Re: [Bug-glpk] 0-ary slice not allowed

[Andrew Makhorin]

>> constraint
> 
>> s.t. cost {i in N, j in N} :
>>   t[i] - t[j] - sum{(i,j) in E} c[i,j] * x[i,j] >= 0;
> 
>> leads to error
> 
>> 0-ary slice not allowed
> 
>> in glpmpl01.c, function expression_list.
> 
>> My expectation was that the sum is 0 if (i,j) is not an element of E and
>> c[i,j] x[i,j] otherwise. This would be in conformance with the usual use
>> of domain parameters.
> 
> No, I do not think so. In the strong mathematical sense a composite
> index must have at least one free dummy variable; otherwise corresponding
> aggregate operator like sum has no meaning. Besides, AMPL also does not
> allow that.

Just for clarity.

Do you agree that the following notation is meaningless?

sum{(2,3) in E} c[i,j] * x[i,j]

This is exactly the same as your example: the composite index has no free
dummy variables.