Mathematica Asked on January 2, 2022

If we have two functions $G,F:mathbb R^2tomathbb R^2$ then the mechanism

$Fcirc G(x,y)=F(G(x,y))$ gives us a new map $Fcirc G:mathbb R^2tomathbb R^2$ called its composition.

In a "schematic" view, and with two functions for an example,

we would write

$$

left(begin{array}{c}x\yend{array}right)

stackrel{G}to

left(begin{array}{c}x^2y\2yend{array}right)qquad {rm and}qquad

left(begin{array}{c}x\yend{array}right)

stackrel{F}to

left(begin{array}{c}x-y\xend{array}right)

$$

then

$$

left(begin{array}{c}x\yend{array}right)

stackrel{Fcirc G}longrightarrow

left(begin{array}{c}x^2y-2y\x^2yend{array}right).

$$

How could this process be programmed in Mathematica12?

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