How to Use Greek Letters with `\polyset` in LaTeX

The command \polyset is provided by the LaTeX package polynom. It configures how that package handles polynomial calculations; it does not define Greek letters. To print a Greek letter, use its usual math-mode command, such as \alpha inside $...$ or \[...\].

The complication is that polynom reads polynomial expressions using its own input syntax. Its parser is not a general-purpose TeX math engine, so a control sequence like \alpha may not be accepted as the polynomial variable even though it typesets correctly in ordinary math mode. A reliable approach is to do the package calculation with a simple variable, then write the Greek-letter version in standard math notation.

Set a variable for polynom

Load the package and use \polyset to configure its variable. For example, \polyset{vars=x} sets x as the variable for the calculation. Then give the polynomial expressions to a command such as \polylongdiv.

Here is a minimal document showing a polynomial calculation with x, followed by the same identity written with \alpha:

\documentclass{article}
\usepackage{polynom}

\begin{document}

\polyset{vars=x}
\polylongdiv{x^2-1}{x-1}

The corresponding identity using a Greek letter is
\[
  \alpha^2-1=(\alpha-1)(\alpha+1).
\]

\end{document}

The polynom package is needed for \polyset and \polylongdiv. The \alpha command in the displayed identity is standard LaTeX math notation; it is not being passed to the polynomial parser. The identity holds for every value of \alpha.

Why \alpha may fail as a parser variable

There are two different jobs involved:

• Typesetting: TeX expands \alpha as a Greek symbol in math mode.
• Polynomial parsing: polynom interprets its input according to the package’s polynomial syntax and variable settings.

A command that is valid in the first context is not automatically valid in the second. For example, placing \alpha in a \polyset option or directly in a polynomial argument does not guarantee that the parser will recognize it as a variable. If the package reports an error or produces unexpected output, first replace the Greek command with a simple variable such as x and check that the calculation works.

A practical substitution method

Suppose you want to divide $\alpha^2+3\alpha+2$ by $\alpha+1$. Use the corresponding calculation with $x$:

$$\frac{x^2+3x+2}{x+1}=x+2,$$

with zero remainder. Then express the result using the intended symbol:

$$\frac{\alpha^2+3\alpha+2}{\alpha+1}=\alpha+2, \qquad \alpha\ne -1.$$

The substitution is valid because the polynomial identity $x^2+3x+2=(x+1)(x+2)$ holds for any value of the variable. The condition excludes the value that makes the denominator zero. For a long-division layout, let polynom work with x, and typeset the final Greek-letter statement separately.

Common mistakes

• Using \alpha outside math mode. Write \(\alpha\) or $\alpha$ in running text, and use \[\alpha\] for a displayed expression.
• Treating \polyset as a Greek-letter command. It configures the polynom package; use \alpha, \beta, and similar commands to print Greek letters.
• Assuming every TeX expression is valid parser input. Polynomial packages often accept a narrower syntax than ordinary LaTeX math. Test with a simple variable and a small polynomial first.
• Putting display notation into the option value. The option vars=x is a package setting, not a place to enter a complete mathematical expression.

If you need the polynomial package to display a Greek symbol directly as its variable, check the documentation for the version you are using to see whether its parser supports that token. If it does not, use a simple placeholder for the calculation and write the final result with the Greek letter in ordinary math mode.