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I am typing a document where the preset font style is Times New Roman. As a result the \mathcal fonts looks as \mathscr fonts.

Is it possible to define somehow the usual mathcal fonts (even for a particular letter only) without altering the rest of the environment?

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    Can you make a minimal working example (MWE)? – user36296 Feb 2 at 14:23
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    There are quite a few Times (New) Roman text and math fonts out there. Which ones would you be using? And, do you use pdfLaTeX, XeLaTeX, or LuaLaTeX? Please advise. – Mico Feb 2 at 15:50
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Yes. In unicode-math, you can use the command:

\setmathfont[ range={cal, bfcal},
              Scale = MatchUppercase
            ]{STIX Two Math}

Or any other math font of your choice. To get the default \mathcal alphabet, replace STIX Two Math with Latin Modern Math.

If you need to use legacy fonts, the best way to change the script alphabets is with mathalpha (formerly mathalfa). For example, you could load the package with:

\usepackage[cal = txupr]{mathalpha}

To get the TX upright \mathcal letters. You can also give the calscaled = option if necessary to make them match the height of the other fonts. Check out the manual for font specimens.

You could also load a legacy font package, for example eucal to load Euler Script as \mathcal.

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