Questions tagged [mathematical-french]

For questions related to French translations of Mathematical texts and reference requests for French texts.

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French term for Overcompleteness

I am looking for the French term for the notion of overcompleteness in linear algebra. The current suggestion I have is "sursaturée", but I couldn't find the term in literature. P.S. I am ...
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What are "suites adjacentes" called in English?

In French two sequences $(a_n)$ and $(b_n)$ are called "suites adjacentes" iff: $(a_n)$ is decreasing $(b_n)$ is increasing $\lim_{n\to \infty}(a_n - b_n)$ = 0 A useful property is that ...
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English Translation of a French Theorem by Brezis

I am interested in an English translation of the French "THEOREME 24" in "Équations et inéquations non linéaires dans les espaces vectoriels en dualité" by Haïm Brézis. It states ...
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How is this random variable $Y$ defined rigorously?

I have come across this question and gave it a try. To not distort the content, I post the original question in French. On se donne $X$ une variable aléatoire tirée selon une loi de Poisson de ...
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Stochastic Systems French translation

What is the english translation for this sentence Principe du Maximum Stochastique en contrôle optimal pour des systèmes avec Changement de Régime I'm stuck in the ''Changement de Régime'' part.
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Translation of "scholie".

What is a good translation for the word "scholie"? This appears in Grothendieck, EGA III 5.1.7, and I don't know its meaning. Neither DeepL nor Google translate nor dict.leo.org know this ...
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What does p.s stand for in french ? And what does it mean in english? [closed]

Soit $X$ et $Y$ des v.a.r dindependantes et supposons que $P(X+Y=a)=1$ ou $a$ est une constante. Montrer que $X$ et $Y$ sont p.s des constantes . So unfortunately I don't know french , what does p.s ...
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The translation in french of «Layer Cake Representation»

I would like to know if there exists a generic way of referring to this identity $$\int_X |f(x)| \mathrm{d} \mu(x) = \int_0^\infty \mu\{x \in X : |f(x)| > t \} \mathrm{d} t$$ in french. In english, ...
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I am attempting the exercise on Hilbert analysis and can't wrap my head around the approach of the answer.

I am doing the last part of question 5 on this website although it is in French It can be followed easily. The question is: Assume that $H=\ell^2(N,C)$, N and C being sets of natural and complex ...
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Name of the formula for divisibility of factorials

Suppose we want to find how many factors of $7$ is in $500!$. We want to find number of factors of $7$ in $N = 500 \cdot 499 \cdot ... \cdot 7 \cdot ... \cdot 2 \cdot 1.$ Of course, we can eliminate ...
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What does $\mathscr{P}_p$ means in the following French text and identity

What does $\mathscr{P}_p$ means in the following identity: (Aubin section 5, page 13): Comme la partie principale de ${R_i^{'j}}_{kl}$, $\mathscr{P}_p({R_i^{'j}}_{kl})$ est à intégrale nulle, nous ...
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Translation of the classic Floquet theory paper

It [1] is a highly cited seminal paper for the Floquet theory, so I guess this paper has already been translated into English. Could anyone please give me a link for it? Thanks in advance. [1] ...
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Reading a french paper: What does "L'application est bornée de H dans X" mean

In a paper by Ginibre "Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d’espace" he utilizes phrases like "des estimations linéaires assurant que l’application $\phi \...
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30 votes
6 answers
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Mathematics in Other Languages

The intention of this community wiki is to aid in learning another language in the restricted topic of mathematics. It does matter whether one wants to learn another language for mathematics or use ...
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Translation Request from French - Comparison of the reals of a topos smooth structures on an elementary topos

I've been reading on Real numbers objects in a Topos, and I want to read this article (starting page 22 on the attached PDF) the nlab references. The problem is that I don't read French, and I haven'...
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proof in English of Proposition on morphisms into affine schemes

Does anybody know where to find an English proof of the following proposition Let $(X, \mathcal{O}_X)$ be a locally ringed space, $Y = \operatorname{Spec} A$ an affine scheme. Then the natural map ...
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Translation of statement in French

Since non-mathematicians might miss some subtleties, I ask for a translation of the following statement: Soit $Y$ un processus positif, optionnel, et de la classe $(D)$, s.c.i à droite. Nous ...
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55 votes
3 answers
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What is the crime of lèse-Bourbaki?

In the foreword to his textbook Algebra, Serge Lang writes (on page vi) I have frequently committed the crime of lèse-Bourbaki by repeating short arguments or definitions to make certain sections ...
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What is the meaning of "support propre"?

At the top of page 278 in Deligne's Weil I paper, he refers to the cohomology group $H_c^i(X,\mathcal{F})$ as having "support propre". This literally translates to "proper support", but in context it ...
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How do I translate the following sentences from Deligne's Weil I?

I worry that I'm misinterpreting the mathematical content of the following sentences from Deligne's "Weil I" paper. I include each sentence in French, followed by my translation of it. Please let me ...
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21 votes
1 answer
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Roots of polynomials with bounded integer coefficients

For $a\in\mathbb N$, let $R_a\subseteq\mathbb{R}$ be the set of real roots of polynomials whose coefficients are integers with absolute value at most $a$. $$R_a=\left\{r\in\mathbb{R}\middle|\sum_{i=0}...
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4 votes
2 answers
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Where can I learn how to read math in French?

I am a graduate student at a University in USA. There is a language requirement to fulfill my grad studies, so I have to take a test that asks to translate a paragraph of a French math book to English....
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How do I translate this sentence from EGA I, part (3.6.2)?

I need some help translating the following sentence to English. It is from (3.6.2) in EGA I. Si $U,V$ sont deux ouverts non vides dans $X$, $U \cap V$ est non vide, donc $\mathcal{F}(X) \to \...
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4 votes
1 answer
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How should I translate "isomorphisme près" to English?

While reading a French mathematical text, I encountered the phrase "unique à un isomorphisme près". How should I translate "isomorphisme près" to English? Does it mean "canonical isomorphism"?
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1 answer
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Meaning of "réduit à 0" in EGA I

In several places in EGA I (for example, statement (1.5.8), which I reproduce below), it says that a ring is "réduit à 0", which I would translate "reduced at 0", but which might also be translated "...
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Meaning of sentence in EGA I, Section 1.7.

In Section 1.7 of EGA I, we have the following: (1.7.1) Étant donné un $A$-module $M$, on appelle support de $M$ et on note $\text{Supp}(M)$ l'ensemble des idéaux premiers $\mathfrak{p}$ de ...
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1 answer
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English word for a triangle in spherical geometry with three right angles?

French has the word trirectangle and Italian the word trirettangolo, which is a term of spherical geometry meaning a triangle with 3 right angles. What is the corresponding English word?
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1 vote
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Translation of 'f agit sur C'

In a French mathematical paper I am reading, there is the following situation: let $f,\sigma:A\rightarrow A$ two group homomorphisms and there is an $N$ such that $\ker (f)\subseteq C = \ker(\sigma^N -...
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What do french mathematicians call a ray?

In the USA we are taught at a young age that a ray is a line with one end, a compromise between a line and a line segment, something like $[0,\infty)$. Is there a word for this in french? I have ...
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Show $A=\{x\in [0.1]\mid \exists\, n \in N\; \exists\, k\in \{0,\ldots, 2^{n} \}, \; x=\frac{k}{2^n} \}$ dense in [0.1]

Let $$\rm{A}=\left\{x\in [0.1]\mid \exists\, n \in \mathbb{N}\; \exists\, k\in \{0,\ldots, 2^{n} \}, \; x=\dfrac{k}{2^n} \right\} $$ Show that A is dense in $[0.1]$ $A$ is dense in $[0.1] \iff \...
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1 vote
1 answer
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Show $(1+\frac{z}{n})^{n} \underset{n \to +\infty}{\longrightarrow }e^{z}$

To show that $$z_n=\left(1+\dfrac{z}{n} \right)^{n} \underset{n \longmapsto +\infty}{\longrightarrow \exp(z)}$$ the author of textbook use the following method but there is some steps that i'm not ...
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0 votes
1 answer
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Show a prime number

Let $ n $ be a natural integer strictly greater than $ 1 $. If $ n $ is not prime, it admits a prime divisor less than or equal to $ \sqrt {n} $. How can I write an assertion expressing the ...
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6 votes
1 answer
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Translation of a theorem in French [closed]

As picture below, what is uno fonction ? I use google translate , it fail to translate it .
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1 vote
0 answers
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"Contre-module" in Bourbaki

I have seen the term "contre-module" in Bourbaki's "Algèbre, Chapitre VIII" in the first few pages. The notion sounds useful in the theory of non-commutative rings, but I couldn't google an equivalent ...
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1 vote
3 answers
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Name for a matrix similar to a companion matrix? Translating "Monogène" matrix from French

I am currently translating a research paper from French (which I do not speak well). I have made good progress with copious use of google translate & switching between French & English ...
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0 votes
2 answers
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Why $z$ is a solution of $(1)$ iff its conjugate $\bar{z}$ is a solution of $(2)$

here is an exercise with its solution from the following book EAN : $9782100727803$ Exercise: Solve equation for unknown $z$ in $\mathbb{C}$ $$(E):\quad (z^{2} + 4^{z} + 1)^{2} + (3^{z} + 5)^{2}=...
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11 votes
1 answer
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Translation of John Nash's 1962 Navier-Stokes paper

Is anyone aware of an English translation of the following paper of John Nash? John Nash, Le Probleme de Cauchy pour les equations differentielles d'un fluide general, Bulletin de la Société ...
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Express some french text into mathematical form

I would like to express those text ( Original text is in french ) into mathematical form $1$. The map $$Z\longmapsto \bar{A} \cup Z $$ is a bijection of the set of All the parts $Z$ of $A$ on the ...
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3 votes
0 answers
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Modern Books on Group Theory in German or French

Except the book of Huppert's Group Theory I (which I have read partly), I am happy to see if there are modern books on group theory in German or French which include (one or many of) the topics on ...
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1 vote
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English - French dictionary(Maths)

I would like to have an English - French dictionary for higher math ( Master, Doctorate ) . Can you suggest me some ( available online) ? Thank you in advance for your help
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2 votes
1 answer
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In French mathematics, what does "hypothèse" mean?

Of course, it seems the answer is obviously "hypothesis". However, that translation does not seem right in the following context, taken from a paper by Bernard Host. Désormais, $p > 1$ est un ...
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6 votes
1 answer
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"Clôture" vs "Fermeture" dans la littérature française

What is the difference between the two terms "clôture" and "fermeture" in mathematical contexts? For example, in topology, is it more common (or more proper) to say "la clôture de l'ensemble A" or "la ...
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3 votes
2 answers
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Who is M. Montel?

From V.I. Arnold's Experimental Mathematics: Not having achieved what they desired, they pretended to desire what they had achieved. –M. Montel Who is M. Montel? Is he related to the French ...
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the main measure

I'm looking for the following notion in english if exists, called in french "la mesure principale" ( the main measure ) Let $\theta$ be an angle in standard position the main measure for $\theta$ is ...
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1 vote
1 answer
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French Math Book PDF that is easy to translate

I have to take a french proficiency exam for my grad program and I need to provide a french math book from which my exam coordinator will choose two pages for me to translate. I was hoping for some ...
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1 vote
1 answer
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A Real Analysis book which is in both French and English Languages.

I need a real analysis book which is in both French and English languages. So, it would be great if anybody does have any idea of this issue.
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5 votes
4 answers
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Is there any difference in mathematical notations between French and English?

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 ...
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8 votes
1 answer
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Slice and comma categories in French

I have to give a presentation in French on category theory, and most of the literature I use is in English. This is not too much of a problem since most of the terms translate fairly easily. However, ...
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8 votes
2 answers
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Mathematics in French

I am pretty good at Français. But I learned mathematics in English. Trying to translate mathematical statements from English to French can often be accompanied with many errors because the way ...
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3 votes
1 answer
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Translation of 'morphisme net'?

In French, one refers to a certain 'morphisme net'. I am looking for the English translation of this. EDIT: The term appears here on p.22 Lemme 2.7.2. Unfortunately I have not been able to find the ...
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