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I am trying to simplify the following expression in sage:

(sqrt(3)/3*cos(x)+1/3*sin(x))

the resulting expression should be:

2/3*cos(pi/6-x)

.simplify_full(), trig_reduce(), or simplify_trig() cannot produce this simplification.

Is sage currently capable of doing this?

I am trying to make a function of a variable with sage for example:

f(x) = sin(x)
f(x+y)

yields:

sin(x+y)

However if It is in a matrix this no longer works:

f(x) = matrix([[sin(x)],[cos(x)]])
f(x+y)

yields:

sin(x)
cos(x)

Is this not possible or am I missing something to make this work?

I am using sage 7.3 on Ubuntu 16.04 with the aims ppa.

I was just curious as to what the current plan for notebooks in sage are. If open the sage notebook server the command windows states "Please wait while the old SageNB Notebook server starts..." But that still seems to be the default. There is also the option to use jupyter notebook. Is that going to be the new default? The ArchWiki seems to state just that: ArchWiki

To summarize, there is "the old SageNB", jupyter, and the Sage Math Cloud notebook, is there a plan for what is the default or recommended option?

In the upstream bug report it seems to have now been fixed.

@krisman thanks!

Reference this question: https://ask.sagemath.org/question/353...

Here is the evaluation of an infinite sum in sage:

var('n')
f(n) = (-1)^(n+1)/(3*n+6*(-1)^n)
sum(f(2*n)+f(2*n+1),n,0,oo)

1/3*log(2) - 7/9

Evaluating the same sum in Mathematica:

f[n_] := (-1)^(n + 1)/(3*n + 6*(-1)^n)
Sum[f[2*n] + f[2*n + 1], {n, 0, Infinity}]

1/6 (-2 + Log[4])

Sage seems to be giving an incorrect solution. Am I missing something?

That is a very good question. I am going to ask another question to see if someone knows. It seems that sage is improperly computing this sum. https://ask.sagemath.org/question/353...

I think you are looking for the roots of the polynomial:

f = x^2 - 30*x + 2817
f.roots()

which gives:

[(-36*I*sqrt(2) + 15, 1), (36*I*sqrt(2) + 15, 1)]

This would mean that your original function is equal to:

$$ x^2-30x+2817 = \left(x-(15-36 \sqrt{-2})\right)\left(x-(15+36\sqrt{-2})\right)$$

You can't get it directly, as far as I know. It seems to be a difficult sum for CAS to solve.