user101214's profile - activity

It doesn't work with expr = p^s itself, or any expression containing it (I found this when looking at expr = p^s / (p^(s+1) - 1). ) I can't figure out why. (I've tried adding an addition expr_t = expr_t.subs({p^s : t}) but that doesn't catch it either.)

I am using a program that outputs elements of the symbolic ring that are rational expressions in an exponential variables $p^s$ for some prime $p$. (Specifically, it is the igusa_zeta() function from here.) For example, one possible output is

(p^(s + 3) - 1)*(p - 1)*p^(2*s)/((p^(s + 1) - 1)*(p^(2*s + 3) - 1))}.

I would like to know if there is an automated way to change to the variable $t = p^s$ such that this expression becomes $$\frac{(p^3 t - 1) (p-1) t^2}{(pt-1) (p^3 t^2 - 1)}.$$

My question is the inverse to this one. Since yesterday I have been unable to print to more than one line in the sage cloud. This is particularly annoying with matrices as the output is now squeezed into one line as in this picture. Line breaks '\n' are ignored entirely. There seems to be nothing that will force printing to a second line, other than word wrap.

I've tested this on several computers and browsers and it is the same each time. Is it a display setting that was somehow activated on my sage cloud account?

I need to evaluate $L$-functions of the form $$\sum_{n=0}^{\infty} \Big( \frac{D}{n} \Big) n^{-s}$$ at integers, where $\Big( \frac{\cdot}{\cdot} \Big)$ is the Kronecker symbol. This is apparently what quadratic_L_function__exact(k,D) does. However I find this unreliable when D is not squarefree.

For example, the value quadratic_L_function__exact(2,4) = pi^2 / 6 is not what I need; the series above is actually pi^2 / 8. However, the value quadratic_L_function__exact(2,12) = 1/18 * sqrt(3) * pi^2 seems correct. I can't tell what's going on.

That's exactly what I need, thanks!

Sage's .simplify() command is unable to simplify the expression $\sqrt{2} \cdot \sqrt{3} \cdot \sqrt{6}$: the output of both

(sqrt(6) * sqrt(3) * sqrt(2)).simplify()

and

(sqrt(6) * sqrt(3) * sqrt(2)).simplify_full()

is just sqrt(6)sqrt(3)sqrt(2) again.

Notably, (sqrt(6)sqrt(3)sqrt(2)).is_integer() also returns false.

Is there a more powerful version of the simplify command that won't get overwhelmed by an expression like this?