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Feb
15
comment The Group of points on the Elliptic curve $y^2=x^3+1$ over $\mathbb{F}_5$
oh CHrist! I forgot about that, thanks.
Feb
15
comment The Group of points on the Elliptic curve $y^2=x^3+1$ over $\mathbb{F}_5$
Yah Wikipedia's is a bit different. Mine's coming from Rational Points on Elliptic Curves by Silverman. But no matter what $(4,0)+(2,2)$ equals, the fact that $(0,1)+(0,1)=(0,1)$ is already nonsense.
Feb
15
revised The Group of points on the Elliptic curve $y^2=x^3+1$ over $\mathbb{F}_5$
added 4 characters in body
Feb
15
comment The Group of points on the Elliptic curve $y^2=x^3+1$ over $\mathbb{F}_5$
Well I just checked again that $2(0,1)=(0,1)$.
Feb
15
asked The Group of points on the Elliptic curve $y^2=x^3+1$ over $\mathbb{F}_5$
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
oh ok I get it.
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
But are you just substituting $\frac{1}{z}$ in for $x$? Because I get $\frac{z}{z^2+1}$.
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
I don't have any background in Riemann surfaces, could you explain your change of coordinates? I can't make sense of it.
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
Ya I've been looking for a good example to try that out, but haven't found one yet.
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
Ah I see good point.
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
Forgive my ignorance but why do we have to split it into two limits? I'm thinking of $\int_{-t}^{t}\frac{x}{x^2+1}dx$ as a specific number dependent on $t$. And that specific number is always zero for every $t$.
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
I'm not sure I quite understand what you mean by we don't know which is larger, can we not just define it to be: $\lim_{t\rightarrow\infty}\int_{-t}^{t}\frac{x}{x^2+1}dx$, which equals zero.
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
By your first statement do you just mean that we generally don't consider double sided improper integrals defined if a single side does not converge?
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
You're probably right Berci.
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
If anything I feel I'm interpreting the concept of a closed curve along the Riemann Sphere incorrectly.
Feb
15
comment Using the Residue Theorem for a contour integral along the Riemann sphere
Well not for sure, it's possible I calculated the residue incorrectly.
Feb
15
revised Using the Residue Theorem for a contour integral along the Riemann sphere
added 1 characters in body
Feb
15
asked Using the Residue Theorem for a contour integral along the Riemann sphere
Feb
2
comment The Process of Choosing Projective Axes to Put an Elliptic Curve into Weierstrass Normal Form
it's 5 o'clock, do you know where your children are?
Jan
30
accepted Proving a group isomorphism from $(S,+)$ to $(S,+')$