Plot points of elliptic curve
I'm interested in plotting points of an elliptic curve over the real numbers. I'm looking to plot a few curves, but one like y^2 = x^3 + 7 would be an example of one. This is simple enough when x is positive, but when it's negative, I'm unsure how to find values. Are there any well-known algorithms for doing this?
elliptic-curves
asked Nov 22 at 7:03
babaloo
1
add a comment |
I'm interested in plotting points of an elliptic curve over the real numbers. I'm looking to plot a few curves, but one like y^2 = x^3 + 7 would be an example of one. This is simple enough when x is positive, but when it's negative, I'm unsure how to find values. Are there any well-known algorithms for doing this?
elliptic-curves
asked Nov 22 at 7:03
babaloo
1
If you have, say $x=-2$, then your equation reads $y^2=-1$. That doesn't have any solutions. Is that what you're asking about?
– Arthur
Nov 22 at 7:06
1
If you want points with real coordinates, it's simple enough to see when the right side is non negative, then for those $x$ a plus or minus squareroot gives the two $y values.
– coffeemath
Nov 22 at 7:07
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 22 at 7:07
@Arthur right, that's true. I think what I'm struggling to wrap my head around is finding points of interest that do have solutions. For instance, how far back should I go before I know that there are no solutions anymore?
– babaloo
Nov 22 at 7:16
1
You get a real point when $x^3+7ge0$, that is iff $xge-sqrt[3]7$.
– Lord Shark the Unknown
Nov 22 at 7:16
add a comment |
I'm interested in plotting points of an elliptic curve over the real numbers. I'm looking to plot a few curves, but one like y^2 = x^3 + 7 would be an example of one. This is simple enough when x is positive, but when it's negative, I'm unsure how to find values. Are there any well-known algorithms for doing this?
elliptic-curves
asked Nov 22 at 7:03
babaloo
1
I'm interested in plotting points of an elliptic curve over the real numbers. I'm looking to plot a few curves, but one like y^2 = x^3 + 7 would be an example of one. This is simple enough when x is positive, but when it's negative, I'm unsure how to find values. Are there any well-known algorithms for doing this?
elliptic-curves
elliptic-curves
asked Nov 22 at 7:03
babaloo
1
asked Nov 22 at 7:03
babaloo
1
asked Nov 22 at 7:03
babaloo
1
asked Nov 22 at 7:03
babaloo
1
asked Nov 22 at 7:03
babaloo
1
1
If you have, say $x=-2$, then your equation reads $y^2=-1$. That doesn't have any solutions. Is that what you're asking about?
– Arthur
Nov 22 at 7:06
1
If you want points with real coordinates, it's simple enough to see when the right side is non negative, then for those $x$ a plus or minus squareroot gives the two $y values.
– coffeemath
Nov 22 at 7:07
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 22 at 7:07
@Arthur right, that's true. I think what I'm struggling to wrap my head around is finding points of interest that do have solutions. For instance, how far back should I go before I know that there are no solutions anymore?
– babaloo
Nov 22 at 7:16
1
You get a real point when $x^3+7ge0$, that is iff $xge-sqrt[3]7$.
– Lord Shark the Unknown
Nov 22 at 7:16
add a comment |
If you have, say $x=-2$, then your equation reads $y^2=-1$. That doesn't have any solutions. Is that what you're asking about?
– Arthur
Nov 22 at 7:06
1
If you want points with real coordinates, it's simple enough to see when the right side is non negative, then for those $x$ a plus or minus squareroot gives the two $y values.
– coffeemath
Nov 22 at 7:07
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 22 at 7:07
@Arthur right, that's true. I think what I'm struggling to wrap my head around is finding points of interest that do have solutions. For instance, how far back should I go before I know that there are no solutions anymore?
– babaloo
Nov 22 at 7:16
1
You get a real point when $x^3+7ge0$, that is iff $xge-sqrt[3]7$.
– Lord Shark the Unknown
Nov 22 at 7:16
If you have, say $x=-2$, then your equation reads $y^2=-1$. That doesn't have any solutions. Is that what you're asking about?
– Arthur
Nov 22 at 7:06
If you have, say $x=-2$, then your equation reads $y^2=-1$. That doesn't have any solutions. Is that what you're asking about?
– Arthur
Nov 22 at 7:06
1
1
If you want points with real coordinates, it's simple enough to see when the right side is non negative, then for those $x$ a plus or minus squareroot gives the two $y values.
– coffeemath
Nov 22 at 7:07
If you want points with real coordinates, it's simple enough to see when the right side is non negative, then for those $x$ a plus or minus squareroot gives the two $y values.
– coffeemath
Nov 22 at 7:07
1
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 22 at 7:07
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 22 at 7:07
@Arthur right, that's true. I think what I'm struggling to wrap my head around is finding points of interest that do have solutions. For instance, how far back should I go before I know that there are no solutions anymore?
– babaloo
Nov 22 at 7:16
@Arthur right, that's true. I think what I'm struggling to wrap my head around is finding points of interest that do have solutions. For instance, how far back should I go before I know that there are no solutions anymore?
– babaloo
Nov 22 at 7:16
1
1
You get a real point when $x^3+7ge0$, that is iff $xge-sqrt[3]7$.
– Lord Shark the Unknown
Nov 22 at 7:16
You get a real point when $x^3+7ge0$, that is iff $xge-sqrt[3]7$.
– Lord Shark the Unknown
Nov 22 at 7:16
add a comment |
2 Answers
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Just plot the positive and negative roots:
answered Nov 22 at 7:44
David G. Stork
9,54721232
add a comment |
Welcome to MSE! If you're familiar with programming, you can compute a list of points $(x,y)$ of the curve on your own. In view of the above curve, as Lord Shark said, real-valued points fulfill $xgeq -sqrt[3]{7}$. Just loop over values $x$ and compute the $y$-values. Its easy with a computer algebra system like Maple.
answered Nov 23 at 18:07
Wuestenfux
3,1661410
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
Just plot the positive and negative roots:
answered Nov 22 at 7:44
David G. Stork
9,54721232
add a comment |
Just plot the positive and negative roots:
answered Nov 22 at 7:44
David G. Stork
9,54721232
add a comment |
Just plot the positive and negative roots:
answered Nov 22 at 7:44
David G. Stork
9,54721232
Just plot the positive and negative roots:
answered Nov 22 at 7:44
David G. Stork
9,54721232
answered Nov 22 at 7:44
David G. Stork
9,54721232
answered Nov 22 at 7:44
David G. Stork
9,54721232
answered Nov 22 at 7:44
David G. Stork
9,54721232
9,54721232
add a comment |
add a comment |
Welcome to MSE! If you're familiar with programming, you can compute a list of points $(x,y)$ of the curve on your own. In view of the above curve, as Lord Shark said, real-valued points fulfill $xgeq -sqrt[3]{7}$. Just loop over values $x$ and compute the $y$-values. Its easy with a computer algebra system like Maple.
answered Nov 23 at 18:07
Wuestenfux
3,1661410
add a comment |
Welcome to MSE! If you're familiar with programming, you can compute a list of points $(x,y)$ of the curve on your own. In view of the above curve, as Lord Shark said, real-valued points fulfill $xgeq -sqrt[3]{7}$. Just loop over values $x$ and compute the $y$-values. Its easy with a computer algebra system like Maple.
answered Nov 23 at 18:07
Wuestenfux
3,1661410
add a comment |
Welcome to MSE! If you're familiar with programming, you can compute a list of points $(x,y)$ of the curve on your own. In view of the above curve, as Lord Shark said, real-valued points fulfill $xgeq -sqrt[3]{7}$. Just loop over values $x$ and compute the $y$-values. Its easy with a computer algebra system like Maple.
answered Nov 23 at 18:07
Wuestenfux
3,1661410
Welcome to MSE! If you're familiar with programming, you can compute a list of points $(x,y)$ of the curve on your own. In view of the above curve, as Lord Shark said, real-valued points fulfill $xgeq -sqrt[3]{7}$. Just loop over values $x$ and compute the $y$-values. Its easy with a computer algebra system like Maple.
answered Nov 23 at 18:07
Wuestenfux
3,1661410
answered Nov 23 at 18:07
Wuestenfux
3,1661410
answered Nov 23 at 18:07
Wuestenfux
3,1661410
answered Nov 23 at 18:07
Wuestenfux
3,1661410
3,1661410
add a comment |
add a comment |
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If you have, say $x=-2$, then your equation reads $y^2=-1$. That doesn't have any solutions. Is that what you're asking about?
– Arthur
Nov 22 at 7:06
1
If you want points with real coordinates, it's simple enough to see when the right side is non negative, then for those $x$ a plus or minus squareroot gives the two $y values.
– coffeemath
Nov 22 at 7:07
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 22 at 7:07
@Arthur right, that's true. I think what I'm struggling to wrap my head around is finding points of interest that do have solutions. For instance, how far back should I go before I know that there are no solutions anymore?
– babaloo
Nov 22 at 7:16
1
You get a real point when $x^3+7ge0$, that is iff $xge-sqrt[3]7$.
– Lord Shark the Unknown
Nov 22 at 7:16