Re: [sage-support] The behavior of empty sums

[John H Palmieri]

On Tuesday, June 25, 2019 at 3:10:29 AM UTC-7, Peter Luschny wrote:
>
> Am Di., 25. Juni 2019 um 10:49 Uhr 'luisfe' :
>
> | When n =0, k ranges from 0 to -1 so there is no k and the list 
> constructed in ib(n,m) 
> |  is just the empty list. Not an empty list of polynomials, just an empty 
> list.
>
> Well, then the way 'sum' is implemented is possibly improvable?
>
> The type information for "binomial(m*n-1, m*k)*polynomial(m,k)" 
> is there, regardless of what the value of the integers m, n, and k is.
>

No, it's not there, that's the problem. Do this:

sage: def list_polys(m, n): return [binomial(m*n-1, 
m*k)*cyclotomic_polynomial(m*(k+1)) for k in (0..n-1)]
sage: list_polys(2,0)
[]

Python evaluates the argument inside sum(...) before applying the sum 
function to it. In this case, it gets an empty list, and so has no way of 
knowing whether it came from a polynomial or anything else. I'm not sure 
what behavior would improve this. If you wanted to try to parse the 
arguments and determine that the expression binomial(m*n-1, 
m*k)*cyclotomic_polynomial(m*(k+1)) was supposed to be a polynomial, you 
need to plug in actual numbers for m, n, and k: Python functions don't have 
defined output types, so you can't tell what "cyclomic_polynomial(m*(k+1))" 
will be until you plug in numbers. In this case, m=2 and n=0, but what 
value should you plug in for k? I can imagine situations where plugging in 
k=0 is right but k=-1 is wrong, and vice versa, so what would a good 
default be?

Sage's solution, as pointed out by slelievre, seems like the right choice.

 

> (The definition of 'polynomial' here does not matter as long as it is a 
> polynomial.) 
>
> To see this try this:
>
> def ib(m, n): 
> R = ZZ['x']
> p = lambda m,n,k: binomial(m*n-1, m*k)*cyclotomic_polynomial(m*(k+1))
> print type(R(p(2,n,0)))
> return [p(m,n,k) for k in (0..n-1)]
>
> for n in (0..3): 
> r = ib(2,n)
> print(type(r), r)
>
> The output includes in *all* cases
>  'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>
>
> So why not use this information to return the zero of this ring if the sum 
> range (a..b) has not a <= b? 
>
>

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Re: [sage-support] The behavior of empty sums

[Peter Luschny]

Am Di., 25. Juni 2019 um 11:29 Uhr schrieb slelievre <
samuel.lelie...@gmail.com>:

> So, replace
>
> sum(binomial(m*n-1, m*k)*OmegaPolynomial(m,k) for k in (0..n-1))
>
> by
>
> sum((binomial(m*n-1, m*k)*OmegaPolynomial(m, k) for k in (0 .. n-1)),
> RR['x'].zero())
>

Now, this is clever! Yes, this works, although I wished this would work
automatically.

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Re: [sage-support] The behavior of empty sums

[Peter Luschny]

Am Di., 25. Juni 2019 um 10:49 Uhr 'luisfe' :

| When n =0, k ranges from 0 to -1 so there is no k and the list
constructed in ib(n,m)
|  is just the empty list. Not an empty list of polynomials, just an empty
list.

Well, then the way 'sum' is implemented is possibly improvable?

The type information for "binomial(m*n-1, m*k)*polynomial(m,k)"
is there, regardless of what the value of the integers m, n, and k is.
(The definition of 'polynomial' here does not matter as long as it is a
polynomial.)

To see this try this:

def ib(m, n):
R = ZZ['x']
p = lambda m,n,k: binomial(m*n-1, m*k)*cyclotomic_polynomial(m*(k+1))
print type(R(p(2,n,0)))
return [p(m,n,k) for k in (0..n-1)]

for n in (0..3):
r = ib(2,n)
print(type(r), r)

The output includes in *all* cases


So why not use this information to return the zero of this ring if the sum
range (a..b) has not a <= b?

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Re: [sage-support] The behavior of empty sums

[slelievre]

Tue 2019-06-25 10:49:44 UTC+2, luisfe:
>
>
> On Tuesday, June 25, 2019 at 10:03:03 AM UTC+2, Peter Luschny wrote:
>>
>> How that? Look at the output above. Sage *knows* that the terms of the 
>> sum 
>> are polynomials. So it should return the zero of that ring, which is the 
>> null polynomial.
>>
>
> Not in the first case, look at what are you passing to sum as argument
>
> sage: sage: R=ZZ['x']
> sage: R=ZZ['x']
> sage: def ib(m, n): return [binomial(m*n-1, 
> m*k)*cyclotomic_polynomial(m*(k+1)) for k in (0..n-1)]
> sage: for n in (0..6):
> : print(ib(2,n))
> : 
> []
> [x + 1]
> [x + 1, 3*x^2 + 3]
> [x + 1, 10*x^2 + 10, 5*x^2 - 5*x + 5]
> [x + 1, 21*x^2 + 21, 35*x^2 - 35*x + 35, 7*x^4 + 7]
> [x + 1, 36*x^2 + 36, 126*x^2 - 126*x + 126, 84*x^4 + 84, 9*x^4 - 9*x^3 + 
> 9*x^2 - 9*x + 9]
> [x + 1, 55*x^2 + 55, 330*x^2 - 330*x + 330, 462*x^4 + 462, 165*x^4 - 
> 165*x^3 + 165*x^2 - 165*x + 165, 11*x^4 - 11*x^2 + 11]
>  
> When n =0, k ranges from 0 to -1 so there is no k and the list constructed 
> in ib(n,m) is just the empty list. Not an empty list of polynomials, just 
> an empty list.
>

This is what makes it necessary to define what the sum starts from;
here, the zero in the polynomial ring (instead of the default which is
the integer zero).

So, replace

sum(binomial(m*n-1, m*k)*OmegaPolynomial(m,k) for k in (0..n-1))

by

sum((binomial(m*n-1, m*k)*OmegaPolynomial(m, k) for k in (0 .. n-1)), 
RR['x'].zero()) 

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Re: [sage-support] The behavior of empty sums

['luisfe' via sage-support]

On Tuesday, June 25, 2019 at 10:03:03 AM UTC+2, Peter Luschny wrote:
>
> How that? Look at the output above. Sage *knows* that the terms of the sum 
> are polynomials. So it should return the zero of that ring, which is the 
> null polynomial.
>
>
Not in the first case, look at what are you passing to sum as argument

sage: sage: R=ZZ['x']
sage: R=ZZ['x']
sage: def ib(m, n): return [binomial(m*n-1, 
m*k)*cyclotomic_polynomial(m*(k+1)) for k in (0..n-1)]
sage: for n in (0..6):
: print(ib(2,n))
: 
[]
[x + 1]
[x + 1, 3*x^2 + 3]
[x + 1, 10*x^2 + 10, 5*x^2 - 5*x + 5]
[x + 1, 21*x^2 + 21, 35*x^2 - 35*x + 35, 7*x^4 + 7]
[x + 1, 36*x^2 + 36, 126*x^2 - 126*x + 126, 84*x^4 + 84, 9*x^4 - 9*x^3 + 
9*x^2 - 9*x + 9]
[x + 1, 55*x^2 + 55, 330*x^2 - 330*x + 330, 462*x^4 + 462, 165*x^4 - 
165*x^3 + 165*x^2 - 165*x + 165, 11*x^4 - 11*x^2 + 11]
 
When n =0, k ranges from 0 to -1 so there is no k and the list constructed 
in ib(n,m) is just the empty list. Not an empty list of polynomials, just 
an empty list.

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Re: [sage-support] The behavior of empty sums

[slelievre]

Would you share the definition of OmegaPolynomial?
This would help figure out / explain what the issue is.

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Re: [sage-support] The behavior of empty sums

[Peter Luschny]

Am Montag, 17. Juni 2019 14:27:40 UTC+2 schrieb luisfe:
>
> On Mon, Jun 17, 2019 at 5:18 AM Peter Luschny  wrote:
>>
>>> def ib(m, n): return sum(binomial(m*n-1, m*k)*OmegaPolynomial(m,k) for k 
>>> in (0..n-1))
>>>
>>> The terms "binomial(m*n-1, m*k)*OmegaPolynomial(m,k)" are of type 
>>> >> 'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'
>>>
>>
>> But shouldn't it return the null polynomial in this case? 
>> And isn't the null polynomial represented by the empty list? 
>>
>> No, because sum has no way to know that you are expecting a polynomial.
>

How that? Look at the output above. Sage *knows* that the terms of the sum 
are polynomials. So it should return the zero of that ring, which is the 
null polynomial.

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Re: [sage-support] The behavior of empty sums

[Vincent Delecroix]

The SageMath function sum accepts an optional "zero" argument precisely
for this purpose

sage: sum([], 0)
0
sage: sum([], 11)
11
sage: sum([], [])
[]

Le 17/06/2019 à 11:18, Peter Luschny a écrit :

Hi,

I think we should be confident that the sum of integers is
again an integer, the sum of rational numbers a rational number
and that the sum of polynomials is a polynomial.

With Sage this is not the case.

def ib(m, n): return sum(binomial(m*n-1, m*k)*OmegaPolynomial(m,k) for k in
(0..n-1))

The terms "binomial(m*n-1, m*k)*OmegaPolynomial(m,k)" are of type


However "for n in (0..6): print(ib(2, n).list())" yields an
AttributeError: 'int' object has no attribute 'list'.

OK, it is not difficult to work around this.
But would you agree to call this behavior a bug?



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Re: [sage-support] The behavior of empty sums

['luisfe' via sage-support]

On Monday, June 17, 2019 at 2:12:58 PM UTC+2, Peter Luschny wrote:

As I see it the problem is that the sum runs over (0..n-1).
> Thus for n = 0 it returns by convention the integer 0 for the
> empty sum (is this correct?) which of course has no list.
>
> But shouldn't it return the null polynomial in this case? 
> And isn't the null polynomial represented by the empty list? 
>
>
No, because sum has no way to know that you are expecting a polynomial. You 
can add a zero polynomial to make the sum over it to obtain a polynomial as 
a result. With David function:

sage: R=ZZ['x']
sage: zero = R(0)
sage: def ib(m, n): return sum([binomial(m*n-1, 
m*k)*cyclotomic_polynomial(m*(k+1)) for k in (0..n-1)], zero)
sage: type(ib(2,2))

sage: ib(2,0)
0
sage: type(ib(2,0))

sage:  for n in (0..6): 
:print(ib(2, n).list())
:   
[]
[1, 1]
[4, 1, 3]
[16, -4, 15]
[64, -34, 56, 0, 7]
[256, -134, 171, -9, 93]
[1024, -494, 539, -165, 638]

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Re: [sage-support] The behavior of empty sums

['luisfe' via sage-support]

On Monday, June 17, 2019 at 2:12:58 PM UTC+2, Peter Luschny wrote:

As I see it the problem is that the sum runs over (0..n-1).
> Thus for n = 0 it returns by convention the integer 0 for the
> empty sum (is this correct?) which of course has no list.
>
> But shouldn't it return the null polynomial in this case? 
> And isn't the null polynomial represented by the empty list? 
>
>
No, because sum is not adding polynomials, it is adding the empty list, 
there is no way that the sum known that you are expecting a polynomial.

sage:  for n in (0..6): 
:print(ib(2, n).list())
:   
[]
[1, 1]
[4, 1, 3]
[16, -4, 15]
[64, -34, 56, 0, 7]
[256, -134, 171, -9, 93]
[1024, -494, 539, -165, 638]
sage: sum([])
0

sage: *def* *ib*(m, n): *return* sum(binomial(m*n-*1*, m*k) *for* k in (*0.*
.n-*1*))

This function should return integers, no polynomials.

If you want to return a flint polynomial, you could instruct to make the 
sum over the polynomial zero using an additional argument. With David 
function

sage: R=ZZ['x']
sage: zero = R(0)
sage: def ib(m, n): return sum([binomial(m*n-1, 
m*k)*cyclotomic_polynomial(m*(k+1)) for k in (0..n-1)], zero)
sage: type(ib(2,2))

sage: ib(2,0)
0
sage: type(ib(2,0))



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Re: [sage-support] The behavior of empty sums

[Peter Luschny]

 

> Are you saying, the error message it spits out,
>>
> AttributeError: 'int' object has no attribute 'list',
> is misleading? 
>

As I see it the problem is that the sum runs over (0..n-1).
Thus for n = 0 it returns by convention the integer 0 for the
empty sum (is this correct?) which of course has no list.

But shouldn't it return the null polynomial in this case? 
And isn't the null polynomial represented by the empty list? 

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Re: [sage-support] The behavior of empty sums

[David Joyner]

On Mon, Jun 17, 2019 at 5:38 AM Peter Luschny 
wrote:

> I don't know what OmegaPolynomial is. However, if you replace it by
>> cyclotomic_polynomial,
>> it seems to work as expected, doesn't it?
>>
>
> No, it does not. You missed the question.
>
>
>>
>> sage: *def* *ib*(m, n): *return* sum(binomial(m*n-*1*,
>> m*k)*cyclotomic_polynomial(m*(k+*1*)) *for* k in (*0.*.n-*1*))
>>
>> sage: ib(*2*,*2*)
>>
>> 3*x^2 + x + 4
>>
>> sage: type(ib(*2*,*2*))
>>
>> > 'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>
>>
>> sage: ib(*2*,*2*).list()
>> [4, 1, 3]
>>
>
> Execute
> for n in (0..6): print(ib(2, n).list()
> as indicated.
>
>

 for n in (1..6):
   print(ib(2, n).list())

works fine for me. Again, I don't know what OmegaPoly
is but my guess is that it's not defined when n=0. For example,

 for n in (0..6):
   print(ib(2, n).list())

doesn't work because the cyclotomic_poly isn't
defined at n=0. Are you saying, the error message it spits out,
AttributeError: 'int' object has no attribute 'list',
is misleading?

I guess I'm being dense this morning but I don't understand
why you think there is something wrong with the sum command.


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Re: [sage-support] The behavior of empty sums

[Peter Luschny]

>
> I don't know what OmegaPolynomial is. However, if you replace it by 
> cyclotomic_polynomial, 
> it seems to work as expected, doesn't it?
>

No, it does not. You missed the question.
 

>
> sage: *def* *ib*(m, n): *return* sum(binomial(m*n-*1*, 
> m*k)*cyclotomic_polynomial(m*(k+*1*)) *for* k in (*0.*.n-*1*))
>
> sage: ib(*2*,*2*)
>
> 3*x^2 + x + 4
>
> sage: type(ib(*2*,*2*))
>
>  'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>
>
> sage: ib(*2*,*2*).list()
> [4, 1, 3]
>

Execute 
for n in (0..6): print(ib(2, n).list()
as indicated.
  

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Re: [sage-support] The behavior of empty sums

[David Joyner]

On Mon, Jun 17, 2019 at 5:18 AM Peter Luschny 
wrote:

> Hi,
>
> I think we should be confident that the sum of integers is
> again an integer, the sum of rational numbers a rational number
> and that the sum of polynomials is a polynomial.
>
> With Sage this is not the case.
>
> def ib(m, n): return sum(binomial(m*n-1, m*k)*OmegaPolynomial(m,k) for k
> in (0..n-1))
>
> The terms "binomial(m*n-1, m*k)*OmegaPolynomial(m,k)" are of type
>  'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>
>
> However "for n in (0..6): print(ib(2, n).list())" yields an
> AttributeError: 'int' object has no attribute 'list'.
>
> OK, it is not difficult to work around this.
> But would you agree to call this behavior a bug?
>
>
I don't know what OmegaPolynomial is. However, if you replace it by
cyclotomic_polynomial,
it seems to work as expected, doesn't it?

sage: *def* *ib*(m, n): *return* sum(binomial(m*n-*1*,
m*k)*cyclotomic_polynomial(m*(k+*1*)) *for* k in (*0.*.n-*1*))

sage: ib(*2*,*2*)

3*x^2 + x + 4

sage: type(ib(*2*,*2*))



sage: ib(*2*,*2*).list()
[4, 1, 3]


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[sage-support] The behavior of empty sums

[Peter Luschny]

Hi,

I think we should be confident that the sum of integers is 
again an integer, the sum of rational numbers a rational number 
and that the sum of polynomials is a polynomial.

With Sage this is not the case.

def ib(m, n): return sum(binomial(m*n-1, m*k)*OmegaPolynomial(m,k) for k in 
(0..n-1))

The terms "binomial(m*n-1, m*k)*OmegaPolynomial(m,k)" are of type 


However "for n in (0..6): print(ib(2, n).list())" yields an
AttributeError: 'int' object has no attribute 'list'.

OK, it is not difficult to work around this. 
But would you agree to call this behavior a bug?

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