如何在Maxima中获取3*x*y的系数？coeff函数使用遇问题

Got it, let's figure out how to grab that coefficient for you! The coeff() function in Maxima is indeed a bit picky—it’s built to work with single variables raised to a power (like x^2), not products of variables such as x*y. That’s why your initial call to coeff(3*x*y, x*y) didn’t give you the result you wanted.

Luckily, there are a couple of easy workarounds:

Method 1: Use substitution #

The simplest trick is to substitute x*y with 1 in your expression. This will strip away the product term and leave you with just the coefficient:

subst(x*y = 1, 3*x*y);

Running this will return 3—exactly what you’re after.

Method 2: Create a custom coefficient function #

If you need to do this kind of extraction often, you can define a small helper function that divides the expression by your product term and simplifies the result:

coeff_product(expr, prod) := ratsimp(expr / prod);

Then call it like this:

coeff_product(3*x*y, x*y);

The ratsimp() ensures that any messy fractions or simplifications are handled cleanly (for example, it would correctly return 3 even if your expression was 6*x*y/2).

Why your initial approach didn’t work #

Just to clarify: Maxima’s coeff(expr, var) is designed to extract coefficients for individual variables (or their powers). When you pass x*y as the second argument, Maxima doesn’t recognize it as a single "term" to match against, so it can’t pull out the coefficient. The workarounds above get around this by treating the product as a single unit either via substitution or division.

内容的提问来源于stack exchange，提问作者Kasper