(Obj. 1) Consider the real elliptic curve given by y? = z - 2r + 4 and the points P (0, 2) and Q = (-2,0). (a) Verify that P and Q are on the given curve. (b) Compute P+Q, showing all work and describing the process. (c) Illustrate the addition P+ Q graphically, either sketching by hand or using Desmos (or the graphing program of your preference). (d) Compute P+ P, showing all work and describing the process. (Note that your answer may not be integer-valued, and that is okay!)
(Obj. 1) Consider the real elliptic curve given by y? = z - 2r + 4 and the points P (0, 2) and Q = (-2,0). (a) Verify that P and Q are on the given curve. (b) Compute P+Q, showing all work and describing the process. (c) Illustrate the addition P+ Q graphically, either sketching by hand or using Desmos (or the graphing program of your preference). (d) Compute P+ P, showing all work and describing the process. (Note that your answer may not be integer-valued, and that is okay!)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. (Obj. 1) Consider the real elliptic curve given by
y = r – 2x + 4
and the points P = (0, 2) and Q = (-2, 0).
(a) Verify that P and Q are on the given curve.
(b) Compute P+ Q, showing all work and describing the process.
(c) Illustrate the addition P+ Q graphically, either sketching by hand or using Desmos (or the
graphing program of your preference).
(d) Compute P+ P, showing all work and describing the process. (Note that your answer may not
be integer-valued, and that is okay!)
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