Sorry my link was private, please find here the shareable one: https://try.lokad.com/s/argmax_example

Sorry my link was private, please find here the shareable one: https://try.lokad.com/s/ranvar_buckets_example

Sorry my link was private, please find here the shareable one: https://try.lokad.com/s/hidden_characters_example

Sorry my link was private, please find here the shareable one: https://try.lokad.com/s/extend_split_example

Sorry my link was private, please find here the shareable one: https://try.lokad.com/s/substr_example

My script was private, please find here the sharable link: https://try.lokad.com/s/over_vector_example

Note that over can also be applied to any vector.
In this example: https://try.lokad.com/ku0dv1ujtnm66?tab=Output , we are computing all the sales done duriing a day before the ticket considered.

In the case of x being positive, the function returns the input text starting at the xth character. The example provided is kind of tedious with an input text of 12 characters... In this script: https://try.lokad.com/s/substr-example?tab=Output I've added a character to the input text to remove the ambiguity.

exp(x) cannot have x exceeding 87, otherwise the script would break
Note that exp(-1000) does not break but the value isn't computed, we all know it is 0 ;)

Note that a show scatter will fail if you are trying to show more than 5,000 points.

Side note on this function: if you extend.split a line not containing any of the S.Separators you will still get the line in the resulting table. This is not the same as an extend.range for instance.
Script to illustrate this case: https://try.lokad.com/s/extend.split

A very common use case is searching for hidden characters in any string (most commonly in Product references).
This script: https://try.lokad.com/s/hiddencharacters shows how we can detect special characters in order to fix any corrupted text.

Ranvars have buckets that spread over multiple values.
The first such bucket is the 65th (meaning that the probability for 65 and 66 are always the same in a ranvar), so dirac(65) actually spread over two values (65 and 66).
We have again 64 buckets with 2 values each,, and then 64 buckets with four values, etc .. so the thresholds are : 64, 196, 452, … (every one being of the form $\sum_{0..n}(64*2^n)$ )

Ranvars have buckets that spread over multiple values.
The first such bucket is the 65th (meaning that the probability for 65 and 66 are always the same in a ranvar), so dirac(65) actually spread over two values (65 and 66).
We have again 64 buckets with 2 values each,, and then 64 buckets with four values, etc .. so the thresholds are : 64, 196, 452, … (every one being of the form $\sum_{0..n}(64*2^n)$ )

Example script: https://try.lokad.com/6rk5wgpaf4mp0?tab=Output

In case of multiple T.a values, the returned T.b value is the first value encountered.
In fact, argmax is a process function scanning the table in its default order and will return different values in case of equality for two equivalent tables ordered in a different way.

This script https://try.lokad.com/5c15t7ajn1j38?tab=Code illustrates this equality management, the usage of the function and highlights the order importance with the Hat.