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.Fri, 21 Jul 2023 10:29:41 +0200How to compute nPr in sagemathhttps://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/
How to compute nPr in sagemath? Please helpSat, 15 Jul 2023 13:42:28 +0200https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/Comment by Max Alekseyev for <p>How to compute nPr in sagemath? Please help</p>
https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?comment=70187#post-id-70187What is nPr?Sat, 15 Jul 2023 14:45:44 +0200https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?comment=70187#post-id-70187Answer by lisbeth for <p>How to compute nPr in sagemath? Please help</p>
https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?answer=70601#post-id-70601The following method avoids computing factorials explicitly, which can be computationally expensive for large values of n and r. Instead, it computes the product of a sequence of values using a generator expression, which is more memory-efficient and faster than computing factorials. You can compute perm(n, r) using a `prod` function, which is a built-in SageMath function that computes the product of a sequence of values.
See the code:
perm(n, r) = prod(n - i for i in range(r))Fri, 21 Jul 2023 10:29:41 +0200https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?answer=70601#post-id-70601Answer by dsejas for <p>How to compute nPr in sagemath? Please help</p>
https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?answer=70189#post-id-70189Hello! I am assuming nPr means "n permutation r". Unfortunately, SageMath doesn't have a command for that purpose. However, if you remember that
$$nPr = \frac{n!}{(n-r)!} = \binom{n}{r}r!,$$
you can make something like this:
perm(n, r) = factorial(n) / factorial(n - r)
or even:
perm(n, r) = binomial(n, r) * factorial(r)
Hope this helps!Sat, 15 Jul 2023 16:20:08 +0200https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?answer=70189#post-id-70189Comment by Emmanuel Charpentier for <p>Hello! I am assuming nPr means "n permutation r". Unfortunately, SageMath doesn't have a command for that purpose. However, if you remember that</p>
<p>$$nPr = \frac{n!}{(n-r)!} = \binom{n}{r}r!,$$</p>
<p>you can make something like this:</p>
<pre><code>perm(n, r) = factorial(n) / factorial(n - r)
</code></pre>
<p>or even:</p>
<pre><code>perm(n, r) = binomial(n, r) * factorial(r)
</code></pre>
<p>Hope this helps!</p>
https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?comment=70270#post-id-70270To my surprise, the former is about 12 times faster than the latter :
sage: %timeit Permutations(5,3).cardinality()
2.31 µs ± 450 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
sage: sage: %timeit binomial(5,3)*factorial(3)
27.3 µs ± 860 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
Go figure...Sun, 16 Jul 2023 20:59:50 +0200https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?comment=70270#post-id-70270Comment by Emmanuel Charpentier for <p>Hello! I am assuming nPr means "n permutation r". Unfortunately, SageMath doesn't have a command for that purpose. However, if you remember that</p>
<p>$$nPr = \frac{n!}{(n-r)!} = \binom{n}{r}r!,$$</p>
<p>you can make something like this:</p>
<pre><code>perm(n, r) = factorial(n) / factorial(n - r)
</code></pre>
<p>or even:</p>
<pre><code>perm(n, r) = binomial(n, r) * factorial(r)
</code></pre>
<p>Hope this helps!</p>
https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?comment=70268#post-id-70268Or `binomial(n,r)*factorial(r)` ?Sun, 16 Jul 2023 20:53:45 +0200https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?comment=70268#post-id-70268Comment by Max Alekseyev for <p>Hello! I am assuming nPr means "n permutation r". Unfortunately, SageMath doesn't have a command for that purpose. However, if you remember that</p>
<p>$$nPr = \frac{n!}{(n-r)!} = \binom{n}{r}r!,$$</p>
<p>you can make something like this:</p>
<pre><code>perm(n, r) = factorial(n) / factorial(n - r)
</code></pre>
<p>or even:</p>
<pre><code>perm(n, r) = binomial(n, r) * factorial(r)
</code></pre>
<p>Hope this helps!</p>
https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?comment=70198#post-id-70198`Permutations(n,r).cardinality()` ?Sat, 15 Jul 2023 22:12:11 +0200https://ask.sagemath.org/question/70185/how-to-compute-npr-in-sagemath/?comment=70198#post-id-70198