Expression 36: "l" Subscript, "o" , Baseline equals StartFraction, "x" cubed Over "p" squared , EndFraction left brace, 0 less than or equal to "x" less than or equal to "p" Subscript, "d" "o" "w" "n" , Baseline , right bracelo=x3p2up0≤x≤pdown
36
band1 lower price: left parenthesis, "p" Subscript, "d" "o" "w" "n" , Baseline , StartFraction, "p" cubed Over "p" squared , EndFraction , right parenthesispdown,p3downp2up
Label:
equals=
left parenthesis, 21.5 7 7 9 8 1 7 , 12.8 1 4 9 3 4 6 , right parenthesis21.5779817,12.8149346
Expression 41: "b" equals StartFraction, "I" Subscript, 1 , Baseline Over "a" plus "f" Subscript, 1 , Baseline , EndFraction minus "g" Subscript, 1 , Baseline left brace, "p" Subscript, "d" "o" "w" "n" , Baseline less than "x" , right braceb=I1a+f1−g1pdown<x
41
AMM price with external oracle price changes
42
Expression 43: "y" equals StartFraction, left parenthesis, "a" plus "f" Subscript, 1 , Baseline , right parenthesis Over left parenthesis, "b" plus "g" Subscript, 1 , Baseline , right parenthesis , EndFraction left brace, "y" less than "u" , "p" Subscript, "u" "p" , Baseline less than "x" , right bracey=a+f1b+g1y<u,pup<x
43
AMM price equals to oracle price
44
Expression 45: "x" equals StartFraction, left parenthesis, "a" plus "f" Subscript, 1 , Baseline , right parenthesis Over left parenthesis, "b" plus "g" Subscript, 1 , Baseline , right parenthesis , EndFractionx=a+f1b+g1
45
Oracle price
46
oracle price: left parenthesis, "o" , 0 , right parenthesiso,0
Label:
equals=
left parenthesis, 28 , 0 , right parenthesis28,0
47
pool price: left parenthesis, 0 , "o" , right parenthesis0,o
Expression 54: "p" Subscript, "u" "p" 2 , Baseline equals "p" Subscript, "u" "p" , Baseline times left parenthesis, StartFraction, "A" Over "A" minus 1 , EndFraction , right parenthesispup2=pup·AA−1
equals=
36.3 3 3 3 3 3 3 3 3 336.3333333333
54
oracle upper2: left parenthesis, "p" Subscript, "u" "p" 2 , Baseline , 0 , right parenthesispup2,0
Label:
equals=
left parenthesis, 36.3 3 3 3 3 3 3 , 0 , right parenthesis36.3333333,0
Expression 58: "u" Subscript, 2 , Baseline equals StartFraction, "x" cubed Over "p" squared , EndFraction left brace, "p" Subscript, "d" "o" "w" "n" 2 , Baseline less than or equal to "x" less than or equal to "p" Subscript, "u" "p" 2 , Baseline , right braceu2=x3p2down2pdown2≤x≤pup2
58
Lower bound2 price
59
Expression 60: "b" Subscript, "q" , Baseline equals StartFraction, "p" Subscript, "u" "p" 2 , Baseline Over "x" , EndFraction left parenthesis, "A" minus 1 , right parenthesis "a" Subscript, 2 , Baseline plus StartFraction, "x" squared Over "p" Subscript, "u" "p" 2 , Baseline , EndFraction "A"bq=pup2xA−1a2+x2pup2A
60
Expression 61: "y" Subscript, 02 , Baseline equals StartFraction, "b" Subscript, "q" , Baseline plus StartRoot, left parenthesis, "b" squared plus 4 "o" "A" "a" "b" , right parenthesis , EndRoot Over 2 "o" "A" , EndFractiony02=bq+b2q+4oAab2oA
61
Expression 62: "I" Subscript, 2 , Baseline equals "x" "A" squared "y" squaredI2=xA2y202
62
Expression 63: "l" Subscript, 2 , Baseline equals StartFraction, "x" cubed Over "p" squared , EndFraction left brace, "p" Subscript, "d" "o" "w" "n" 2 , Baseline less than or equal to "x" less than or equal to "p" Subscript, "u" "p" 2 , Baseline , right bracel2=x3p2up2pdown2≤x≤pup2
63
Expression 64: "l" Subscript, 2 "o" , Baseline equals StartFraction, "x" cubed Over "p" squared , EndFraction left brace, 0 less than or equal to "x" less than or equal to "p" Subscript, "d" "o" "w" "n" 2 , Baseline , right bracel2o=x3p2up20≤x≤pdown2
64
Expression 65: "f" Subscript, 2 , Baseline equals StartFraction, "x" squared Over "p" Subscript, "u" "p" 2 , Baseline , EndFraction "A" "y" Subscript, 02 , Baseline left brace, 0 less than "x" , right bracef2=x2pup2Ay020<x
65
Expression 66: "g" Subscript, 2 , Baseline equals StartFraction, "p" Subscript, "u" "p" 2 , Baseline Over "x" , EndFraction left parenthesis, "A" minus 1 , right parenthesis "y" Subscript, 02 , Baseline left brace, 0 less than "x" , right braceg2=pup2xA−1y020<x
66
Expression 67: "a" Subscript, "m" "a" "x" 2 , Baseline equals StartFraction, "o" "A" squared "y" squared Over StartNestedFraction, "p" Subscript, "u" "p" 2 , Baseline NestedOver "o" , EndNestedFraction left parenthesis, "A" minus 1 , right parenthesis "y" Subscript, 02 , Baseline , EndFraction minus StartFraction, "o" squared Over "p" Subscript, "u" "p" 2 , Baseline , EndFraction "A" "y" Subscript, 02 , Baselineamax2=oA2y202pup2oA−1y02−o2pup2Ay02
67
Expression 68: "a" Subscript, 2 , Baseline equals 100a2=100
00
40004000
68
Expression 69: "b" Subscript, 2 , Baseline equals StartFraction, "I" Subscript, 2 , Baseline Over "a" Subscript, 2 , Baseline plus "f" Subscript, 2 , Baseline , EndFraction minus "g" Subscript, 2 , Baseline left brace, "p" Subscript, "d" "o" "w" "n" , Baseline less than "x" , right braceb2=I2a2+f2−g2pdown<x
69
Expression 70: "y" equals StartFraction, left parenthesis, "a" Subscript, 2 , Baseline plus "f" Subscript, 2 , Baseline , right parenthesis Over left parenthesis, "b" Subscript, 2 , Baseline plus "g" Subscript, 2 , Baseline , right parenthesis , EndFraction left brace, "p" Subscript, "d" "o" "w" "n" 2 , Baseline less than "x" , right bracey=a2+f2b2+g2pdown2<x
