Franklin syntax sandbox

This page is meant as a sandbox for Franklin Syntax so that you can quickly practice or experience things.

Sandbox

Write whatever you want here to practice Franklin Syntax:

using LinearAlgebra, Random
Random.seed!(135)
a, b = randn(50), randn(50)
println(dot(a, b))
println(sum(ai * bi for (ai, bi) ∈ zip(a, b)))

11.037891465873654
11.037891465873649

(yet another example that floating point arithmetics can be complicated).

\[ \forall x \in \mathbb R:\quad \langle x, x \rangle \ge 0 \]

Surely some people remember the ordering, but I always forget:

\[ \varphi(\mathbb E[X]) \le \mathbb E[\varphi(X)] \]

for \(\varphi\) convex.