March 21, 2023 
Math 302 Cryptography
Spring 2023

T. Ratliff, Wheaton College
ratliff_thomas@wheatoncollege.edu

Commands used during class for E: (Y^2) = (X^3)- 2X +5,    (Subscript[P, 1])=(-2,1), (Subscript[P, 2])=(2,3)

Since Y is not a function of X, we need to use the contourplot[ ] command

ContourPlot[ y^2 == x^3 - 2x + 5, {x,-5,5},{y,-5,5},Axes->True]

p1=ContourPlot[ y^2 == x^3 - 2x + 5, {x,-5,5},{y,-5,5},Axes->True];
p2=Plot[x/2 + 2, {x,-5,5},PlotStyle->Red];
Show[p1,p2]

Notice that we use the double == since we are asserting equality of the left and right sides, not assigning the left side to be equal to the right side

Solve[ (x/2+2)^2 ==  x^3 - 2x + 5]

This is Mathematica’s syntax to substitute a value into an expression
The arrow comes from hyphen-greater than ->

x^3 - 2x + 5 /. x -> 1/4

Sqrt[%]