Speaking as a software developer, I would suggest you use pattern instead of form.
1.2. A regular and intelligible form or sequence discernible in the way in which something happens or is done.
The dictionary lists a complicated and vague definition, but what you call a "form" falls under this listed definition.
A less abstract definition is found in on the Wikipedia page for software design patterns:
In software engineering, a software design pattern is a general reusable solution to a commonly occurring problem within a given context in software design.
I found these mentions on the Wikipedia page for pattern:
Patterns have an underlying mathematical structure; indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern.
Mathematics is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed.
If I understand you correctly, when you say:
We recognize a u'/u form.
You actually mean
We can recognize the generalized u'/u problem, which we can solve using the generalized solution for **u'/u*.
Thus suggesting that it can be solved in the same way that you solve any u'/u problem.
If that is correct, then pattern is the correct word here:
We recognize a u'/u pattern.
Maybe it's easier to understand with a more general mathematical example:
All odd integers follow the
This example nicely proves the case why pattern fits for what you call a "form".