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Pollard method for discrete logarithms (sage code) I'm trying to run the following Sage code from Introduction to Crypto

This might not work since the containment test for Sage elements does something similar, see the source code at: sage:

This might not work since the containment test for Sage elements does something similar, see the source code at: sage:

If x denotes your algebraic number, you can provide a way to reconstruct it by copying the output of: sage: sage_input(

If x denotes your algebraic number, you can provide a way to reconstruct it by copying the output of: sage: sage_input(

How do I turn on and off line numbers? I get the sage prompt, but it has no line number. Example: sage: 4+5 9 sage:%h

Partial answer : for a single representation, you can use the sum_of_k_squares function : sage: sum_of_k_squares(3, 123

Partial answer : for a single representation, you can use the sum_of_k_squares function : sage: sum_of_k_squares(3, 123

Could you please provide a concrete example of a matrix you want to deal with. The answer might depend on its parent.

Would something like the following help ? def f(n): return sum(SR.var('x_{}'.format(k))*SR.var('x_{}'.format(k+1))

Would something like the following help ? sage: def f(n): ....: return sum(SR.var('x_{}'.format(k))*SR.var('x_{}'.f

Would something like the following help ? sage: def f(n): ....: return sum(SR.var('x_{}'.format(k))SR.var('x_{}'.fo

Could you please provide the code to construct P, x and A so that we can reproduce your issue ?

You can print the endpoints of the interval: sage: print(a.endpoints()) (0.000000000000000, 1.00000000000000)

To express the fact that $t=x^2$ you can define a quotient: sage: R.<x,t> = PolynomialRing(QQ) sage: p = x^4+x^2+

To express the fact that $t=x^2$ you can define a quotient: sage: R.<x,t> = PolynomialRing(QQ) sage: p = x^4+x^2+

You have to define the polynomial ring in the undeterminate t, and then use the subs method: sage: R.<x> = Polyno

Let L denote your first list: sage: L = [['1.1 1.2 1.3'], ['2.1 2.2 2.3'], ['3.1 3.2 3.3'], ['4.1 4.2 4.3']] You can

Fixed now !

It is indeed now fixed: sage: n = var('n') sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity) 1/64*pi^2

Indeed: sage: bool(-1/2*csc(3/8*pi + x)^2/cot(3/8*pi + x) + 1/cos(1/4*pi + 2*x) == 0) False

You found a bug!! When, you call show, Sage calls view and latex functions, and the latex function produced with Z5 is t

This is now fixed: sage: h.roots(ring=G) [(a*b^2 + (a + 1)*b + a + 1, 1), (b^3 + b^2 + b + a, 1), (a*b^3 + a*b^2 + (a

This is now fixed: sage: h.roots(ring=G) [(a*b^2 + (a + 1)*b + a + 1, 1), (b^3 + b^2 + b + a, 1), (a*b^3 + a*b^2 + (a

This bug is fixed: sage: n = var('n') ....: sum(1/((2*n-1)^2*(2*n+1)^2*(2*n+3)^2), n, 0, oo) 3/256*pi^2 Setting tags

I guess this would be useless since the generation algorithm works by augment edges (see the doc of the corresponding op

The library that is used by the graphs generator is nauty, which is supposed to return non-isomorphic graphs (as graphs,

The library that is used by the graphs generator is nauty, which is supposed to return non-isomorphic graphs.

I updated my answer, thanks !

You can have a look at the questions tagged graph_generation for more details and explanations about the following, see

You can have a look at the questions tagged graph_generation for more details and explanations about the following, see

Added confirmed_bug tag, see https://ask.sagemath.org/questions/scope:all/sort:activity-desc/tags:confirmed_bug/page:1/

Do you want to achieve equiprobability of each subgraph ? If yes, first selecting the vertices and then the eges might n

How large is n ? Could you please provide a tuple (n,k) that you would like to be solved ?

How large is n ?

Is it homework ? Could you please tell us what didi you try to solve that problem ?

Is it homework ? Are the characters ρ , r and ι copy-pasted ? What is the relationship between ρx and x ?