American Citizen on Mon, 14 Oct 2024 01:44:22 +0200


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question on the apply function, when the return values > 1


I am using the x-coordinates to an elliptic curve and want to use the apply() function to return the points on the curve. I know the curve, c and the x-coordinates, L. However when using the ellordinate(E,x) function, usually 2 values for y are returned, not one.

? c=[0,0,0,16900,0]
%25 = [0, 0, 0, 16900, 0]

? e=ellinit(c);

? L=[5, 8, 117, 1/5, 1/8, 1/117, 9/13, 13/9, 49/128, 65/72, 72/65, 128/49, 968/14625, 1568/5329, 1805/3481, 2080/3969, 3481/1805, 3969/2080, 5329/1568, 14625/968] %27 = [5, 8, 117, 1/5, 1/8, 1/117, 9/13, 13/9, 49/128, 65/72, 72/65, 128/49, 968/14625, 1568/5329, 1805/3481, 2080/3969, 3481/1805, 3969/2080, 5329/1568, 14625/968]

? apply(x->[[130*x,ellordinate(e,130*x)[1]],[130*x,ellordinate(e,130*x)[2]]],L) %28 = [[[650, 16900], [650, -16900]], [[1040, 33800], [1040, -33800]], [[15210, 1875900], [15210, -1875900]], [[26, 676], [26, -676]], [[65/4, 4225/8], [65/4, -4225/8]], [[10/9, 3700/27], [10/9, -3700/27]], [[90, 1500], [90, -1500]], [[1690/9, 84500/27], [1690/9, -84500/27]], [[3185/64, 502775/512], [3185/64, -502775/512]], [[4225/36, 409825/216], [4225/36, -409825/216]], [[144, 2328], [144, -2328]], [[16640/49, 2298400/343], [16640/49, -2298400/343]], [[1936/225, 1289816/3375], [1936/225, -1289816/3375]], [[203840/5329, 326034800/389017], [203840/5329, -326034800/389017]], [[234650/3481, 246925900/205379], [234650/3481, -246925900/205379]], [[270400/3969, 302915600/250047], [270400/3969, -302915600/250047]], [[90506/361, 30670796/6859], [90506/361, -30670796/6859]], [[3969/16, 282303/64], [3969/16, -282303/64]], [[346385/784, 212504825/21952], [346385/784, -212504825/21952]], [[950625/484, 928887375/10648], [950625/484, -928887375/10648]]]

What I would like to see is this

%28 = [[650, 16900], [650, -16900], [1040, 33800], [1040, -33800], [15210, 1875900], [15210, -1875900], [26, 676], [26, -676], [65/4, 4225/8], [65/4, -4225/8], [10/9, 3700/27], [10/9, -3700/27], [90, 1500], [90, -1500], [1690/9, 84500/27], [1690/9, -84500/27], [3185/64, 502775/512], [3185/64, -502775/512], [4225/36, 409825/216], [4225/36, -409825/216], [144, 2328], [144, -2328], [16640/49, 2298400/343], [16640/49, -2298400/343], [1936/225, 1289816/3375], [1936/225, -1289816/3375], [203840/5329, 326034800/389017], [203840/5329, -326034800/389017], [234650/3481, 246925900/205379], [234650/3481, -246925900/205379], [270400/3969, 302915600/250047], [270400/3969, -302915600/250047], [90506/361, 30670796/6859], [90506/361, -30670796/6859], [3969/16, 282303/64], [3969/16, -282303/64], [346385/784, 212504825/21952], [346385/784, -212504825/21952], [950625/484, 928887375/10648], [950625/484, -928887375/10648]]

Is this possible when using apply() ?