Is there any difference in mathematical notations between French and English?

Question

I studied Mathematics mainly in French and now I am going to write research articles in English. I would like to know if there are some important differences in mathematical notations between French and English.

For instance, I noticed that the decimal mark in English is a dot (.) whereas in French it is a comma (,).

Answer 1

I think you know this one already, the open/closed intervals:

$\underset{\text{french}}{]a,b]} = \underset{\text{english}}{(a,b]}$ e.t.c.

Then as far as I know Corps (could be translated as Field) in French is usually not necessarily commutative, while the english expression Field always requires commutativity.

These are just two things I noticed, but I think that is already all I know, neither french nor english is my native language.

Answer 2

In traditional French typography for maths, uppercase letters and Greek letters should be upright.

Some functions names were different tg and cotg for tan and cot, sh, ch and th for sinh, cosh and tanh. The inverse trigonometric functions had an initial capital (Arcsin, instead of arcsin). The inverse hyperbolic functions are (were?) denoted argsh, argch, argth, instead of arsinh, arcosh, artanh.

In linear algebra, the transpose of a matrix is usually denoted with a prescript roman t: ${}^{\mathrm t\!}A$.

Answer 3

I have seen $\mathrm{Vect}(u_1, u_2, u_3)$ used to denote a linear subspace of $V$ generated by the vectors $u_1, u_2, u_3 \in V$, which I would normally write as $\langle u_1, u_2, u_3\rangle$.

I don't know how common $\mathrm{Vect}$ is used but here are some examples where I've seen it:

• https://math.unice.fr/~ah/ens/cours/alg10/sousesp.pdf
• https://fr.wikipedia.org/w/index.php?title=Sous-espace_vectoriel_engendr%C3%A9&oldid=178218559