By hand, I computed $f(x,y) = x \oplus xy = (0, 0, 1, 0)$ since, in ascending (lexicographical) order,
$f(0,0) = 0 \\ f(0,1) = 0 \\f(1,0) = 1 \\ f(1,1) = 0$
However, using the following code on sagemath
R.<x,y> = BooleanPolynomialRing(2) B = BooleanFunction( x+x*y) B.truth_table(format='int')
The answer is
(0, 1, 0, 0). I tried with other Boolean functions of two variables and I'm getting different answers from what I calculate by hand. Another example is $f(x,y) = x$. By hand, the answer is $f = (0,0,1,1)$ but using sage, it is $(0, 1, 0, 1)$.
Is it that the order in which the bits are calculated is incorrect?
A few details for context
I'm specifically interested in the convention regarding Boolean functions. For example, there are tasks that ask to find the ANF of a boolean function given in the $f = (b_1,b_2, \ldots , b_n)$ where $b_i$ is either $0$ or $1$. In the textbooks I have checked, it is often assumed that these values are in ascending order. In this answer, for instance, the truth table was calculated in ascending order