JupyterLab is a powerful, browser-based interactive computing environment that blends code, text, and visualization in a single interface. Much like Mathematica, it allows users to write and execute code alongside narrative text, mathematical expressions, plots, and interactive widgets. But unlike Mathematica, JupyterLab is open-source, free to use, and part of the larger Project Jupyter ecosystem. It supports multiple programming languages (most commonly Python) and is widely used in scientific research, data analysis, machine learning, and education.
What makes JupyterLab particularly attractive is its flexibility. Users can arrange notebooks, consoles, terminals, and text files into a customizable interface, enabling a seamless workflow for complex tasks. Whether you’re visualizing data with matplotlib, solving equations with sympy, or training models with TensorFlow, JupyterLab provides a clean, intuitive environment to do it all. It feels very much like a modern version of Mathematica—but running in your browser, on your own machine, or even in the cloud.
In practice, there are three popular ways to use Jupyter today. The first is JupyterLite, a lightweight version that runs entirely in your browser using WebAssembly-based Python like Pyodide. This means you can execute Python code without installing anything or connecting to a server. While performance is limited and some features (like file access or advanced libraries) may not work, it’s excellent for quick demos, educational use, and offline exploration. You can try it instantly from the official website at jupyter.org.
The second option is Google Colab, a free service provided by Google that offers cloud-based Jupyter notebooks with access to CPUs, GPUs, and even TPUs. Colab comes with most popular Python libraries pre-installed and integrates directly with Google Drive. It’s a fantastic choice if you need more computing power or want to avoid setting up a Python environment on your own machine. While there are some limitations—such as session timeouts and occasional disconnections—Colab remains one of the most convenient ways to run notebooks with minimal setup.
The third and most developer-friendly option is to use the Jupyter extension in Visual Studio Code. This approach lets you run notebooks on your local machine using your own Python installation. By combining the Jupyter and Python extensions in VS Code, you gain the power of a full IDE with version control, debugging, and package management, all while working in the notebook format. It’s ideal for researchers, engineers, and developers who want full control over their environment and code.
| Method | Installation Required | Runs Where | Strengths | Limitations |
|---|---|---|---|---|
| JupyterLite | ❌ None | In your browser | No setup needed, fast to launch, fully offline | Limited performance, restricted libraries and file access |
| Google Colab | ❌ None | Cloud (Google) | Free cloud compute (GPU/TPU), Drive integration | Session timeouts, internet required |
| VS Code + Jupyter Extension | ✅ Yes (Python + VS Code) | Locally on your PC | Full control, access to local files and packages | Needs setup, no free GPU like Colab |
In summary, JupyterLab brings together the interactive elegance of Mathematica with the openness and flexibility of the Python ecosystem. Whether you’re using JupyterLite in your browser, Google Colab in the cloud, or running notebooks locally in VS Code, Jupyter offers a rich and accessible environment for computation and discovery.
Of course. Here is a single, comprehensive table that combines the information from the previous two. It shows the standard functional syntax alongside the postfix/method-chaining style for both SymPy and Mathematica.
Notes on Syntax
| Category | Problem Description | SymPy (Standard Form) | SymPy (Method Chaining Style) | Mathematica (Standard Form) | Mathematica (Postfix Style) |
|---|---|---|---|---|---|
| Calculator | Basic arithmetic | 3 + 46 - 12 | (N/A) | 3 + 46 - 12 | (N/A) |
| Exponentiation | 3**110 | (N/A) | 3^110 | (N/A) | |
| Exact fraction | Rational(5, 6) | (N/A) | 5/6 | (N/A) | |
| Polynomials | Expand an expression | expand((x+y)**5) | ((x+y)**5).expand() | Expand[(x+y)^5] | (x+y)^5 // Expand |
| Expand rational function | expand((x+y)**4 / (x-y)**2) | ((x+y)**4 / (x-y)**2).expand() | Expand[(x+y)^4 / (x-y)^2] | (x+y)^4 / (x-y)^2 // Expand | |
| Factor an expression | factor(x**2 - y**2) | (x**2 - y**2).factor() | Factor[x^2 - y^2] | x^2 - y^2 // Factor | |
| Simplify an expression | simplify((x**3+y**3)/(x+y)) | ((x**3+y**3)/(x+y)).simplify() | Simplify[(x^3+y^3)/(x+y)] | (x^3+y^3)/(x+y) // Simplify | |
| Get coefficients | Poly(x**2 + x + 2*y, x).coeffs() | Poly(x**2 + x + 2*y, x).coeffs() | CoefficientList[x^2 + x + 2*y, x] | x^2 + x + 2*y // CoefficientList[#, x]& | |
| Partial fraction decomp. | apart(1/(x**2+5*x+6), x) | (1/(x**2+5*x+6)).apart(x) | Apart[1/(x^2+5*x+6), x] | 1/(x^2+5*x+6) // Apart[#, x]& | |
| Sum & Product | Summation | summation(2*k, (k, 1, 20)) | (N/A) | Sum[2k, {k, 1, 20}] | (N/A) |
| Product | product(x+y, (x, 1, 5)) | (N/A) | Product[x+y, {x, 1, 5}] | (N/A) | |
| Complex | Get the real part | re(3 + 4*I) | (3 + 4*I).as_real_imag()[0] | Re[3 + 4*I] | 3 + 4*I // Re |
| Get the imaginary part | im(3 + 4*I) | (3 + 4*I).as_real_imag()[1] | Im[3 + 4*I] | 3 + 4*I // Im | |
| Get the absolute value | Abs(3 + 4*I) | Abs(3 + 4*I) | Abs[3 + 4*I] | 3 + 4*I // Abs | |
| Equations | Solve single variable | solve(x**2 + a*x - 4*b, x) | (N/A) | Solve[x^2 + a*x - 4*b == 0, x] | x^2 + a*x - 4*b == 0 // Solve[#, x]& |
| Solve a polynomial | solve(x**6 - 1, x) | (N/A) | Solve[x^6 == 1, x] | x^6 == 1 // Solve[#, x]& | |
| Solve system of eqns. | solve([2*x+3*y-6, -2*x+4*y-9]) | (N/A) | Solve[{2x+3y==6, -2x+4y==9}] | {2x+3y==6, -2x+4y==9} // Solve | |
| Find roots of a poly. | roots(x**3 + 2*x + 2, x) | (N/A) | Roots[x^3 + 2*x + 2 == 0, x] | x^3 + 2*x + 2 == 0 // Roots[#, x]& | |
| Calculus | Limit | limit(sin(x)/x, x, 0) | (N/A) | Limit[Sin[x]/x, x -> 0] | Sin[x]/x // Limit[#, x -> 0]& |
| First derivative | diff(sin(x), x) | sin(x).diff(x) | D[Sin[x], x] | Sin[x] // D[#, x]& | |
| Second derivative | diff(cos(x)/(x+sin(x)), x, 2) | (cos(x)/(x+sin(x))).diff(x, 2) | D[Cos[x]/(x+Sin[x]), {x, 2}] | Cos[x]/(x+Sin[x]) // D[#, {x, 2}]& | |
| Indefinite integral | integrate(x**2, x) | (x**2).integrate(x) | Integrate[x^2, x] | x^2 // Integrate[#, x]& | |
| Taylor series | series(exp(x), x, 0, 5) | exp(x).series(x, 0, 5) | Series[Exp[x], {x, 0, 4}] | Exp[x] // Series[#, {x, 0, 4}]& |