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MathGroup Archive 2005

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Re: How to draw elliptical curve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62766] Re: [mg62757] How to draw elliptical curve
  • From: "David Park" <djmp at earthlink.net>
  • Date: Mon, 5 Dec 2005 03:37:05 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Needs["Graphics`ImplicitPlot`"]

ImplicitPlot[y^2 == x^3 + x + 1, {x, -2, 8}, {y, -10, 10},
    PlotPoints -> 40];

Or we can make a parametric plot if we get the minimum value for x.

xmin = x /. First@Solve[x^3 + x + 1 == 0]
-(2/(3*(-9 + Sqrt[93])))^(1/3) + 
  ((1/2)*(-9 + Sqrt[93]))^(1/3)/3^(2/3)

ParametricPlot[
{{x, Sqrt[x^3 + x + 1]}, {x, -Sqrt[x^3 + x + 1]}}, {x, xmin, 6}, 
  Frame -> True,
  Axes -> False]

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 


From: Berlid [mailto:jean_lee1998id at hotmail.com]
To: mathgroup at smc.vnet.net

Hello, everyone. Here, I want to draw elliptical curve something like
y^2=x^3+x+1 in screen with Mathematica4, and I have tried ellipticExp
and EllipticLog but in vain. Could anyone tell me in detail how to draw
elliptical curves? thanks.



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