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

[Aurel Page <aurel.page@normalesup.org>]

Dear Randall,

On 14/10/2024 01:44, American Citizen wrote:
> 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() ?
You can simply call concat on the output.

Best,
Aurel