ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 14 Feb 2021 16:40:39 +0100prove an identity for any integerhttps://ask.sagemath.org/question/55699/prove-an-identity-for-any-integer/Let $n$ be a positive integer and $m = (m_1, \ldots, m_n)$ an $n$-dimensional vector of real numbers.
Let $g$ be a real number.
I want to prove, for any $n$ and $m$, an equality of the form
$$ \sum_{i=1}^n f_i (m,g) = 0 $$
where the function $f_i$ is a rational function of $m$ and $g$.
Of course it's easy to check this by substituting finite values of $n$, but is there a way in Sage to prove it for any integer?Sat, 13 Feb 2021 21:40:36 +0100https://ask.sagemath.org/question/55699/prove-an-identity-for-any-integer/Comment by Max Alekseyev for <p>Let $n$ be a positive integer and $m = (m_1, \ldots, m_n)$ an $n$-dimensional vector of real numbers.
Let $g$ be a real number.</p>
<p>I want to prove, for any $n$ and $m$, an equality of the form
$$ \sum_{i=1}^n f_i (m,g) = 0 $$
where the function $f_i$ is a rational function of $m$ and $g$.</p>
<p>Of course it's easy to check this by substituting finite values of $n$, but is there a way in Sage to prove it for any integer?</p>
https://ask.sagemath.org/question/55699/prove-an-identity-for-any-integer/?comment=55700#post-id-55700Sage supports [symbolic computations](https://doc.sagemath.org/html/en/reference/calculus/sage/calculus/calculus.html) like in this example:
sage: k, m = var('k, m')
sage: sum(1/k^4, k, 1, oo)
1/90*pi^4
sage: sum(binomial(m,k), k, 0, m)
2^mSat, 13 Feb 2021 22:01:08 +0100https://ask.sagemath.org/question/55699/prove-an-identity-for-any-integer/?comment=55700#post-id-55700Comment by rue82 for <p>Let $n$ be a positive integer and $m = (m_1, \ldots, m_n)$ an $n$-dimensional vector of real numbers.
Let $g$ be a real number.</p>
<p>I want to prove, for any $n$ and $m$, an equality of the form
$$ \sum_{i=1}^n f_i (m,g) = 0 $$
where the function $f_i$ is a rational function of $m$ and $g$.</p>
<p>Of course it's easy to check this by substituting finite values of $n$, but is there a way in Sage to prove it for any integer?</p>
https://ask.sagemath.org/question/55699/prove-an-identity-for-any-integer/?comment=55703#post-id-55703Thanks, I did see that, although in my case it just prints the sums and does not simplify them to zero.Sun, 14 Feb 2021 10:05:48 +0100https://ask.sagemath.org/question/55699/prove-an-identity-for-any-integer/?comment=55703#post-id-55703Comment by Max Alekseyev for <p>Let $n$ be a positive integer and $m = (m_1, \ldots, m_n)$ an $n$-dimensional vector of real numbers.
Let $g$ be a real number.</p>
<p>I want to prove, for any $n$ and $m$, an equality of the form
$$ \sum_{i=1}^n f_i (m,g) = 0 $$
where the function $f_i$ is a rational function of $m$ and $g$.</p>
<p>Of course it's easy to check this by substituting finite values of $n$, but is there a way in Sage to prove it for any integer?</p>
https://ask.sagemath.org/question/55699/prove-an-identity-for-any-integer/?comment=55705#post-id-55705Then it's possible that your problem is out for reach for Sage and needs to be addressed by analytic rather than computational methods. You may ask for help at https://math.stackexchange.com/Sun, 14 Feb 2021 16:40:39 +0100https://ask.sagemath.org/question/55699/prove-an-identity-for-any-integer/?comment=55705#post-id-55705