I have this numbering problem for days, checking this website to find these https://tex.stackexchange.com/a/25212/34618 and https://tex.stackexchange.com/a/5694/34618
but these are not what I want really, because their directions would means to renew many commands for user-defined theorems, lemmas, exercises and problems, not to mention other default setting that \thechapter hack carries over to equations, figures and tables.
Here is my question.
In the chapter running head, I have
I. Chapter for heading
and what follows are many sections in the chapter body.
II. Chapter for heading
and many sections ...
III. Chapter for heading
and many sections ...
In TOC, I would like the following style.
A. Chapter name,
1.1 section,
1.2 section,
B. Chapter name,
2.1 section,
2.2 section,
C. Chapter name,
3.1 section,
3.2 section,
In short, all numbering styles (Romanic, alphabetic, numeral) are different. I can figure out how to tackle the heading problem by redefining command @makechapterhead but don't know how to deal those in TOC. Flipping through definition of l@chapter, numberline, etc, never hit me with how, thus needing guru helps.
I can foresee solving this problem may benefit different numbering styles available for non-English languages.
PS. I also know some prevailing packages may achieve this goal, but those are not what I want either.

