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2024-05-15 21:55:05 +0200 marked best answer How to find linear dependences between rational functions
  • Assume I have a list of multivariable rational functions
  • Assume I know (or Iat least I have good reasons to hope) that there is a linear relation, let say with integer coefficients, between all these rational functions. How can I find it?

For example, let

  • C1=1/x
  • C2=1/(x+y)
  • C3=y/(x*(x+y))

then, it is easy to check that C1-C2-C3=0. However, how to find this relation automatically?

It does not seem that pari lindep can do it (which indeed is quite clear when reading pari doc):

x,y=var('x,y')
C1=1/x
C2=1/(x+y)
C3=y/(x*(x+y))
pari.lindep([C1,C2,C3])

returns

PariError: incorrect type in lindep_Xadic (t_RFRAC)

NB. Any Sagemath solution is welcome, even without using pari!

2024-05-15 14:22:16 +0200 asked a question How to find linear dependences between rational functions

How to find linear dependences between rational functions Assume I have a list of multivariable rational functions Assu

2024-05-15 14:22:14 +0200 asked a question How to find linear dependences between rational functions

How to find linear dependences between rational functions Assume I have a list of multivariable rational functions Assu

2024-05-01 21:12:55 +0200 received badge  Editor (source)
2024-05-01 21:12:55 +0200 edited question What does Gosper_term ?

What does Gosper_term ? To evaluate a hypergeometric sum $$\sum_{n=1}^{N}f(n)$$ where $f(n+1)/f(n)$ is a rational fracti

2024-05-01 17:54:05 +0200 asked a question What does Gosper_term ?

What does Gosper_term ? To evaluate a hypergeometric sum $$\sum_{n=1}^{N}f(n)$$ where $f(n+1)/f(n)$ is a rational fracti

2024-03-26 15:16:11 +0200 marked best answer Powers in modular arithmetic

How can I detect if an integer n modulo q (not necessary a prime number) is a b-power for a given integer b?

Something like Integers(q)(n).is_power(b) that would return:

  • true if there exists $k$ such that n=k^b\pmod{q}
  • false otherwise.
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2024-03-26 15:02:10 +0200 commented answer Powers in modular arithmetic

That's perfect, thanks! I had forgotten how to access pari commands...

2024-03-26 12:10:20 +0200 asked a question Powers in modular arithmetic

Powers in modular arithmetic How can I detect if an integer n modulo q (not necessary a prime number) is a b-power for a

2024-02-11 12:30:04 +0200 commented answer Improve time to plot a set of points

Thank you for your reply. However, I don't see how to change the color with the creation of a single graphical object, w

2024-02-09 12:14:03 +0200 asked a question Improve time to plot a set of points

Improve time to plot a set of points I try to draw clouds of coloured dots. The coordinates of the points are given by a

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2024-01-26 13:03:11 +0200 marked best answer Draw a list of continuously colored points

I have a list of point and use list_point to draw it. Let’s say

L=[[k,sqrt(k)] for k in range (1000)]
list_plot(L)

I'd like to color the points in a continuous way, to remember the order in which they were drawn. Let's say from the black for the first point on the list to the red for the last.

How can I achieve my goal?

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2024-01-25 18:31:09 +0200 asked a question Draw a list of continuously colored points

Draw a list of continuously colored points I have a list of point and use list_point to draw it. Let’s say L=[[k,sqrt(k