Revisions to Sage: Evaluation precision for elliptic curves over p-adic fields

Space edit.

Source Link

edited Sep 23, 2018 at 3:38

2.8k
12
20

If you are willing to use another CAS system then PARI/GP can do the job:

> gp -q
? E = ellinit(ellfromeqn(-y^2 + x^3 + 23*x + 11));
? p = 257; x1 = 920547770587 + O(p^5); y1=sqrty1 = sqrt(x1^3 + 23*x1 + 11);
? ellisoncurve(E, s = [x1, y1])
1
? ellpow(E, s, 84) - s
[O(257^5), O(257^5)]
? x1
7 + 18*257 + 236*257^2 + 3*257^3 + 211*257^4 + O(257^5)
? y1
1 + 246*257 + 148*257^2 + 175*257^3 + 186*257^4 + O(257^5)

You can even use $\texttt{gp}$ from within Sage.

If you are willing to use another CAS system then PARI/GP can do the job:

> gp -q
? E = ellinit(ellfromeqn(-y^2 + x^3 + 23*x + 11));
? p = 257; x1 = 920547770587 + O(p^5); y1=sqrt(x1^3 + 23*x1 + 11);
? ellisoncurve(E, s = [x1, y1])
1
? ellpow(E, s, 84) - s
[O(257^5), O(257^5)]
? x1
7 + 18*257 + 236*257^2 + 3*257^3 + 211*257^4 + O(257^5)
? y1
1 + 246*257 + 148*257^2 + 175*257^3 + 186*257^4 + O(257^5)

You can even use $\texttt{gp}$ from within Sage.

If you are willing to use another CAS system then PARI/GP can do the job:

> gp -q
? E = ellinit(ellfromeqn(-y^2 + x^3 + 23*x + 11));
? p = 257; x1 = 920547770587 + O(p^5); y1 = sqrt(x1^3 + 23*x1 + 11);
? ellisoncurve(E, s = [x1, y1])
1
? ellpow(E, s, 84) - s
[O(257^5), O(257^5)]
? x1
7 + 18*257 + 236*257^2 + 3*257^3 + 211*257^4 + O(257^5)
? y1
1 + 246*257 + 148*257^2 + 175*257^3 + 186*257^4 + O(257^5)

You can even use $\texttt{gp}$ from within Sage.

Fixed a typo.

Source Link

edited Sep 23, 2018 at 2:38

Somos

2.8k
12
20

If you are willing to use another CAS system then PARI/GP can do the job:

> gp -q
? E = ellinit(ellfromeqn(-y^2 + x^3 + 23*x + 11));
? p = 257; x1 = 920547770587 + O(p^5); y1=sqrt(x1^3 + 23*x1 + 11);
? ellisoncurve(E, s = [x1, y1])
1
? ellpow(E, s, 84) - s]s
[O(257^5), O(257^5)]
? x1
7 + 18*257 + 236*257^2 + 3*257^3 + 211*257^4 + O(257^5)
? y1
1 + 246*257 + 148*257^2 + 175*257^3 + 186*257^4 + O(257^5)

You can even use $\texttt{gp}$ from within Sage.

If you are willing to use another CAS system then PARI/GP can do the job:

> gp -q
? E = ellinit(ellfromeqn(-y^2 + x^3 + 23*x + 11));
? p = 257; x1 = 920547770587 + O(p^5); y1=sqrt(x1^3 + 23*x1 + 11);
? ellisoncurve(E, s = [x1, y1])
1
? ellpow(E, s, 84) - s]
[O(257^5), O(257^5)]
? x1
7 + 18*257 + 236*257^2 + 3*257^3 + 211*257^4 + O(257^5)
? y1
1 + 246*257 + 148*257^2 + 175*257^3 + 186*257^4 + O(257^5)

You can even use $\texttt{gp}$ from within Sage.

If you are willing to use another CAS system then PARI/GP can do the job:

> gp -q
? E = ellinit(ellfromeqn(-y^2 + x^3 + 23*x + 11));
? p = 257; x1 = 920547770587 + O(p^5); y1=sqrt(x1^3 + 23*x1 + 11);
? ellisoncurve(E, s = [x1, y1])
1
? ellpow(E, s, 84) - s
[O(257^5), O(257^5)]
? x1
7 + 18*257 + 236*257^2 + 3*257^3 + 211*257^4 + O(257^5)
? y1
1 + 246*257 + 148*257^2 + 175*257^3 + 186*257^4 + O(257^5)

You can even use $\texttt{gp}$ from within Sage.

Light edits. Added check ellisoncurve().

Source Link

edited Sep 23, 2018 at 0:53

Somos

2.8k
12
20

If you are willing to use another CAS system then PariPARI/GP can do the job:

> gp -q
? E = ellinit(ellfromeqn(-y^2 + x^3 + 23*x + 11));
? p = 257; x1 = 920547770587 + O(p^5); y1=sqrt(x1^3 + 23*x1 + 11);
? ellisoncurve(E, s = [x1, y1];y1])
1
? ellpow(E, s, 84) - ss]
[O(257^5), O(257^5)]
? x1
7 + 18*257 + 236*257^2 + 3*257^3 + 211*257^4 + O(257^5)
? y1
1 + 246*257 + 148*257^2 + 175*257^3 + 186*257^4 + O(257^5)

You can even use "gp"$\texttt{gp}$ from within Sage.

If you are willing to use another CAS system then Pari/GP can do the job:

> gp -q
? E = ellinit(ellfromeqn(-y^2 + x^3 + 23*x + 11));
? p = 257; x1 = 920547770587 + O(p^5); y1=sqrt(x1^3 + 23*x1 + 11);
? s = [x1, y1]; ellpow(E, s, 84) - s
[O(257^5), O(257^5)]
? x1
7 + 18*257 + 236*257^2 + 3*257^3 + 211*257^4 + O(257^5)
? y1
1 + 246*257 + 148*257^2 + 175*257^3 + 186*257^4 + O(257^5)

You can even use "gp" from within Sage.

If you are willing to use another CAS system then PARI/GP can do the job:

> gp -q
? E = ellinit(ellfromeqn(-y^2 + x^3 + 23*x + 11));
? p = 257; x1 = 920547770587 + O(p^5); y1=sqrt(x1^3 + 23*x1 + 11);
? ellisoncurve(E, s = [x1, y1])
1
? ellpow(E, s, 84) - s]
[O(257^5), O(257^5)]
? x1
7 + 18*257 + 236*257^2 + 3*257^3 + 211*257^4 + O(257^5)
? y1
1 + 246*257 + 148*257^2 + 175*257^3 + 186*257^4 + O(257^5)

You can even use $\texttt{gp}$ from within Sage.

Simplify code. eliminate print().

Source Link

edited Sep 23, 2018 at 0:01

Somos

2.8k
12
20

Loading

Added values of x1,y1.

Source Link

edited Sep 22, 2018 at 23:53

Somos

2.8k
12
20

Loading

Source Link

created Sep 22, 2018 at 23:41

Somos

2.8k
12
20

Loading

Stack Exchange Network

Return to Answer