solver: graph level-structure nested dissection and a fill count (George & Liu 1978)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

crates/solver/src/cholesky.rs

@@ -151,6 +151,11 @@ fn ereach(a: &UpperColumns, k: usize, parent: &[usize], stack: &mut [usize], mar
     top
 }
 
+/// The entries of the Cholesky factor of `a`'s pattern, in its own order, without values.
+pub(crate) fn factor_entries(a: &UpperColumns) -> usize {
+    symbolic(a).1.iter().sum()
+}
+
 /// The elimination tree and the entry count of each column of L, without computing values.
 fn symbolic(a: &UpperColumns) -> (Vec<usize>, Vec<usize>) {
     let parent = etree(a);