How to implement the Russian typographical traditions?

As is well known, TEX uses four styles in mathematics: display (D), text (T), script (S) and script-script (SS). This style deﬁnes the size of fractions and mathematical operators, the style for how the upper and lower limits and indices are attached to mathematical operators, the default letter size used in mathematics, etc. The style in formulæ embedded in text starts from T, the style of formulæ placed in a separate block starts with D, and the styles are switched automatically in fractions, integrals, arrays, etc., as it is shown below:

Main style D T S SS

Numerators and denominators T S SS SS

Indices S S SS SS

Contrary to this scheme there are only three font scalings associated with four mathematical styles since D-mode and T-mode use letters of the same size. (It is not true for mathematical operators which are greater in D-mode than in T-mode.) Say for the document at 10 pt, D and T correspond to the font at 10 pt, S---to the font at 7 pt, SS---to the font at 5 pt.

In Russian literature there is no difference between the styles of mathematical operators embedded in text and those placed separately. But four font sizes are used instead of three: say, for the document at 10 dd these are 10 dd, 8 dd, 6 dd and 4 dd, and for the document at 12dd—12dd, 10 dd, 8 dd and 6 dd. (Russian typography is based on Didot points---it follows French traditions, not English ones,---and for this reason Russian fonts and spaces are a little bit greater.)

Switching of font sizes in mathematical books is the following:

Main size 10 8 6 4

Numerators and denominators 8 6 4 4

Indices 6 6 4 4

(For newspapers and rapid communications, it is allowed not to decrease the font size for multilevel formulæ at all.)

Suppose there is a fraction typed in display style---i. e., when 10 pt is the main font size and 7 pt is the font size for superscripts and subscripts. In TEX the numerator and denominator of this fraction are set in the 10 pt font and their subscripts and superscripts are set at 7 pt as well, but their ‘big operators’ use the \textstylemode instead of \displaystyle. The numerator and denominator of the nested fraction are set at 7 pt with the subscripts and superscripts set at 5 pt, the next level fraction sets both numerator/denominator and their subscripts/superscripts at 5 pt, more levels remain the font sizes unchanged.

In Russian mathematical publications the ﬁrst level fraction has the numerator and denominator set at 8 pt (8 dd) with subscripts and superscripts still unchanged (i. e., at 6 pt) and with big operators set in \textstyle mode. It is essential that for the nested fractions these speciﬁcations remain the same irrespective of the nesting level. (That is, switching to script style and scriptscript style takes place for nested indices, not for nested fractions, square roots, etc.)

As a result, enclosed fractions do not decrease in size so strongly as in TEX andmultilevel formulæ aremuch higher in Russian mathematics. To simulate this effect, enclosed fractions are generally typed in \displaystyle which is closer to the original style than that used in TEX. Notwithstanding don't be worry about it. In fact, LaTeX is able to work with different units, Didot points and ciceros included. We can work with those units for the layout, but I don't know how we can set up LaTeX for use them for all the typographical computations. Perhaps we need to program something, create a package or at least create a preamble where you can convert those sizes, i.e. if 1157 dd = 1238 pt, 12 dd should be 12.84 pt and then you should find a way of set this size as the normalsize and make the same with the other sizes you use. And with \newcommand and \renewcommand try to fix them all.