public static IEnumerable <FunctionTerm> GetDerivatives(this FunctionTerm term)
{
if (term is Sum)
{
Variable x = new Variable(1, "x");
Variable y = new Variable(1, "y");
return(Enumerables.Create
(
Term.Constant(1).Abstract(x, y),
Term.Constant(1).Abstract(x, y)
));
}
if (term is Product)
{
Variable x = new Variable(1, "x");
Variable y = new Variable(1, "y");
return(Enumerables.Create
(
y.Abstract(x, y),
x.Abstract(x, y)
));
}
if (term is Exponentiation)
{
Variable x = new Variable(1, "x");
Variable y = new Variable(1, "y");
return(Enumerables.Create
(
Term.Product(y, Term.Exponentiation(x, Term.Difference(y, Term.Constant(1)))).Abstract(x, y),
Term.Product(Term.Logarithm(x), Term.Exponentiation(x, y)).Abstract(x, y)
));
}
if (term is Logarithm)
{
Variable x = new Variable(1, "x");
return(Enumerables.Create(Term.Invert(x).Abstract(x)));
}
if (term is FunctionDefinition)
{
FunctionDefinition functionDefinitionTerm = (FunctionDefinition)term;
IEnumerable <FunctionTerm> derivatives = GetDerivatives(functionDefinitionTerm.Function).ToArray();
return
((
from index in Enumerable.Range(0, derivatives.Count())
let derivative = derivatives.ElementAt(index)
select new FunctionDefinition
(
string.Format("{0}_d{1}", functionDefinitionTerm.Name, index),
Rewriting.CompleteNormalization.Rewrite(derivative),
new BasicSyntax(string.Format("{0}'{1}", functionDefinitionTerm.Syntax.GetText(), index.ToString().ToSuperscript()))
)
)
.ToArray());
}
if (term is Abstraction)
{
Abstraction abstractionTerm = (Abstraction)term;
return
((
from variable in abstractionTerm.Variables
from derivative in GetDerivatives(abstractionTerm.Term, variable)
select derivative.Abstract(abstractionTerm.Variables)
)
.ToArray());
}
throw new InvalidOperationException();
}
// identity function
public static FunctionTerm Identity(int dimension)
{
Variable x = new Variable(dimension, "x");
return(new FunctionDefinition(string.Format("identity_{0}", dimension), x.Abstract(x), new BasicSyntax("id")));
}
