Algebraic expressions are fundamental to mathematics, representing relationships between variables, constants, and mathematical operations. An algebraic expression evaluator takes a given mathematical expression, often containing variables, and computes its numerical value when specific values are assigned to those variables. This is precisely what tools like the Google Calculator (when used for algebraic expressions) or dedicated scientific calculators and programming libraries do.
How it Works
The process involves parsing the input expression, identifying variables, and then substituting their assigned values. After substitution, the expression is evaluated following the standard order of operations (PEMDAS/BODMAS):
Parentheses / Brackets
Exponents / Orders
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Mathematical Operations Supported:
A typical evaluator supports standard arithmetic operations:
Addition: +
Subtraction: -
Multiplication: *
Division: /
Exponents/Powers: ^ or ** (depending on the implementation)
It can also often handle:
Parentheses for grouping: ( )
Mathematical functions like sin(), cos(), log(), sqrt(), etc. (though this basic calculator focuses on arithmetic).
Use Cases:
Evaluating algebraic expressions is crucial in many fields:
Science and Engineering: Calculating physical quantities based on formulas (e.g., physics equations, chemical reaction rates).
Computer Programming: Used in scripting, data analysis, and creating interactive applications.
function evaluateExpression() {
var expressionString = document.getElementById("expression").value;
var variableValuesString = document.getElementById("variableValues").value;
var resultDiv = document.getElementById("result").querySelector("span");
resultDiv.style.color = "#004a99"; // Reset color
if (!expressionString) {
resultDiv.textContent = "Please enter an expression.";
return;
}
var variables = {};
if (variableValuesString) {
try {
variables = JSON.parse(variableValuesString);
if (typeof variables !== 'object' || variables === null) {
throw new Error("Parsed JSON is not an object.");
}
} catch (e) {
resultDiv.textContent = "Invalid JSON format for variable values.";
return;
}
}
// Basic sanitization and parsing logic
// This is a simplified evaluator. For complex expressions, a dedicated library or
// more robust parsing (like using an AST) would be necessary.
// We'll attempt to use JavaScript's built-in eval, but with caution and
// ensuring variables are defined in the scope.
var scope = {};
for (var key in variables) {
if (variables.hasOwnProperty(key)) {
var value = variables[key];
if (typeof value === 'number' && !isNaN(value)) {
scope[key] = value;
} else {
resultDiv.textContent = "Invalid number format for variable '" + key + "'.";
return;
}
}
}
// Replace common math functions if needed (example: sqrt)
// This is highly simplified and only handles basic arithmetic for now.
// For a robust solution, a math expression parser library is recommended.
// Attempt to evaluate using eval() with a controlled scope.
// WARNING: eval() can be a security risk if the input is not trusted.
// For this example, we assume the user is providing the input.
try {
// Create a function to execute in a controlled scope
var keys = Object.keys(scope);
var vals = Object.values(scope);
// Adding basic math constants/functions that might be expected.
// For this specific calculator, we'll stick to basic arithmetic as per the example.
var functionBody = "return " + expressionString + ";";
// Use a Function constructor for better scope isolation than direct eval
var evaluator = new Function(keys, functionBody);
var result = evaluator.apply(null, vals);
if (typeof result === 'number' && !isNaN(result)) {
resultDiv.textContent = "Result: ";
var resultSpan = document.createElement('span');
resultSpan.textContent = result;
resultSpan.style.color = '#28a745'; // Success green
resultDiv.appendChild(resultSpan);
} else {
resultDiv.textContent = "Evaluation resulted in an invalid value.";
}
} catch (error) {
resultDiv.textContent = "Error: " + error.message;
resultDiv.style.color = "#dc3545"; // Error red
}
}