from manimlib.imports import *
import numpy as np
class LinearFunctional(Scene):
	def construct(self):
		big_box=Rectangle().scale(2.7)		
		box = Rectangle(height=2,width=2,color=DARK_GREY).set_fill(color=PURPLE,opacity=350)
		arrow1 = Arrow(color=RED).shift(1.8*LEFT+0.5*UP)
		arrow2 = Arrow(color=RED).shift(1.8*LEFT+0.5*DOWN)
		arrow3 = Arrow(color=GREEN).shift(0.5*UP+1.8*RIGHT)
		arrow4 = Arrow(color=GREEN).shift(0.5*DOWN+1.8*RIGHT)
		Linear = TextMobject("LINEAR",color=BLACK).scale(0.5).shift(0.2*UP)
		Functional = TextMobject("FUNCTIONAL",color=BLACK).scale(0.5).shift(0.2*DOWN)
		u = TextMobject(r"$\vec{u}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*UP)
		v = TextMobject(r"$\vec{v}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*DOWN)	
		f1 = TextMobject(r"$f_1$",color=YELLOW).scale(0.7).shift(2.8*RIGHT+0.5*UP)
		f2 = TextMobject(r"$f_2$",color=YELLOW).scale(0.7).shift(2.8*RIGHT+0.5*DOWN)		
		text = TextMobject(r"The Linear Functional is a function that takes $\vec{u}, \vec{v} \in$ V as inputs and gives the output $f_1, f_2\in$ F.").scale(0.55).shift(2*DOWN)
		self.play(ShowCreation(big_box))
		self.play(ShowCreation(box))
		self.play(ShowCreation(Linear),ShowCreation(Functional))
		self.wait(2)
		self.play(ShowCreation(arrow1),ShowCreation(u))
		self.play(ShowCreation(arrow3),ShowCreation(f1))
		self.wait(0.7)
		self.play(ShowCreation(arrow2),ShowCreation(v))
		self.play(ShowCreation(arrow4),ShowCreation(f2))		
		self.wait(1)
		self.play(ShowCreation(text))
		self.wait(4)