Table of Contents
Instiki
Markdown+itex2MML Sandbox
Play around below . Your changes will, periodically, be rolled back.
Some examples
(1) min w h p h + w r p r + w l p l \mathop{min} w_h p_h + w_r p_r + w_l p_l
Here’s an equation
(2) ∫ − ∞ ∞ e − x 2 / 2 d x = 2 π \int_{-\infty}^\infty e^{-x^2/2} \mathrm{d}x = \sqrt{2\pi}
which we can later refer1 (2) .
The Dirac equation:
( i ／ D + m ) ψ = 0 (i\slash{D}+m)\psi =0
Here’s the table of Clifford2 ℝ
j 0 1 2 3 4 5 6 7 8 𝒞 ℓ j − ℝ ℂ ℍ ℍ ⊕ ℍ ℍ ( 2 ) ℂ ( 4 ) ℝ ( 8 ) ℝ ( 8 ) ⊕ ℝ ( 8 ) ℝ ( 16 ) 𝒞 ℓ j + ℝ ℝ ⊕ ℝ ℝ ( 2 ) ℂ ( 2 ) ℍ ( 2 ) ℍ ( 2 ) ⊕ ℍ ( 2 ) ℍ ( 4 ) ℂ ( 8 ) ℝ ( 16 )
where the generators of 𝒞 ℓ j ±
γ i γ j + γ j γ i = ± 2 δ i j \gamma_i\gamma_j +\gamma_j \gamma_i =\pm 2\delta_{i j}
and 𝒞 ℓ n + 8 ± = 𝒞 ℓ n ± ⊗ ℝ ( 16 )
(3) lim n → ∞ ∑ k = 1 n 1 k 2 = π 2 6 \lim_{n \to \infty}
\sum_{k=1}^n \frac{1}{k^2}
= \frac{\pi^2}{6}
More Examples
(4) ∇ × E ⇀ = − ∂ B ⇀ ∂ t \nabla \times \vec{E} = - \frac {\partial \vec{B}}{\partial t}
(5) ∮ B ⋅ d l = μ 0 I enc \oint \mathbf{B}\cdot \mathrm{d}\mathbf{l} = \mu_0 I_\text{enc}
H 1 ( 𝒵 , 𝒪 ( − k ) ) G = ( V , E ) w : V → [ 0,1 ]
(6) { Q i , Q j } = δ ij ℋ . \{Q_i, Q_j\} = \delta_{ij}\mathcal{H}.
Here is a groupoid 𝒢 3 ( mod 5 )
Problems?
Maybe the notation should be different than the Latex counterparts, but these do not seem to be rendering correctly (JD: They look fine to me. A font problem in your browser?) (JB: That was exactly the problem, thanks for the suggestion. The braces weren’t stretching correctly with my old fonts.):
Complicated commutative diagrams (equations in SVG)
Complicated commutative diagram, realized in SVG
1 1 1 1 Id Id A B ρ H H K K ′ ϕ 1 ϕ 2 N A N B N A ∨ N B ∨
In SU ( 3 )
Rank-2 Symmetric Tensor Representation
⊗
Fundamental Representation
=
Adjoint Representation
⊕
Rank-3 Symmetric Tensor Representation
r a + 1 = { 0 with prob. exp ( − θ r a ) max { δ r a , z } with prob. 1 − exp ( − θ r a ) r_{a+1} = \begin{cases} 0 & \text{with prob.}\quad \exp(-\theta r_a) \\
\max \lbrace \delta r_a, z \rbrace & \text{with prob.}\quad 1 - \exp(-\theta r_a) \\
\end{cases}
q a ( z ) = σ a − 1 exp [ − γ + z σ a ] q_a(z) = \sigma_a^{-1} \exp{\left[ -\frac{\gamma + z}{\sigma_a} \right]}
Linearity of Quadrature Rules
∑ i = 1 N ( α f ( x i ) + β g ( x i ) ) w i = α ∑ i = 1 N f ( x i ) w i + β ∑ i = 1 N g ( x i ) w i \sum_{i = 1}^N {\left( {\alpha f(x_i ) + \beta g(x_i )} \right)w_i } = \alpha \sum_{i = 1}^N {f(x_i )w_i } + \beta \sum_{i = 1}^N {g(x_i )w_i }
∫ a b ( α f ( x ) + β g ( x ) ) dx = α ∫ a b f ( x ) dx + β ∫ a b g ( x ) dx {\int_a^b {\left( {\alpha f(x)\, + \beta g(x)} \right)dx = } \alpha \int_a^b {f(x)\,dx} + \beta \int_a^b {g(x)\,dx} }
p 3 ( x ) = ( 1 2 ) ( x − 1 2 ) ( x − 3 4 ) ( x − 1 ) ( 1 4 − 1 2 ) ( 1 4 − 3 4 ) ( 1 4 − 1 ) + ( 1 2 ) ( x − 1 2 ) ( x − 3 4 ) ( x − 1 ) ( 1 4 − 1 2 ) ( 1 4 − 3 4 ) ( 1 4 − 1 ) + ( 1 2 ) ( x − 1 2 ) ( x − 3 4 ) ( x − 1 ) ( 1 4 − 1 2 ) ( 1 4 − 3 4 ) ( 1 4 − 1 ) + ( 1 2 ) ( x − 1 2 ) ( x − 3 4 ) ( x − 1 ) ( 1 4 − 1 2 ) ( 1 4 − 3 4 ) ( 1 4 − 1 ) p_3 (x) = \left( {\frac{1}{2}} \right)\frac{{\left( {x - \frac{1}{2}} \right)\left( {x - \frac{3}{4}} \right)\left( {x - 1} \right)}}{{\left( {\frac{1}{4} - \frac{1}{2}} \right)\left( {\frac{1}{4} - \frac{3}{4}} \right)\left( {\frac{1}{4} - 1} \right)}} + \left( {\frac{1}{2}} \right)\frac{{\left( {x - \frac{1}{2}} \right)\left( {x - \frac{3}{4}} \right)\left( {x - 1} \right)}}{{\left( {\frac{1}{4} - \frac{1}{2}} \right)\left( {\frac{1}{4} - \frac{3}{4}} \right)\left( {\frac{1}{4} - 1} \right)}} + \left( {\frac{1}{2}} \right)\frac{{\left( {x - \frac{1}{2}} \right)\left( {x - \frac{3}{4}} \right)\left( {x - 1} \right)}}{{\left( {\frac{1}{4} - \frac{1}{2}} \right)\left( {\frac{1}{4} - \frac{3}{4}} \right)\left( {\frac{1}{4} - 1} \right)}} + \left( {\frac{1}{2}} \right)\frac{{\left( {x - \frac{1}{2}} \right)\left( {x - \frac{3}{4}} \right)\left( {x - 1} \right)}}{{\left( {\frac{1}{4} - \frac{1}{2}} \right)\left( {\frac{1}{4} - \frac{3}{4}} \right)\left( {\frac{1}{4} - 1} \right)}}
P 1 ( Y ) → P 1 ( X ) ↓ ⇓ ∼ ↓ T ′ → T \array{
P_1(Y) &\to& P_1(X)
\\
\downarrow &\Downarrow^\sim& \downarrow
\\
T' &\to& T
}
Will indented code work
This should be code
And thisyep
(7)
A_n Quiver
v 1 v 2 v n 1
≡ ( U ( k ) n 1 , { v i } ) \array{\arrayopts{\rowalign{center}}\begin{svg}
A_n Quiver
v 1 v 2 v n 1
\end{svg}& \equiv \left({U(k)}^{n_1},\{v_i\}\right)}