Several softwares/tools are available to grammar-check a document (research paper, report, book, etc.). But, all of them have trouble performing when there are inline mathematical equations in the sentences.
Do you know a grammar-check tool that does the job even when the document contains (plenty of) inline equations?
The main task I want the tool to carry out is to identify the grammatical role of the equation (i.e. as noun or as verb), and use that information to figure out grammatical errors.
Among the tools I tested, Quillbot performed better (and even that one failed at the task just mentioned).
Testing Done (this section is only for test data & test results)
To test the efficiency of grammar-check tools, I have used a number of test documents. I think the following sample text is a decent one. I have tested it on google doc, grammarly, quillbot and a few others; but, none of them found the grammatical errors.
Sample Text 1
Since $x^2-1$ is positive, $y=4x^3+2$ false is.
Hence, $x^2+2$.
Therefore, $y>x^2+2$.
Since $x<y$, $y$ is greater than $x$.
Since $x$, $y$ is not greater than $x$.
Since $z<y$, $z$ is greater not than $y$.
Since $x<z$, $x$ is greater than not $z$.
Sample Text 1
Since $x^2-1$ is positive, $y=4x^3+2$ false is. Hence, $x^2+2$. Therefore, $y>x^2+2$.
Since $x<y$, $y$ is greater than $x$. Since $x$, $y$ is not greater than $x$. Since $z<y$, $z$ is greater not than $y$. Since $x<z$, $x$ is greater than not $z$.
The corrections I expect in this sample text are the following.
Since $x^2-1$ is positive, $y=4x^3+2$ is false. ==============> Fix the word order (or at least report error) - Error 1 (E1)
Hence, $x^2+2$. ===============> Report incomplete sentence (E2)
Therefore, $y>x^2+2$.
Since $x<y$, $y$ is greater than $x$.
Since $x$, $y$ is not greater than $x$. ===============> Report incomplete phrase (E3)
Since $z<y$, $z$ is greater not than $y$. ==============> Report error (E4)
Since $x<z$, $x$ is greater than not $z$. ==============> Report error (E5)
I tested Sample Text 1 by making a pdf from a latex file with sample text 1 as content, and then following the steps described here. The following sample text is obtained from Sample Text 1 by replacing all noun equations by f(x) and all verb equations by f(x)<f(y).
Sample Text 2
Since f(x) is positive, f(x)<f(y) false is. Hence, f(x). Therefore, f(x)<f(Y).
Since f(x)<f(y), f(x) is greater than f(x). Since f(x), f(x) is not greater than f(x). Since f(x)<f(y), f(x) is greater not than f(x). Since f(x)<f(y), f(x) is greater than not f(x).
My experiecnce
For both Text Sample 1 and Text Sample 2, Quillbot performed better compared to Google Doc and Grammarly; but, Quillbot was also eager to rephrase correct sentence and thus had false positives as well.
PS: Quillbot had trouble understading the less than symbol for some reason. Quillbot produced much better results after I replaced "f(x)<f(y)" by "f(x) = f(y)".