Math & Science ⇒ Translate from German to English

[micatske]

I just get LaTeX source code from my friend for one of the lectures in Germany. Is there any easy way to translate the German document into English?
I would like to give a example of what I am going to translate.

Code: Select all

\begin{Definition}
	Eine \textbf{parametrische Kurve} ist eine stetige Abbildung $c : I \rightarrow X$, wobei $X$ eine topologischer Raum ist. Sei $(X,d)$ darüber hinaus ein metrischer Raum. Dann definieren wir 
	\begin{equation*}\label{key}
		L(c) = \sup \left\{ \sum_{i=1}^{h} d \left( c(t_{i-1}),c(t_i) \right) \suchthat t_0 \leq t_1 \leq \cdots \leq t_k \in I \right\}.
	\end{equation*}
	als die Länge von $c$ bezüglich der Parametrisierung $h$.
\end{Definition}

Wenn $h$ verkleinert wird, kann die Länge $L(c)$ nicht kleiner werden. Eine Kurve heißt rehlifizierbar falls $L(c) < \infty$. Eine Kurve kann auch Umparametrisiert werden: Sei $\varphi : I \rightarrow \widetilde{I}$ stetig, surjektiv und monoton. Dann folgt für $t < t'$ das $\varphi(t) \leq \varphi(t')$ oder $\varphi(t') \leq \varphi(t)$. Definiere $\widetilde{c} := c \circ \varphi : \widetilde{I} \rightarrow X$ and we have $\widetilde{L}(c) = L(c)$.

[cgnieder]

I just get LaTeX source code from my friend for one of the lectures in Germany. Is there any easy way to translate the German document into English?

Do you mean automatically? Not that I know of. A good translation will always need a native speaker for the language a text is translated to.

[Stefan Kottwitz]

I hope the mathematical content is ok, because there are several mistakes in grammar in this short text, and "rehlifizierbar" doesn't exist.

For automated translation, one could process the HTML or PDF or TXT output (pdftotext) with a standard translator tool or with google translate. As Clemens, I think there's no way yet of translating directly within LaTeX markup.

Stefan

[mitrg]

I had this problem when translating long LaTeX documents from English to Russian. I wrote a tool gtexfix (https://github.com/drgulevich/gtexfix) which enables translation of .tex documents using Google Translate without breaking the LaTeX.

[Ijon Tichy]

DeepL translates the shown code block into:

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\begin{definition}
    	A \textbf{parametric curve} is a continuous figure $c : I \rightarrow X$, where $X$ is a topological space. Be $(X,d)$ beyond that a metric space. Then we define 
    	\begin{equation*}\label{key}
    		L(c) = \sup \left\{ \sum_{i=1}^{h} d \left( c(t_{i-1}),c(t_i) \right) \search t_0 \leq t_1 \leq \cdots \leq t_k \in I \right\}.
    	\end{equation}
    	than the length of $c$ with respect to the parameterization $h$.
    \end{definition}
     
    If $h$ is reduced, the length $L(c)$ cannot become smaller. A curve is called rehabilitative if $L(c) < \infty$. A curve can also be reparameterized: Be $\varphi : I \rightarrow \widetilde{I}$ steady, surjective and monotonous. Then follows for $t < t'$ the $\varphi(t) \leq \varphi(t')$ or $\varphi(t') \leq \varphi(t)$. Define $\widetilde{c} := c \circ \varphi : \widetilde{I} \rightarrow X$ and we have $\widetilde{L}(c) = L(c)$.

I can find only one syntax mistake: \end{equation*} has been changed into \end{equation}.

The free-to-use translator is limited to 5000 characters. I often use it to make a first version of translations.