary <string, SymbolicVariable>(StringComparer.OrdinalIgnoreCase);
foreach (var vv in SourceTerm.AddedTerms)
{
// get rid of divided term here because I already include it for the source term above
var TSubTerm = TargetSubTerm.Numerator;
var newv = Multiply(vv.Value, TSubTerm);
newAddedVariables.Add(newv.WholeValueBaseKey, newv);
}
SourceTerm._AddedTerms = newAddedVariables;
}
// Extra Terms of a
if (SourceTerm.ExtraTerms.Count > 0)
{
List <ExtraTerm> newExtraTerms = new List <ExtraTerm>();
foreach (var et in SourceTerm.ExtraTerms)
{
var eterm = et.Term;
if (et.Negative)
{
eterm = Multiply(NegativeOne, eterm);
}
var newe = Multiply(eterm, TargetSubTerm);
newExtraTerms.Add(new ExtraTerm {
Term = newe
});
}
SourceTerm._ExtraTerms = newExtraTerms;
}
// now source term which is the first parameter cloned, have the new calculated value.
int subIndex = 0;
SymbolicVariable total = SourceTerm;
while (subIndex < b.AddedTerms.Count)
{
// we should multiply other parts also
// then add it to the current instance
// there are still terms to be consumed
// this new term is a sub term in b and will be added to all terms of a.
TargetSubTerm = b.AddedTerms.ElementAt(subIndex).Value.Clone();
TargetSubTerm.DividedTerm = b.DividedTerm; // this line is important because I extracted this added term from a bigger term with the same divided term
// and when I did this the extracted term lost its divided term
var TargetTermSubTotal = Multiply(a, TargetSubTerm);
total = Add(total, TargetTermSubTotal);
subIndex = subIndex + 1; //increase
}
// for extra terms {terms that has different divided term}
int extraIndex = 0;
while (extraIndex < b.ExtraTerms.Count)
{
var eTerm = b.ExtraTerms[extraIndex];
TargetSubTerm = eTerm.Term;
if (eTerm.Negative)
{
TargetSubTerm = Multiply(NegativeOne, TargetSubTerm);
}
var TargetTermSubTotal = Multiply(a, TargetSubTerm);
total = Add(total, TargetTermSubTotal);
extraIndex++;
}
AdjustSpecialFunctions(ref total);
AdjustZeroPowerTerms(total);
AdjustZeroCoeffecientTerms(ref total);
return(total);
}
/// <summary>
/// Multiply Coeffecients of second argument into first argument.
/// </summary>
/// <param name="SourceTerm"></param>
/// <param name="TargetSubTerm"></param>
private static void DivideCoeffecients(ref SymbolicVariable SourceTerm, SymbolicVariable TargetSubTerm)
{
// Note: I will try to avoid the primary coeffecient so it doesn't hold power
// and only hold coeffecient itself.
foreach (var cst in TargetSubTerm.Constants)
{
if (SourceTerm._CoeffecientPowerTerm == null && cst.ConstantPower == null)
{
SourceTerm.Coeffecient /= cst.ConstantValue;
}
// there is a coeffecient power term needs to be injected into the source
else
{
// no the coeffecient part is not empty so we will test if bases are equal
// then make use of the fusedsymbols to add our constant
double sbase = Math.Log(SourceTerm.Coeffecient, cst.ConstantValue);
if (SourceTerm.Coeffecient == cst.ConstantValue)
{
// sample: 2^x/2^y = 2^(x-y)
var cpower = cst.ConstantPower;
if (cpower == null)
{
cpower = One;
}
if (SourceTerm._CoeffecientPowerTerm == null)
{
SourceTerm._CoeffecientPowerTerm = One;
}
SourceTerm._CoeffecientPowerTerm -= cpower;
}
else if ((sbase - Math.Floor(sbase)) == 0.0 && sbase > 0) // make sure there are no
{
// then we can use the target base
// 27/3^x = 3^3/3^x = 3^(3-x)
var cpower = cst.ConstantPower;
if (cpower == null)
{
cpower = new SymbolicVariable("1");
}
SourceTerm._CoeffecientPowerTerm = SymbolicVariable.Subtract(new SymbolicVariable(sbase.ToString(CultureInfo.InvariantCulture)), cpower);
SourceTerm.Coeffecient = cst.ConstantValue;
}
else
{
// sample: 2^(x+y)*log(2)*3^y * 3^z can't be summed.
HybridVariable SameCoeffecient;
if (SourceTerm.FusedConstants.TryGetValue(cst.ConstantValue, out SameCoeffecient))
{
SameCoeffecient.SymbolicVariable -= cst.ConstantPower;
SourceTerm.FusedConstants[cst.ConstantValue] = SameCoeffecient;
}
else
{
// Add Target coefficient symbol to the fused symbols in source, with key as the coefficient number itself.
if (cst.ConstantPower != null)
{
SourceTerm.FusedConstants.Add(
cst.ConstantValue,
new HybridVariable
{
NumericalVariable = -1, // power
SymbolicVariable = Subtract(Zero, cst.ConstantPower)
});
}
else
{
// coeffecient we working with is number only
// First Attempt: to try to get the power of this number with base of available coeffecients
// if no base produced an integer power value then we add it into fused constants as it is.
if (cst.ConstantValue == 1.0)
{
continue; // ONE doesn't change anything so we bypass it
}
double?SucceededConstant = null;
double ower = 0;
foreach (var p in SourceTerm.Constants)
{
ower = Math.Log(cst.ConstantValue, p.ConstantValue);
if (ower == Math.Floor(ower))
{
SucceededConstant = p.ConstantValue;
break;
}
}
if (SucceededConstant.HasValue)
{
if (SourceTerm.Coeffecient == SucceededConstant.Value)
{
SourceTerm._CoeffecientPowerTerm -= new SymbolicVariable(ower.ToString(CultureInfo.InvariantCulture));
}
else
{
var rr = SourceTerm.FusedConstants[SucceededConstant.Value];
rr.SymbolicVariable -= new SymbolicVariable(ower.ToString(CultureInfo.InvariantCulture));
SourceTerm.FusedConstants[SucceededConstant.Value] = rr;
}
}
else
{
SourceTerm.FusedConstants.Add(
cst.ConstantValue,
new HybridVariable
{
NumericalVariable = -1, // power
});
}
}
}
}
}
}
}
public static SymbolicVariable Pow(SymbolicVariable a, double power)
{
return(a.RaiseToSymbolicPower(new SymbolicVariable(power.ToString())));
}