refactor: extract math solver boundary

include/fesa/Math/SparsePattern.hpp

@@ -0,0 +1,30 @@
+#pragma once
+
+#include "fesa/Core/Types.hpp"
+
+#include <algorithm>
+#include <vector>
+
+namespace fesa {
+
+struct SparsePatternEntry {
+  EquationId row = 0;
+  EquationId col = 0;
+};
+
+struct SparsePattern {
+  EquationId equation_count = 0;
+  std::vector<SparsePatternEntry> entries;
+
+  SparseIndex nonzeroCount() const {
+    return static_cast<SparseIndex>(entries.size());
+  }
+
+  bool contains(EquationId row, EquationId col) const {
+    return std::any_of(entries.begin(), entries.end(), [&](const SparsePatternEntry& entry) {
+      return entry.row == row && entry.col == col;
+    });
+  }
+};
+
+}  // namespace fesa