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Project: SD70
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%gp factor(2^192-1)
[ 3 2] [ 5 1] [ 7 1] [ 13 1] [ 17 1] [ 97 1] [ 193 1] [ 241 1] [ 257 1] [ 641 1] [ 673 1] [ 65537 1] [ 6700417 1] [ 22253377 1] [18446744069414584321 1]
︠fc618ecd-6c90-4ad7-8713-b40dbe3973f9︠ %var x y z g = golden_ratio; r = 4.77 p = 2 - (cos(x + g*y) + cos(x - g*y) + cos(y + g*z) + cos(y - g*z) + cos(z - g*x) + cos(z + g*x)) show(implicit_plot3d(p, (x, -r, r), (y, -r, r), (z, -r, r), plot_points=30, color='orange', mesh=1, opacity=.7), spin=1)
3D rendering not yet implemented
a = 2 + 3
5
a = plot(sin)
gp.ellanalyticrank?
File: /projects/sage/sage-6.9/local/lib/python2.7/site-packages/sage/interfaces/gp.py Signature : gp.ellanalyticrank(*args, **kwds) Docstring : ellanalyticrank(e, {eps}): returns the order of vanishing at s=1 of the L-function of the elliptic curve e and the value of the first non- zero derivative. To determine this order, it is assumed that any value less than eps is zero. If no value of eps is given, a value of half the current precision is used.