English
The degree of X_j with respect to i is 1 if i = j and 0 otherwise (under appropriate nontriviality assumptions).
Русский
Степень X_j по i равна 1, если i = j, и 0 иначе (при соответствующих условиях не тривиальности).
LaTeX
$$$\deg_i(X_j) = \begin{cases} 1, & i = j \\ 0, & i \neq j \end{cases}$$$
Lean4
theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
degreeOf i (X j : MvPolynomial σ R) = if i = j then 1 else 0 := by
classical
by_cases c : i = j
· simp only [c, if_true, degreeOf_def, degrees_X, Multiset.count_singleton]
simp [c, degreeOf_def, degrees_X]