ipython-math-syntax

Write textbook mathematical notation—implicit multiplication (2x), superscripts (x²), roots (√x, ∛x), integrals (∫₀¹ 3x² dx), derivatives (d/dx, ∂²/∂x∂y, ∂ₓ, f′(x), ẋ), vector calculus (∇, ∇⋅, ∇×, ∇²), Einstein summation (ein(Aᵢⱼ Bⱼₖ)), Kronecker & Levi-Civita tensors (δᵢⱼ, εᵢⱼₖ), Dirac bra-kets (|0⟩, ⟨+|σ_x|+⟩), and more—directly inside Jupyter Notebooks, JupyterLab, and IPython.

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Installation

pip install .

Or install directly from GitHub:

pip install git+https://github.com/iDagas/ipython-math-syntax.git

Quick Start

In any Jupyter Notebook or IPython session, load the extension in one line:

%load_ext math_syntax

To unload at any time:

%unload_ext math_syntax

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Supported Notation Reference

Category	Math Syntax	What It Computes
Implicit Multiplication	2x, 3π, 2(x+1), (a+b)(c+d), x²y	2*x, 3*π, 2*(x+1), (a+b)*(c+d), x**(2)*y (preserves 1e-5, 0xFF)
Superscripts & Subscripts	x², ℯ⁻ˣ², 2ⁿ⁺¹, x₁, aᵢ	x**(2), exp(-x**2), 2**(n+1), x_1, a_i
Trig Powers & Inverses	sin²(θ) + cos²(θ), sin⁻¹(1/2), h⁻¹(y)	(sin(θ))**2 + (cos(θ))**2, asin(1/2), symbolic inverse $h^{-1}(y)$
Roots & Postfix Ops	√x, ∛x, ∜x, n!, n!!, 30°	sqrt(x), cbrt(x), fourth_root(x), factorial(n), factorial2(n), radians(30)
Indefinite & Definite Integrals	∫ x² dx, ∫₀¹ 3x² dx, ∫₋∞^∞ ℯ⁻ˣ² dx, ∬ (6x⋅y²) dx dy	Exact symbolic integrals via SymPy (sp.integrate)
Evaluation Bar	(x³ / 3)|₀³, (-cos(x))|₀^π	Fundamental theorem evaluation $F(b) - F(a)$
Derivatives	d/dx(sin(x²)), ∂²/∂x∂y(x³y²), ∂ₓᵧ(x²y³), g′(x), ẋ, ẍ	Leibniz, subscript PDE, Lagrange prime, and Newton time-dot derivatives
Vector Calculus	∇f, ∇⋅F, ∇×F, ∇²f (or ∆f), jacobian, hessian	Gradient, divergence, 3D curl, Laplacian, Jacobian, Hessian
Prefix Sums & Products	∑ᵢ₌₁ⁿ i², ∑ₙ₌₁^∞ (1/n²), ∏ₖ₌₁⁵ k, ∑_{n=1}^{∞} (1/2ⁿ)	Symbolic/numerical $\sum$, $\prod$, $\bigcup$, $\bigcap$
Limits & Taylor Series	lim((1 + 1/n)ⁿ, n → ∞), lim(1/x, x → 0⁺), taylor(sin(x))	Symbolic one/two-sided limits and Taylor expansions
Integral Transforms & ODEs	ℒ(sin(2t)), ℒ⁻¹(1/(s²+1)), ℱ(ℯ^(-x²)), solve(y″ + y ≟ 0)	Laplace, Inverse Laplace, Fourier transforms, and ODE/algebraic solver
Tensors & Einstein Sum	δᵢⱼ, εᵢⱼₖ, ein(Aᵢᵢ), ein(Aᵢⱼ Bⱼₖ), ein(εᵢⱼₖ uⱼ vₖ)	Kronecker delta, Levi-Civita, and automatic index contraction
Products & Algebra	u × v, A ⊗ B, u ∧ v, A ⊕ B, u ⊛ v, A ⊡ B	3D cross / Cartesian product, Kronecker product, wedge product, direct sum, convolution, double contraction
Quantum Bra-Kets	|0⟩, |+⟩, ⟨0|1⟩, |0⟩⟨0|, ⟨+|σ_x|+⟩, ⟦σ_z, σ_x⟧	Qubit kets/bras, projectors, expectation values, commutators
Overloaded Bars & Norms	|-7|, |3 + 4𝕚|, |A|, |{1,2,3}|, ‖v‖, ‖v‖₁, ‖v‖∞	Abs, complex modulus, matrix determinant, set cardinality, and $L_p$ norms
Combinatorics & Number Theory	⁵C₂, ⁵P₂, 17 ≡ 2 (mod 5), 7 ∣ 42, 8 ⊥ 15	Binomial, k-permutation, modular congruence, divisibility, coprimality / orthogonality
Sets, Domains & Quantifiers	√2 ∈ ℝ ∧ √2 ∉ ℚ, {x² ∣ x ∈ A : x > 2}, ∀x ∈ A: P(x), ∃, ∄	Number domains ($\mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb{C}$), set-builder comprehension, quantifiers

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Example Showcase

%load_ext math_syntax

# 1. Calculus & Integrals
print(∫₀¹ 3x² dx)                  # 1
print(∫₋∞^∞ ℯ⁻ˣ² dx)               # sqrt(pi)
print(∂²/∂x∂y(x³y²))               # 6*x**2*y

# 2. Summations & Einstein Contraction
print(sp.factor(∑ᵢ₌₁ⁿ i²))         # n*(n + 1)*(2*n + 1)/6
print(∑ₙ₌₁^∞ (1/n²))               # pi**2/6
A = Matrix([[1, 2], [3, 4]])
B = Matrix([[5, 6], [7, 8]])
print(ein(Aᵢⱼ Bⱼₖ))                # Matrix([[19, 22], [43, 50]])

# 3. Differential Equations & Transforms
print(solve(y″ + y ≟ 0))           # Eq(y(x), C1*sin(x) + C2*cos(x))
print(ℒ(sin(2t)))                  # 2/(s**2 + 4)

# 4. Quantum Mechanics
σ_x = Matrix([[0, 1], [1, 0]])
print(⟨+|σ_x|+⟩)                   # 1