Functional equation

[@christophoilet]

me commenting on this from home during school hours be like

[@chicken_rice0123]

what are you doing bruh

[@chicken_rice0123]

why didn't you come

[@chicken_rice0123]

also we're playing kinetic energy in band

[@chicken_rice0123]

also in math we did a participation quiz and there's a paper homework so haha

[@chicken_rice0123]

the teacher didn't post the homework so yeah you can't get the hw

[@christophoilet]

jimmy has to cook for the AUGSAOM problem 3 because aint no way he can solve problem 10:
\[
\left\{
\begin{array}{lll}
\min\limits_{x \in \mathbb{R}^{24}} & \frac{\displaystyle \int_{0}^{\infty} \int_{0}^{x_1} \int_{0}^{x_2} \int_{0}^{x_3} \dots \int_{0}^{x_{24}} \prod_{i=1}^{24} \sin(x_i) \exp(x_i^2) \, dx_{24} \cdots dx_1}{\displaystyle \prod_{i=1}^{24} (1 + x_i^2) + \sum_{i=1}^{24} \Gamma(x_i) + \zeta(3) + \operatorname{erf}(x_{24})} \\[10pt]
\hspace{0.2cm} \text{s.t.} &
abla f(x) = \begin{bmatrix} \frac{\partial}{\partial x_1} \left( \prod_{i=1}^{24} \cos(x_i)
ight) \\ \vdots \\ \frac{\partial}{\partial x_{24}} \left( \sum_{i=1}^{24} \exp(x_i) \sin(x_i)
ight) \end{bmatrix}, \\[10pt]
& \mathbf{M}x = \begin{bmatrix} \Gamma(x_1) \\ \sin(x_2 + x_3) \\ \vdots \\ \zeta(x_{24}) \end{bmatrix}, \text{ where } \mathbf{M} \in \mathbb{R}^{24 \times 24}, \\[10pt]
& \displaystyle \sum_{i=1}^{24} x_i^2 - \prod_{i=1}^{24} x_i \leq 1, \\[10pt]
& \displaystyle \int_{0}^{\pi/2} \prod_{i=1}^{24} \sin(x_i t) dt \leq \exp\left(\sum_{i=1}^{24} x_i
ight), \\[10pt]
& x_i \geq 0, \, i = 1, 2, \dots, 24.
\end{array}

ight.
\]

[@chicken_rice0123]

hell nah i'm not doing that

[@christophoilet]

@chicken_rice0123 that's nothing compared to the equivalent AGIMO problem:
\[
\left\{
\begin{array}{lll}
\min\limits_{\mathbf{x} \in \mathbb{H}^{1024}} &
\frac{\displaystyle
\int_{0}^{\infty} \cdots \int_{0}^{x_1} \prod_{i=1}^{1024} \sin\left(x_i^2
ight) \exp\left(x_i^3
ight)
\prod_{j=1}^{1024} \cos\left(\sum_{k=1}^j x_k
ight) dx_{1024} \cdots dx_1}
{\displaystyle \prod_{i=1}^{1024} \left(1 + x_i^4
ight) + \sum_{i=1}^{1024} \Gamma(x_i) + \zeta(4) + \operatorname{erf}\left(\sum_{i=1}^{1024} x_i^2
ight)} \\[20pt]
\text{s.t.} &
abla f(\mathbf{x}) = \begin{bmatrix}
\frac{\partial}{\partial x_1} \left( \prod_{i=1}^{1024} \cos(x_i^3 + x_i) + \sum_{j=1}^{1024} \zeta(x_j)
ight) \\
\frac{\partial}{\partial x_2} \left( \prod_{k=1}^{1024} \Gamma(x_k) \sin\left(x_k^2
ight)
ight) \\
\vdots \\
\frac{\partial}{\partial x_{1024}} \left( \sum_{m=1}^{1024} x_m^5 \cos\left(x_m^2
ight) + \prod_{j=1}^{1024} \exp\left(x_j
ight)
ight)
\end{bmatrix} \\[20pt]
& \mathbf{M}_1 \mathbf{x} + \mathbf{M}_2 \mathbf{x}^2 + \mathbf{M}_3 \mathbf{x}^3 = \begin{bmatrix}
\Gamma(x_1) + \prod_{j=1}^{1024} \sin(x_j^2) \\
\sum_{k=1}^{1024} \cos(x_k^3) + \zeta(x_2) \\
\vdots \\
\prod_{p=1}^{1024} \left(\Gamma(x_p) + x_p^4
ight)
\end{bmatrix}, \quad \mathbf{M}_1, \mathbf{M}_2, \mathbf{M}_3 \in \mathbb{R}^{1024 \times 1024}, \\[20pt]
& \sum_{i=1}^{1024} x_i^3 - \prod_{i=1}^{1024} x_i^2 + \sum_{j=1}^{1024} \prod_{k=1}^j \sin(x_k^3) \leq 1, \\[20pt]
& \int_{0}^{\pi/2} \prod_{i=1}^{1024} \sin(x_i t) dt \leq \exp\left(\sum_{i=1}^{1024} x_i + \sum_{j=1}^{1024} x_j^2
ight), \\[20pt]
& \sum_{i=1}^{1024} \left(x_i^2 + \left|x_i
ight|_{\mathbb{H}}
ight) \leq 1024, \\[20pt]
& \mathbf{A} \mathbf{x} \mathbf{B} + \mathbf{C} \mathbf{x}^2 \mathbf{D} = \mathbf{x}, \quad \mathbf{A}, \mathbf{B}, \mathbf{C}, \mathbf{D} \in \mathbb{C}^{1024 \times 1024}, \\[20pt]
& \prod_{j=1}^{1024} \sum_{k=1}^j \sin\left(x_j^3 + x_k^2 + \zeta(x_k)
ight) = \zeta\left(\prod_{i=1}^{1024} x_i
ight) + \Gamma\left(\sum_{i=1}^{1024} x_i^5
ight), \\[20pt]
& \prod_{i=1}^{1024} \cos\left(\sum_{j=1}^i \prod_{k=1}^j x_k^2
ight) = \int_{0}^\infty \prod_{i=1}^{1024} \sin(x_i^3 t) dt, \\[20pt]
& x_i \geq 0, \quad i = 1, 2, \dots, 1024, \quad x_i \in \mathbb{H}.
\end{array}

ight.
\]

[@christophoilet]

@chicken_rice0123 my dad got 11/25 on the AMC 8Z

[@christophoilet]

@chicken_rice0123 my dad got 11/25 on the AMC 8Z.

[@christophoilet]

@chicken_rice0123 my dad got 11/25 on the AMC 8Z