import * as math from 'mathjs';
export const laplaceTransform = (expr, t, s) => {
try {
const node = math.parse(expr);
// Using numerical integration for a basic approximation
const upperLimit = 100; // Approximation of infinity
const steps = 1000;
const dt = upperLimit / steps;
let result = math.complex(0, 0);
for (let i = 0; i < steps; i++) {
const time = i * dt;
const scope = { [t]: time };
const ft = node.evaluate(scope);
const expTerm = math.exp(math.multiply(math.complex(-s, 0), time));
result = math.add(result,
math.multiply(ft, expTerm, dt));
}
return result.toString();
} catch (e) {
throw new Error(`Laplace Transform error: ${e.message}`);
}
};
export const fourierTransform = (expr, t, omega) => {
try {
const node = math.parse(expr);
// Using numerical integration for a basic approximation
const limit = 50; // Approximation of infinity
const steps = 1000;
const dt = (2 * limit) / steps;
let result = math.complex(0, 0);
for (let i = 0; i < steps; i++) {
const time = -limit + i * dt;
const scope = { [t]: time };
const ft = node.evaluate(scope);
const expTerm = math.exp(
math.multiply(
math.complex(0, -1),
omega,
time
)
);
result = math.add(result,
math.multiply(ft, expTerm, dt));
}
return result.toString();
} catch (e) {
throw new Error(`Fourier Transform error: ${e.message}`);
}
};
export const zTransform = (expr, n, z, limit = 100) => {
if (limit > 10000) throw new Error('Limit too large for safety');
try {
const node = math.parse(expr);
let result = math.complex(0, 0);
for (let k = 0; k <= limit; k++) {
const scope = { [n]: k };
const fn = node.evaluate(scope);
const zTerm = math.pow(z, -k);
result = math.add(result, math.multiply(fn, zTerm));
}
return result.toString();
} catch (e) {
throw new Error(`Z-Transform error: ${e.message}`);
}
};
