Elliptic curve over reals

*To*: mathgroup at smc.vnet.net*Subject*: [mg51596] Elliptic curve over reals*From*: "flip" <flip_alpha at safebunch.com>*Date*: Wed, 27 Oct 2004 01:53:56 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello, I am working on some elliptic curve (EC) cryptography stuff for a presentation. I have a routine that selects the the quadratic residues of an EC and than I pass that to a routine that finds the modular square roots of those QR points. Here are those two routines. *** selectQRList[a_, b_, p_] := Select[Range[p] - 1, JacobiSymbol[#^3 + a # + b, p] != -1 &]; ECPointList[a_, b_, p_, S_List] := Flatten[MapThread[Outer[List, #1, #2] &, {Partition[S, 1], SqrtModList[#^3 +a # + b, p] & /@ S}], 2]; *** Next, I want to draw the EC over the "reals" that corresponds to the ECPointList above. For example: The EC: y^2 = x^3 + 2x + 1 (mod 5) has the following solutions: sols = {{0, 1}, {0, 4}, {1, 2}, {1, 3}, {3, 1}, {3, 3}} plus the point at infinity. These points over the reals (say without moding out by mod 5) is: integerpoints = {{0, 1}, {0, -1}, {1, 2}, {1, -2}, {8, 23}, {8, -23}}; Is there any way to be able to show both these lists of points using the above routines? Thank you, Flip email: --------------flip at nethere.com******************* Remove the "-" and the "*"