Evaluation of sum function in callable expression

[BDesco]

Hello,

i'm running Sagemath 8.0 in Jupyter Notebook on Windows 10.

I'm fairly new to Sagemath.

running this:

rrun=2
h2(h2rrunrest)= binomial(h2n-rrun-h2rrunrest-1,h2rrest-h2rrunrest)+h2n
h3(h3rrest)=sum(h2(h3rrunrest,h2rrest=h3rrest,h2n=h3n),h3rrunrest,0,h3rrest)
print(h3(3,h3n=5))

works fine: result: 21

but just adding a multiplication:

rrun=2
h2(h2rrunrest)= 2*binomial(h2n-rrun-h2rrunrest-1,h2rrest-h2rrunrest)+h2n
h3(h3rrest)=sum(h2(h3rrunrest,h2rrest=h3rrest,h2n=h3n),h3rrunrest,0,h3rrest)
print(h3(3,h3n=5))

I get: sum(5, h3rrunrest, 0, 3) instead of the result 22 (5+5+5+7).

I found: https://groups.google.com/forum/#!newtopic/sage-support/sage-support/LG1xiaxA2cE

But didn't work for me. I'm not sure why.

Thanks!

[Ralf Stephan]

This looks like a bug, you get the sum unevaluated. You can as a workaround evaluate it manually. I get:

print(h3(3,h3n=5).unhold())

20

Thanks for the report.

[Ralf Stephan]

BTW instead of unhold() you can also use n() to get the value of an unevaluated definite sum.

[Ralf Stephan]

Also I think that results other than 20 are wrong for both formulae because the binomial part always amounts to binomial(2-n,3-n), i.e. zero, and you're just adding 5 four times. But I'm not 100 per cent on that.

[BDesco]

for n=3. I get binomial(-1,0) = 1

I don't know why.

Secondly the sum stays 20. But when I calculate the terms I get 5+5+5+7.

At least both results should be the same. Both 20 or both 22.

Thanks. 

[BDesco]

Sorry for my late reply. Thanks for your help.

 

unhold works fine but I could not find any documentation on it.

Bart 

[slelievre]

Tue 2017-12-26 08:03:44 UTC, BDesco:

>
> for n=3. I get binomial(-1,0) = 1
> I don't know why.

You can look at the documentation of binomial:

    sage: binomial?

You will see it indicates that the definition is extended:

    We extend this definition to include cases when [...]

and as a result, for any numerical value of x,

     binomial(x, 0)

returns 1.

[slelievre]

Tue 2017-12-26 08:04:59 UTC, BDesco:

> Sorry for my late reply. Thanks for your help.
> unhold works fine but I could not find any documentation on it.

You can get the documentation of .unhold by using ".unhold?":

    sage: k, n = SR.var('k n')

    sage: s = sum(n^5, n, 0, k, hold=True)

    sage: s

    sum(n^5, n, 0, k)

    sage: s.unhold()

    1/6*k^6 + 1/2*k^5 + 5/12*k^4 - 1/12*k^2

    sage: s.unhold?