Conditions on indices

Conditions on indices: $\sum\limits_{\substack{i \in I \\ i \neq \frac{n}{2}}}^n f_i$ , $\sum\limits_{i=0}^n \sum\limits_{\substack{j = 0 \\ j \neq i}}^m f_{i,j}$ , ...

Sometimes, you will see conditions added to iteration variables. These are generally written below the initial index and may use any kind of statement, that must be true. If it isn't true, then the index is skipped. Usually, these conditions are not very complicated and often even allow for a way to calculate these indices without explicitly going over each value.

The general form will look something like this:

\sum\limits_{\substack{i = 0 \\ \operatorname{p}(i)}}^n f_i

Here, $\operatorname{p}$ is any condition, for example $\operatorname{mod}(i,2) = 0$ .

Code $\sum\limits_{\substack{i = 0 \\ \operatorname{p}(i)}}^n f_i$ :

Conditions on indices: ∑i∈Ii≠n2nfi\sum\limits_{\substack{i \in I \\ i \neq \frac{n}{2}}}^n f_ii∈Ii=2n​​∑n​fi​ , ∑i=0n∑j=0j≠imfi,j\sum\limits_{i=0}^n \sum\limits_{\substack{j = 0 \\ j \neq i}}^m f_{i,j}i=0∑n​j=0j=i​∑m​fi,j​, ...

Conditions on indices: $\sum\limits_{\substack{i \in I \\ i \neq \frac{n}{2}}}^n f_i$ , $\sum\limits_{i=0}^n \sum\limits_{\substack{j = 0 \\ j \neq i}}^m f_{i,j}$ , ...