private Operand FactorScalar(string vectorName, Sum sum, Context context)
{
List <string> basisVectorList = context.ReturnBasisVectors();
Sum remainderSum = sum.Copy() as Sum;
Sum modifiedSum = new Sum();
foreach (string basisVectorName in basisVectorList)
{
if (context.BilinearForm(vectorName, basisVectorName).IsAdditiveIdentity)
{
continue;
}
bool found = false;
foreach (Blade blade in remainderSum.operandList.Select(term => term as Blade))
{
if (blade.Grade == 0 && blade.scalar is SymbolicScalarTerm scalarTerm)
{
foreach (SymbolicScalarTerm.Factor factor in scalarTerm.factorList)
{
if (factor is SymbolicScalarTerm.SymbolicDot symbolicDot && symbolicDot.InvolvesVectors(vectorName, basisVectorName))
{
remainderSum.operandList.Remove(blade);
scalarTerm.factorList.Remove(symbolicDot);
blade.vectorList.Add(basisVectorName);
modifiedSum.operandList.Add(blade);
found = true;
break;
}
}
}
if (found)
{
break;
}
}
if (!found)
{
return(null);
}
}
Sum resultSum = new Sum();
resultSum.operandList.Add(new InnerProduct(new List <Operand>()
{
new Blade(vectorName), new FactorDot(new List <Operand>()
{
modifiedSum
})
}));
resultSum.operandList.Add(new FactorDot(new List <Operand>()
{
remainderSum
}));
return(resultSum);
}
private Operand FactorBlade(string vectorName, Sum sum, Context context)
{
List <string> basisVectorList = context.ReturnBasisVectors();
basisVectorList = basisVectorList.Where(basisVectorName => !context.BilinearForm(vectorName, basisVectorName).IsAdditiveIdentity).ToList();
List <int> emptyBladeOffsetList = new List <int>();
foreach (List <int> bladeOffsetList in this.IteratePotentiallyFactorableBladesLists(emptyBladeOffsetList, sum, basisVectorList, vectorName))
{
List <Operand> modifiedOperandList = new List <Operand>();
for (int i = 0; i < bladeOffsetList.Count; i++)
{
string basisVectorName = basisVectorList[i];
Blade blade = sum.operandList[bladeOffsetList[i]].Copy() as Blade;
SymbolicScalarTerm term = blade.scalar as SymbolicScalarTerm;
int j = blade.vectorList.IndexOf(basisVectorName);
if (j % 2 == 1)
{
term.scalar = new GeometricProduct(new List <Operand>()
{
new NumericScalar(-1.0), term.scalar
});
}
blade.vectorList.Remove(basisVectorName);
term.factorList = term.factorList.Where(factor => !(factor is SymbolicScalarTerm.SymbolicDot symbolicDot && symbolicDot.InvolvesVectors(vectorName, basisVectorName))).ToList();
modifiedOperandList.Add(ExhaustEvaluation(blade, context));
}
bool canFactor = Enumerable.Range(0, modifiedOperandList.Count - 1).All(j => {
Operand bladeA = modifiedOperandList[j];
Operand bladeB = modifiedOperandList[j + 1];
Operand difference = new Sum(new List <Operand>()
{
bladeA.Copy(), new GeometricProduct(new List <Operand>()
{
new NumericScalar(-1.0), bladeB.Copy()
})
});
difference = ExhaustEvaluation(difference, context);
return(difference.IsAdditiveIdentity);
});
if (canFactor)
{
Sum remainderSum = new Sum(sum.operandList.Where(operand => !bladeOffsetList.Contains(sum.operandList.IndexOf(operand))).ToList());
Sum resultSum = new Sum();
resultSum.operandList.Add(new OuterProduct(new List <Operand>()
{
new Blade(vectorName), modifiedOperandList[0]
}));
resultSum.operandList.Add(new FactorDot(new List <Operand>()
{
remainderSum
}));
return(resultSum);
}
}
return(null);
}
private IEnumerable <List <int> > IteratePotentiallyFactorableBladesLists(List <int> bladeOffsetList, Sum sum, List <string> basisVectorList, string vectorName)
{
if (bladeOffsetList.Count == basisVectorList.Count)
{
yield return(bladeOffsetList);
}
else
{
string basisVectorName = basisVectorList[bladeOffsetList.Count];
for (int i = 0; i < sum.operandList.Count; i++)
{
if (bladeOffsetList.Contains(i))
{
continue;
}
Blade blade = sum.operandList[i] as Blade;
if (blade.vectorList.Contains(basisVectorName))
{
if (blade.scalar is SymbolicScalarTerm term)
{
if (term.factorList.Any(factor => factor is SymbolicScalarTerm.SymbolicDot symbolicDot && symbolicDot.InvolvesVectors(vectorName, basisVectorName)))
{
bladeOffsetList.Add(i);
foreach (List <int> otherBladeOffsetList in IteratePotentiallyFactorableBladesLists(bladeOffsetList, sum, basisVectorList, vectorName))
{
yield return(otherBladeOffsetList);
}
bladeOffsetList.Remove(i);
}
}
}
}
}
}
// Note that here that we do not consider unary operator precedence.
// So for example, if we have -1~, we don't try to choose between (-1)~ and -(1~),
// though both are the same in this particular case. Also, we don't recognize unary
// operator stacking. E.g., -~1 will not parse as -(~1) would. In short, working with
// unary operators will sometimes requires parenthesis.
public Operand BuildOperandTree(List <Token> tokenList)
{
while (tokenList.Count > 0)
{
int count = tokenList.Count;
if (tokenList[0].kind == Token.Kind.LEFT_PARAN && tokenList[0].paranType == Token.ParanType.ROUND)
{
int i = FindMatchingParan(tokenList, 0);
if (i == tokenList.Count - 1)
{
tokenList.RemoveAt(0);
tokenList.RemoveAt(tokenList.Count - 1);
}
}
if (tokenList.Count == count)
{
break;
}
}
if (tokenList.Count == 0)
{
throw new ParseException("Encountered empty token list.");
}
if (tokenList.Count == 1)
{
Token token = tokenList[0];
switch (token.kind)
{
case Token.Kind.SYMBOL:
{
if (token.data[0] == '@')
{
return(new Variable(token.data.Substring(1)));
}
if (token.data[0] == '$')
{
return(new SymbolicScalarTerm(token.data.Substring(1)));
}
string vectorName = token.data;
bool isBasisVector = false;
List <string> basisVectorList = context.ReturnBasisVectors();
if (basisVectorList != null)
{
isBasisVector = basisVectorList.Contains(vectorName);
if (basisVectorsOnly && !isBasisVector)
{
Sum sum = new Sum();
foreach (string basisVectorName in basisVectorList)
{
InnerProduct dot = new InnerProduct(new List <Operand>()
{
new Blade(vectorName), new Blade(basisVectorName)
});
sum.operandList.Add(new GeometricProduct(new List <Operand>()
{
dot, new Blade(basisVectorName)
}));
}
return(sum);
}
}
generatedSymbolicVector = !isBasisVector;
return(new Blade(vectorName));
}
case Token.Kind.NUMBER:
{
double value;
if (!double.TryParse(token.data, out value))
{
throw new ParseException(string.Format("Encountered non-parsable number ({0}).", token.data));
}
return(new NumericScalar(value));
}
default:
{
throw new ParseException(string.Format("Encountered lone token ({0}) that isn't handled.", token.data));
}
}
}
else if (tokenList[0].kind == Token.Kind.OPERATOR && (ParansMatch(tokenList, 1, tokenList.Count - 1) || tokenList.Count == 2 || IsFunctionPattern(tokenList.Skip(1).ToList())))
{
Token token = tokenList[0];
if (token.data == "-")
{
return(new GeometricProduct(new List <Operand>()
{
new Blade(-1.0), BuildOperandTree(tokenList.Skip(1).ToList())
}));
}
throw new ParseException(string.Format("Encounterd unary operator ({0}) that isn't recognized on the left.", token.data));
}
else if (tokenList[tokenList.Count - 1].kind == Token.Kind.OPERATOR && (ParansMatch(tokenList, 0, tokenList.Count - 2) || tokenList.Count == 2 || IsFunctionPattern(tokenList.Take(tokenList.Count - 1).ToList())))
{
Token token = tokenList[tokenList.Count - 1];
if (token.data == "~")
{
return(new Reverse(new List <Operand>()
{
BuildOperandTree(tokenList.Take(tokenList.Count - 1).ToList())
}));
}
throw new ParseException(string.Format("Encountered unary operator ({0}) that isn't recognized on the right.", token.data));
}
else if (IsFunctionPattern(tokenList))
{
Token token = tokenList[0];
Operation operation = context.CreateFunction(token.data);
if (operation == null)
{
throw new ParseException(string.Format("Encountered unknown function \"{0}\".", token.data));
}
List <List <Token> > argumentList = ParseListOfTokenLists(tokenList.Skip(2).Take(tokenList.Count - 3).ToList());
foreach (List <Token> subTokenList in argumentList)
{
operation.operandList.Add(BuildOperandTree(subTokenList));
}
return(operation);
}
else if (tokenList[0].paranType == Token.ParanType.SQUARE && ParansMatch(tokenList, 0, tokenList.Count - 1))
{
List <List <Operand> > listOfOperandLists = new List <List <Operand> >();
List <List <Token> > rowList = ParseListOfTokenLists(tokenList.Skip(1).Take(tokenList.Count - 2).ToList());
foreach (List <Token> rowTokenList in rowList)
{
listOfOperandLists.Add(new List <Operand>());
List <List <Token> > colList;
if (rowTokenList[0].paranType == Token.ParanType.SQUARE && ParansMatch(rowTokenList, 0, rowTokenList.Count - 1))
{
colList = ParseListOfTokenLists(rowTokenList.Skip(1).Take(rowTokenList.Count - 2).ToList());
}
else
{
colList = new List <List <Token> >()
{
rowTokenList
}
};
foreach (List <Token> subTokenList in colList)
{
listOfOperandLists[listOfOperandLists.Count - 1].Add(BuildOperandTree(subTokenList));
}
}
return(new Matrix(listOfOperandLists));
}
else
{
// Our goal here is to find an operator of lowest precedence. It will never be
// at the very beginning or end of the entire token sequence.
List <Token> opTokenList = null;
foreach (Token token in WalkTokensSkipSubexpressions(tokenList))
{
if (token.kind != Token.Kind.OPERATOR)
{
continue;
}
// Only unary operators can be at the start or end of the token list.
if (tokenList.IndexOf(token) == 0 || tokenList.IndexOf(token) == tokenList.Count - 1)
{
continue;
}
// Ignore unary operators on left.
if (token.data == "-" && tokenList[tokenList.IndexOf(token) - 1].kind == Token.Kind.OPERATOR)
{
continue;
}
// Ignore unary operators on right.
if (token.data == "~" && tokenList[tokenList.IndexOf(token) + 1].kind == Token.Kind.OPERATOR)
{
continue;
}
// At this point we should be reasonably sure it's a binary operator we're looking at.
if (opTokenList == null || PrecedenceLevel(opTokenList[0].data) > PrecedenceLevel(token.data))
{
opTokenList = new List <Token>()
{
token
}
}
;
else if (opTokenList != null && PrecedenceLevel(opTokenList[0].data) == PrecedenceLevel(token.data))
{
opTokenList.Add(token);
}
}
if (opTokenList == null)
{
throw new ParseException("Did not encounter binary operator token.");
}
Token operatorToken = null;
switch (OperatorAssociativity(opTokenList[0].data))
{
case Associativity.LEFT_TO_RIGHT:
operatorToken = opTokenList[opTokenList.Count - 1];
break;
case Associativity.RIGHT_TO_LEFT:
operatorToken = opTokenList[0];
break;
}
Operation operation = null;
if (operatorToken.data == ";")
{
operation = new Sequence();
}
else if (operatorToken.data == "+" || operatorToken.data == "-")
{
operation = new Sum();
}
else if (operatorToken.data == "*" || operatorToken.data == "/")
{
operation = new GeometricProduct();
}
else if (operatorToken.data == ".")
{
operation = new InnerProduct();
}
else if (operatorToken.data == "^")
{
operation = new OuterProduct();
}
else if (operatorToken.data == "=")
{
operation = new Assignment();
}
else if (operatorToken.data == ":=")
{
operation = new Assignment(false);
}
if (operation == null)
{
throw new ParseException(string.Format("Did not recognized operator token ({0}).", operatorToken.data));
}
int i = tokenList.IndexOf(operatorToken);
Operand leftOperand = BuildOperandTree(tokenList.Take(i).ToList());
Operand rightOperand = BuildOperandTree(tokenList.Skip(i + 1).Take(tokenList.Count - 1 - i).ToList());
operation.operandList.Add(leftOperand);
if (operatorToken.data == "-")
{
operation.operandList.Add(new GeometricProduct(new List <Operand>()
{
new NumericScalar(-1.0), rightOperand
}));
}
else if (operatorToken.data == "/")
{
operation.operandList.Add(new Inverse(new List <Operand>()
{
rightOperand
}));
}
else
{
operation.operandList.Add(rightOperand);
}
return(operation);
}
}
