public static Entity Eval(List <Entity> args)
{
MathFunctions.AssertArgs(args.Count, 2);
var r1 = args[0].InnerEval();
var r2 = args[1].InnerEval();
args = new List <Entity> {
r1, r2
};
if (r1.entType == Entity.EntType.NUMBER && r2.entType == Entity.EntType.NUMBER)
{
return(new NumberEntity((r1 as NumberEntity).Value * (r2 as NumberEntity).Value));
}
else if (MathFunctions.IsOneNumber(args, 1))
{
return(MathFunctions.GetAnotherEntity(args, 1));
}
else if (MathFunctions.IsOneNumber(args, 0))
{
return(0);
}
else
{
return(r1 * r2);
}
}
public static Entity Simplify(List <Entity> args)
{
MathFunctions.AssertArgs(args.Count, 2);
var r1 = args[0].InnerSimplify();
var r2 = args[1].InnerSimplify();
if (r1.entType == Entity.EntType.NUMBER && r2.entType == Entity.EntType.NUMBER)
{
// TODO: Consider cases like sqrt(12) which could be simplified to 2 sqrt(3)
var(n1, n2) = ((r1 as NumberEntity).Value, (r2 as NumberEntity).Value);
return(InnerSimplifyAdditionalFunctional.KeepIfBad(Number.Pow(n1, n2), MathS.Pow(r1, r2), n1, n2));
}
else if (r1 == 0 || r1 == 1)
{
return(r1);
}
else if (r2 == 1)
{
return(r1);
}
else if (r2 == 0)
{
return(1);
}
else
{
return(r1.Pow(r2));
}
}
public static Entity Simplify(List <Entity> args)
{
MathFunctions.AssertArgs(args.Count, 2);
var r1 = args[0].InnerSimplify();
var r2 = args[1].InnerSimplify();
args = new List <Entity> {
r1, r2
};
if (MathFunctions.IsOneNumber(args, 1))
{
return(MathFunctions.GetAnotherEntity(args, 1));
}
else if (MathFunctions.IsOneNumber(args, 0))
{
return(0);
}
else if (r1.entType == Entity.EntType.NUMBER && r2.entType == Entity.EntType.NUMBER)
{
var(n1, n2) = ((r1 as NumberEntity).Value, (r2 as NumberEntity).Value);
return(InnerSimplifyAdditionalFunctional.KeepIfBad(n1 * n2, r1 * r2, n1, n2));
}
else
{
return(r1 * r2);
}
}
public static Entity Eval(List <Entity> args)
{
MathFunctions.AssertArgs(args.Count, 2);
var r = args[0].InnerEval();
var n = args[1].InnerEval();
args = new List <Entity> {
r, n
};
if (r.entType == Entity.EntType.NUMBER && n.entType == Entity.EntType.NUMBER)
{
return(new NumberEntity(Number.Log((r as NumberEntity).Value.Real, (n as NumberEntity).Value)));
}
else if (r == n)
{
return(1);
}
else if (r == 1)
{
return(0);
}
else
{
return(r.Log(args[1]));
}
}
public static Entity Eval(List <Entity> args)
{
MathFunctions.AssertArgs(args.Count, 2);
var r1 = args[0].InnerEval();
var r2 = args[1].InnerEval();
if (r1.entType == Entity.EntType.NUMBER && r2.entType == Entity.EntType.NUMBER)
{
return(new NumberEntity(Number.Pow((r1 as NumberEntity).Value, (r2 as NumberEntity).Value)));
}
else if (r1 == 0 || r1 == 1)
{
return(r1);
}
else if (r2 == 1)
{
return(r1);
}
else if (r2 == 0)
{
return(1);
}
else
{
return(r1.Pow(r2));
}
}
// arccotan(x)' = -1 / (1 + x^2)
public static Entity Derive(List <Entity> args, VariableEntity variable)
{
MathFunctions.AssertArgs(args.Count, 1);
var a = args[0];
return(-1 / (1 + MathS.Sqr(a)) * a.Derive(variable));
}
// tan(a) = -1 / sin(a) ^ 2
public static Entity Derive(List <Entity> args, VariableEntity variable)
{
MathFunctions.AssertArgs(args.Count, 1);
var a = args[0];
return(-1 / a.Sin().Pow(2) * a.Derive(variable));
}
// (a * b)' = a' * b + b' * a
public static Entity Derive(List <Entity> args, VariableEntity variable)
{
MathFunctions.AssertArgs(args.Count, 2);
var a = args[0];
var b = args[1];
return(a.Derive(variable) * b + b.Derive(variable) * a);
}
// log(a, b) = (ln(a) / ln(b))' = (ln(a)' * ln(b) - ln(a) * ln(b)') / ln(b)^2 = (a' / a * ln(b) - ln(a) * b' / b) / ln(b)^2
public static Entity Derive(List <Entity> args, VariableEntity variable)
{
MathFunctions.AssertArgs(args.Count, 2);
var a = args[0];
var b = args[1];
return((a.Derive(variable) / a * MathS.Ln(b) - MathS.Ln(a) * b.Derive(variable) / b) / (MathS.Ln(b).Pow(2)));
}
public static Entity Eval(List <Entity> args)
{
MathFunctions.AssertArgs(args.Count, 1);
var arg = args[0].InnerEval();
if (arg.entType == Entity.EntType.NUMBER)
{
return(new NumberEntity(Number.Arccotan((arg as NumberEntity).Value)));
}
else
{
return(Arccotanf.Hang(arg));
}
}
public static Entity Eval(List <Entity> args)
{
MathFunctions.AssertArgs(args.Count, 1);
var r = args[0].InnerEval();
if (r.entType == Entity.EntType.NUMBER)
{
return(new NumberEntity(Number.Cotan((r as NumberEntity).Value)));
}
else
{
return(r.Cotan());
}
}
public static Entity Simplify(List <Entity> args)
{
MathFunctions.AssertArgs(args.Count, 1);
var r = args[0].InnerSimplify();
ComplexNumber evaled = null;
if (MathS.CanBeEvaluated(r))
{
evaled = r.Eval();
}
if (!(evaled is null))
{
var n = evaled;
if (InnerSimplifyAdditionalFunctional.KeepIfBad(Number.Sin(n), out var res, true, n))
{
return(res);
}
// (a ^ b)' = e ^ (ln(a) * b) * (a' * b / a + ln(a) * b')
// (a ^ const)' = const * a ^ (const - 1)
// (const ^ b)' = e^b * b'
public static Entity Derive(List <Entity> args, VariableEntity variable)
{
MathFunctions.AssertArgs(args.Count, 2);
var a = args[0];
var b = args[1];
if (b.entType == Entity.EntType.NUMBER)
{
var cons = (b as NumberEntity).Value - 1;
var res = b * (a.Pow(cons)) * a.Derive(variable);
return(res);
}
else if (a.entType == Entity.EntType.NUMBER)
{
return(a.Pow(b) * MathS.Ln(a) * b.Derive(variable));
}
else
{
return(a.Pow(b) * (a.Derive(variable) * b / a + MathS.Ln(a) * b.Derive(variable)));
}
}
public static Entity Simplify(List <Entity> args)
{
MathFunctions.AssertArgs(args.Count, 2);
var r1 = args[0].InnerSimplify();
var r2 = args[1].InnerSimplify();
if (r1.entType == Entity.EntType.NUMBER && r2.entType == Entity.EntType.NUMBER)
{
var(n1, n2) = ((r1 as NumberEntity).Value, (r2 as NumberEntity).Value);
return(InnerSimplifyAdditionalFunctional.KeepIfBad(n1 / n2, r1 / r2, n1, n2));
}
else if (r1 == 0)
{
return(0);
}
else if (r2 == 1)
{
return(r1);
}
else
{
return(r1 / r2);
}
}
