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2023-11-27 11:28:22 +0100 edited question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers) I want to expand $\cos\left( \dfrac{2\pi}

2023-11-27 09:58:52 +0100 commented answer Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

I think, if it can't calc for the Fermat prime $n=257$, it wont be able to calc for the Fermat prime $n=65537$.

2023-11-27 09:55:52 +0100 edited question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers) I want to expand $\cos\left( \dfrac{2\pi}

2023-11-27 09:55:22 +0100 edited question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers) I want to expand $\cos\left( \dfrac{2\pi}

2023-11-27 09:54:06 +0100 edited question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

Expand cos(2*pi/n) for n=5, 17, 257, 65537 (Fermat prime numbers) to Radicals I want to expand $\cos\left( \dfrac{2\pi}

2023-11-27 09:53:46 +0100 edited question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals I want to expand $\cos\left( \dfrac{2\pi}{n} \right)$ for $n=5,~

2023-11-26 21:52:35 +0100 commented answer Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

@Max Alekseyev Did you test this with your code?

2023-11-26 19:03:12 +0100 commented answer Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

Thx. Works fine for n=17; but not for n=5 or n=257... (at my cocalc).

2023-11-26 19:02:36 +0100 commented answer Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

Thx. Works fine for n=17; but not for n=5 or n=257...

2023-11-26 17:21:42 +0100 edited question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

Expand cos(2*pi/n) for n=5,17, 257, 65537 to Radicals I want to expand $\cos\left( \dfrac{2\pi}{n} \right)$ for $n=5,~1

2023-11-26 14:57:47 +0100 commented question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

@Max Alekseyev Oh, I am sorry. 1) Can I use this when using online https://sagecell.sagemath.org/? 2) Could you give me

2023-11-26 14:35:22 +0100 commented question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

@Max Alekseyev I'm asking in the here about a solution with SageMath / Python. The fact that there are basically program

2023-11-26 14:35:16 +0100 commented question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

@MaxAlekseyev I'm asking in the here about a solution with SageMath / Python. The fact that there are basically programs

2023-11-26 14:01:11 +0100 asked a question Expand cos(2*pi/n) for n=5, 17, 257, 65537 to Radicals (Fermat prime numbers)

Expand cos(2*pi/n) for n=5,17, 257, 65537 to Radicals I want to expand $\cos\left( \dfrac{2\pi}{n} \right)$ for $n=5,~1

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2020-10-21 18:20:48 +0100 commented answer How to get access of a single solution from a bunch of solutions

Ah, nice ;)

2020-10-21 14:12:04 +0100 asked a question How to get access of a single solution from a bunch of solutions

I do not use the thing for longer time, so I had a question.

If I say

a,b,c,d,e,x = var('a b c d e x')
f(x)=a*x^4+b*x^3+c*x^2+d*x+e
f1(x)=diff(f(x),x)
f2(x)=diff(f(x),x,2)
sols = solve([f(0)==-2, f(2)==0,  f1(4)==0, f(4)==8,  f2(2)==0], a,b,c,d,e)
print(sols)

I get

 [
[a == (3/16), b == (-41/16), c == (87/8), d == -12, e == -2]
]

How can I have these single value separately?
That means: I want to get an output f(x) = 3/16*x^4 -41/16*x^3 +87/8*x^2 -12*x -2
(which I can copy and paste).

2020-10-21 12:56:23 +0100 commented answer Plot the solution of a system of equations

TYVM. Helps me good. ;)

2020-10-21 12:07:25 +0100 asked a question Plot the solution of a system of equations

With

a,b,c,d,e,x = var('a b c d e x')
f(x)=a*x^4+b*x^3+c*x^2+d*x+e
f1(x)=diff(f(x),x)
f2(x)=diff(f(x),x,2)
solve([f(0)==-3, f(2)==0, f2(4)==0, f1(6)==0, f(6)==4], a,b,c,d,e)

I get [[a == (-7/432), b == (43/216), c == (-5/6), d == (5/2), e == -3]]

How can I plot f(x) with these values?

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2020-04-06 13:54:57 +0100 commented answer Syntax to define a Layout of a Plot

I have to use your code in the kind
Layout = dict(frame=False, axes_labels=['$k$','$B(k,{},{})$'.format(n,float(p))]) bar_chart([binom_dist.pmf(x) for x in range(n)], **Layout)

But this way it works.

2020-04-06 13:50:54 +0100 commented answer How to get a nice bar chart?

Very good, too. :()

2020-04-06 13:50:40 +0100 marked best answer How to get a nice bar chart?

I have

image description

reset()
import scipy.stats
n = 2000
p = 0.2
binom_dist = scipy.stats.binom(n,p)
bar_chart([binom_dist.pmf(x) for x in range(n)], axes_labels=['$k$','$B(k,{},{})$'.format(n,float(p))])

How could I create something nicer, like

image description

2020-04-06 13:50:37 +0100 commented answer How to get a nice bar chart?

Very good. And yes, I note that as well. ;)

2020-04-06 13:02:48 +0100 commented answer Syntax to define a Layout of a Plot

Ah, very good! ;)

2020-04-06 13:02:37 +0100 marked best answer Syntax to define a Layout of a Plot

Just for interest:
I have

reset()
import scipy.stats
n = 2000
p = 0.2
binom_dist = scipy.stats.binom(n,p)
bar_chart([binom_dist.pmf(x) for x in range(n)], frame=True, axes_labels=['$k$','$B(k,{},{})$'.format(n,float(p))])

How could outsource the part like
Layout = frame=True, axes_labels=['$k$','$B(k,{},{})$'.format(n,float(p))]?

And then

bar_chart([binom_dist.pmf(x) for x in range(n)], Layout)