# Function Tree

Welcome to function_tree, a simple library for parsing strings into callable function-trees.

## Parsing strings as mathematical expressions

At the simplest (and least efficient) level, we can interpret strings as mathematical expressions:

final expressions = [
"2 + 2",
"(3 + 2)^3",
"3 * pi / 4",
"3 * sin(5 * pi / 6)",
"e^(-1)"
];
for (final expression in expressions) {
print("'$expression' ->${expression.interpret()}");
}


'2 + 2' -> 4.0
'(3 + 2)^3' -> 125.0
'3 * pi / 4' -> 2.356194490192345
'3 * sin(5 * pi / 6)' -> 1.5000000000000009
'e^(-1)' -> 0.36787944117144233


## Function Trees

The library supports two types of callable, function-trees, namely SingleVariableFunction and MultiVariableFunction.

### Single variable functions

We can create a single variable function from a string either by constructing a SingleVariableFunction instance or by calling the toSingleVariableFunction string extension directly on a string, as in the following example.

final f = "20 * (sin(x) + 1)".toSingleVariableFunction(),
pi = "pi".interpret();
for (var x = 0.0; x < 2 * pi; x += pi / 20) {
print("|" + " " * f(x).round() + "*");
}


|                    *
|                       *
|                          *
|                             *
|                                *
|                                  *
|                                    *
|                                      *
|                                       *
|                                        *
|                                        *
|                                        *
|                                       *
|                                      *
|                                    *
|                                  *
|                                *
|                             *
|                          *
|                       *
|                    *
|                 *
|              *
|           *
|        *
|      *
|    *
|  *
| *
|*
|*
|*
| *
|  *
|    *
|      *
|        *
|           *
|              *
|                 *


### Multi-variable functions

Similarly, we can construct a MultiVariableFunction instance or call the toMultiVariableFunction string extension to create a multi-variable function tree, as in the following example.

final times = "a * b".toMultiVariableFunction(["a", "b"]),
values = [1, 2, 3, 4, 5];
for (final a in values) {
final sb = StringBuffer();
for (final b in values) {
sb
..write(times({"a": a, "b": b}).floor())
..write("\t");
}
print(sb);
}


1	2	3	4	5
2	4	6	8	10
3	6	9	12	15
4	8	12	16	20
5	10	15	20	25


## TeX expressions

Function tree instances have a tex property for TeX expressions:

final f = "x * cos(y) + y * sin(x)".toMultiVariableFunction(["x", "y"]);
print(f.tex);


x cdot \cos\left( y \right) + y cdot \sin\left( x \right)


## Derivatives

Derivative trees can be constructed through the SingleVariableFunction.derivative and MultiVariableFunction.partial methods.

final f = "(2 * x) ^ (1 / (x ^ 2))".toSingleVariableFunction(),
fDash = f.derivative("x");
print("x      y      y'");
for (var x = 0.5; x < 3.0; x += 0.25) {
print(
"${x.toStringAsFixed(4)} " "${f(x).toStringAsFixed(4)} "
"${fDash(x).toStringAsFixed(4)}"); }  x y y' 0.5000 1.0000 8.0000 0.7500 2.0561 0.9215 1.0000 2.0000 -0.7726 1.2500 1.7976 -0.7663 1.5000 1.6295 -0.5780 1.7500 1.5054 -0.4229 2.0000 1.4142 -0.3134 2.2500 1.3460 -0.2373 2.5000 1.2937 -0.1837 2.7500 1.2529 -0.1452  final f = "sin(u ^ 2 + 2 * v)".toMultiVariableFunction(["u", "v"]), fu = f.partial("u"), fv = f.partial("v"), pi = "pi".interpret(), u = pi / 3, v = pi / 4; for (final fun in [f, fu, fv]) { print("${fun({"u": u, "v": v})}");
}

0.4566033934365143
-1.8633212348878314
-1.779340710602958


## Interpreter

The interpreter has support for the following:

### Functions

#### One-parameter functions

abs     acos    asin    atan    ceil
cos     cosh    cot     coth    csc
csch    exp     fact    floor   ln
log     round   sec     sech    sin
sinh    sqrt    tan     tanh


#### Two-parameter functions

log     nrt     pow


### Constants

e       pi      ln2     ln10    log2e
log10e  sqrt1_2 sqrt2


### Operations

+  -  *  /  %  ^


## Thanks

Thanks for your interest in this library. Please file any bugs or requests here.

## Libraries

function_tree
A library for parsing and evaluating numerical functions built from strings.