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, 14 Aug 2015 16:04:10 +0200Binomial Coefficients are inconsistent with Partition Coefficientshttps://ask.sagemath.org/question/28740/binomial-coefficients-are-inconsistent-with-partition-coefficients/In Sage:
binomial(-1,-1) = 0
I have complaint about this before: [ask-sage](http://ask.sagemath.org/question/24418/the-value-of-binomial-1-1-is/) and proposed the natural binomial(x,x) = 1 for all x.
I discussed the arguments in detail at sagemath-track where I opened a [ticket](http://trac.sagemath.org/ticket/17123).
One answer was: "Having binomial(z, z) != 1 is collateral damage."
There is also the damage of inconsistency.
For me inconsistency is what this code shows:
PartitionCoefficient = lambda p: mul(binomial(p[j], p[j+1]) for j in range(len(p)-1))
for n in (0..6):
for k in (0..n):
P = Partitions(n, max_part=k, inner=[k])
print sum(PartitionCoefficient(p) for p in P), binomial(n-1,k-1)
1 0
0 0
1 1
0 0
1 1
1 1
0 0
1 1
2 2
1 1
0 0
1 1
3 3
3 3
1 1
0 0
1 1
4 4
6 6
4 4
1 1
0 0
1 1
5 5
10 10
10 10
5 5
1 1
Another said: "Apparently Maple and Mathematica use the proposed
version. Is that sufficient justification to change our version?"
*Question:* Is the internal consistency of Sage enough justification?Fri, 31 Jul 2015 14:18:25 +0200https://ask.sagemath.org/question/28740/binomial-coefficients-are-inconsistent-with-partition-coefficients/Comment by John Palmieri for <p>In Sage: </p>
<pre><code>binomial(-1,-1) = 0
</code></pre>
<p>I have complaint about this before: <a href="http://ask.sagemath.org/question/24418/the-value-of-binomial-1-1-is/">ask-sage</a> and proposed the natural binomial(x,x) = 1 for all x.</p>
<p>I discussed the arguments in detail at sagemath-track where I opened a <a href="http://trac.sagemath.org/ticket/17123">ticket</a>.</p>
<p>One answer was: "Having binomial(z, z) != 1 is collateral damage."</p>
<p>There is also the damage of inconsistency.</p>
<p>For me inconsistency is what this code shows:</p>
<pre><code>PartitionCoefficient = lambda p: mul(binomial(p[j], p[j+1]) for j in range(len(p)-1))
for n in (0..6):
for k in (0..n):
P = Partitions(n, max_part=k, inner=[k])
print sum(PartitionCoefficient(p) for p in P), binomial(n-1,k-1)
1 0
0 0
1 1
0 0
1 1
1 1
0 0
1 1
2 2
1 1
0 0
1 1
3 3
3 3
1 1
0 0
1 1
4 4
6 6
4 4
1 1
0 0
1 1
5 5
10 10
10 10
5 5
1 1
</code></pre>
<p>Another said: "Apparently Maple and Mathematica use the proposed
version. Is that sufficient justification to change our version?"</p>
<p><em>Question:</em> Is the internal consistency of Sage enough justification?</p>
https://ask.sagemath.org/question/28740/binomial-coefficients-are-inconsistent-with-partition-coefficients/?comment=28741#post-id-28741I think that the sage-devel Google group is the right place to discuss this. The ask.sagemath.org website doesn't get enough traffic to have a good discussion.Fri, 31 Jul 2015 16:40:25 +0200https://ask.sagemath.org/question/28740/binomial-coefficients-are-inconsistent-with-partition-coefficients/?comment=28741#post-id-28741Comment by vdelecroix for <p>In Sage: </p>
<pre><code>binomial(-1,-1) = 0
</code></pre>
<p>I have complaint about this before: <a href="http://ask.sagemath.org/question/24418/the-value-of-binomial-1-1-is/">ask-sage</a> and proposed the natural binomial(x,x) = 1 for all x.</p>
<p>I discussed the arguments in detail at sagemath-track where I opened a <a href="http://trac.sagemath.org/ticket/17123">ticket</a>.</p>
<p>One answer was: "Having binomial(z, z) != 1 is collateral damage."</p>
<p>There is also the damage of inconsistency.</p>
<p>For me inconsistency is what this code shows:</p>
<pre><code>PartitionCoefficient = lambda p: mul(binomial(p[j], p[j+1]) for j in range(len(p)-1))
for n in (0..6):
for k in (0..n):
P = Partitions(n, max_part=k, inner=[k])
print sum(PartitionCoefficient(p) for p in P), binomial(n-1,k-1)
1 0
0 0
1 1
0 0
1 1
1 1
0 0
1 1
2 2
1 1
0 0
1 1
3 3
3 3
1 1
0 0
1 1
4 4
6 6
4 4
1 1
0 0
1 1
5 5
10 10
10 10
5 5
1 1
</code></pre>
<p>Another said: "Apparently Maple and Mathematica use the proposed
version. Is that sufficient justification to change our version?"</p>
<p><em>Question:</em> Is the internal consistency of Sage enough justification?</p>
https://ask.sagemath.org/question/28740/binomial-coefficients-are-inconsistent-with-partition-coefficients/?comment=28792#post-id-28792gp gives
? binomial(-1,-1)
0Sun, 09 Aug 2015 12:20:41 +0200https://ask.sagemath.org/question/28740/binomial-coefficients-are-inconsistent-with-partition-coefficients/?comment=28792#post-id-28792Comment by kcrisman for <p>In Sage: </p>
<pre><code>binomial(-1,-1) = 0
</code></pre>
<p>I have complaint about this before: <a href="http://ask.sagemath.org/question/24418/the-value-of-binomial-1-1-is/">ask-sage</a> and proposed the natural binomial(x,x) = 1 for all x.</p>
<p>I discussed the arguments in detail at sagemath-track where I opened a <a href="http://trac.sagemath.org/ticket/17123">ticket</a>.</p>
<p>One answer was: "Having binomial(z, z) != 1 is collateral damage."</p>
<p>There is also the damage of inconsistency.</p>
<p>For me inconsistency is what this code shows:</p>
<pre><code>PartitionCoefficient = lambda p: mul(binomial(p[j], p[j+1]) for j in range(len(p)-1))
for n in (0..6):
for k in (0..n):
P = Partitions(n, max_part=k, inner=[k])
print sum(PartitionCoefficient(p) for p in P), binomial(n-1,k-1)
1 0
0 0
1 1
0 0
1 1
1 1
0 0
1 1
2 2
1 1
0 0
1 1
3 3
3 3
1 1
0 0
1 1
4 4
6 6
4 4
1 1
0 0
1 1
5 5
10 10
10 10
5 5
1 1
</code></pre>
<p>Another said: "Apparently Maple and Mathematica use the proposed
version. Is that sufficient justification to change our version?"</p>
<p><em>Question:</em> Is the internal consistency of Sage enough justification?</p>
https://ask.sagemath.org/question/28740/binomial-coefficients-are-inconsistent-with-partition-coefficients/?comment=28843#post-id-28843Yeah, I think this one really depends a lot upon what (or whether there is) a consensus in this field is. Is this a case of Zero factorial = 1, or of zero to the zero = 1 (even the latter there is sort of a consensus in computers, but not as broad as factorial/gamma).Fri, 14 Aug 2015 16:04:10 +0200https://ask.sagemath.org/question/28740/binomial-coefficients-are-inconsistent-with-partition-coefficients/?comment=28843#post-id-28843