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2017-03-04 00:46:51 +0100 commented answer Exponential change of variables in symbolic ring

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.)

2017-03-03 06:36:54 +0100 asked a question Exponential change of variables in symbolic ring

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 $$\frac{(p^3 t - 1) (p-1) t^2}{(pt-1) (p^3 t^2 - 1)}.$$

2017-02-10 21:08:37 +0100 asked a question How to not print equations and numbers on a single line

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?

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2017-02-09 07:00:24 +0100 asked a question Behavior of quadratic_L_function__exact()

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.

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2016-10-23 22:16:21 +0100 commented answer Simplify an expression of square roots

That's exactly what I need, thanks!

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2016-10-23 21:02:30 +0100 asked a question Simplify an expression of square roots

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()


(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?