Custom Environments

Texpr allows you to define custom variables and functions that persist across multiple evaluations. This is useful for creating interactive sessions, REPLs, or complex calculations where values need to be reused.

Variables

You can define variables using the let keyword. Once defined, these variables can be used in subsequent expressions.

let x = 5
let y = 10
x + y  // Result: 15

Syntax

let <variable_name> = <expression>

• Variable Names: Must start with a letter and can contain letters. They are case-sensitive.
• Expression: Any valid LaTeX math expression.

Persistence

Variables defined with let are stored in the Texpr instance's global environment. They persist until you explicitly clear them or the instance is destroyed.

final texpr = Texpr();
texpr.evaluate('let a = 10');
print(texpr.evaluate('a + 5').asNumeric()); // 15.0

Functions

You can define custom functions using the standard function notation.

f(x) = x^2 + 1
g(a, b) = a * b

Syntax

<function_name>(<parameter_list>) = <expression>

• Function Name: The name of the function (e.g., f, myFunc).
• Parameter List: Comma-separated list of parameter names (e.g., x, a, b).
• Expression: The function body, using the parameters.

Defining and Calling Functions

Once defined, custom functions can be called just like built-in functions.

final texpr = Texpr();

// Define a function
texpr.evaluate(r'f(x) = x^2');

// Call the function
print(texpr.evaluate('f(3)').asNumeric());        // 9.0
print(texpr.evaluate('f(5)').asNumeric());        // 25.0

// Multi-parameter functions
texpr.evaluate(r'g(a, b) = a + b');
print(texpr.evaluate('g(2, 3)').asNumeric());     // 5.0

// Nested function calls
print(texpr.evaluate('f(g(1, 2))').asNumeric());  // 9.0 (f(3) = 9)

Using LaTeX in Function Bodies

Function bodies can use any valid LaTeX expressions:

texpr.evaluate(r'area(r) = \pi r^2');
print(texpr.evaluate('area(2)').asNumeric());  // 12.566...

texpr.evaluate(r'h(x) = \sin{x} + \cos{x}');
print(texpr.evaluate('h(0)').asNumeric());     // 1.0

Accessing Global Variables

Functions can use variables from the global environment:

texpr.evaluate(r'let rate = 0.05');
texpr.evaluate(r'interest(principal) = principal * rate');
print(texpr.evaluate('interest(1000)').asNumeric()); // 50.0

Scoping and Shadowing

The Texpr environment has two layers:

1. Global Environment: Persistent items defined via let or function definitions.
2. Local Environment: Temporary variables passed to evaluate or evaluateParsed.

Local variables shadow global variables.

final texpr = Texpr();
texpr.evaluate('let x = 10');

// Use global 'x'
print(texpr.evaluate('x').asNumeric()); // 10.0

// Shadow global 'x' with local 'x'
print(texpr.evaluate('x', {'x': 20}).asNumeric()); // 20.0

// Global 'x' is unchanged
print(texpr.evaluate('x').asNumeric()); // 10.0

Managing the Environment

You can clear the persistent global environment using clearEnvironment().

texpr.clearEnvironment();
// 'x' is no longer defined