diff --git a/libsolutil/CMakeLists.txt b/libsolutil/CMakeLists.txt
index 077d9f1e6..32aaf5264 100644
--- a/libsolutil/CMakeLists.txt
+++ b/libsolutil/CMakeLists.txt
@@ -32,6 +32,7 @@ set(sources
 	Numeric.cpp
 	Numeric.h
 	picosha2.h
+	LinearExpression.cpp
 	LinearExpression.h
 	Result.h
 	SetOnce.h
diff --git a/libsolutil/LinearExpression.cpp b/libsolutil/LinearExpression.cpp
new file mode 100644
index 000000000..487a2b43a
--- /dev/null
+++ b/libsolutil/LinearExpression.cpp
@@ -0,0 +1,124 @@
+/*
+	This file is part of solidity.
+
+	solidity is free software: you can redistribute it and/or modify
+	it under the terms of the GNU General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	solidity is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU General Public License for more details.
+
+	You should have received a copy of the GNU General Public License
+	along with solidity.  If not, see <http://www.gnu.org/licenses/>.
+*/
+// SPDX-License-Identifier: GPL-3.0
+
+#include <libsolutil/LinearExpression.h>
+
+using solidity::util;
+
+void SparseMatrix::multiplyRowByFactor(size_t _row, rational const& _factor)
+{
+	Entry* e = m_row_start[_row];
+	while (e)
+	{
+		e->value *= _factor;
+		Entry* next = e->next_in_row;
+		if (!e->value)
+			remove(*e);
+		e = next;
+	}
+}
+
+void SparseMatrix::addMultipleOfRow(size_t _sourceRow, size_t _targetRow, rational const& _factor)
+{
+	Entry* source = m_row_start[_sourceRow];
+	Entry* target = m_row_start[_targetRow];
+
+	while (source)
+	{
+		while (target && target->col < source->col)
+			target = target->next_in_row;
+		if (target && target->col == source->col)
+		{
+			target->value += _factor * source->value;
+			if (!target->value)
+			{
+				Entry* next = target->next_in_row;
+				remove(*target);
+				target = next;
+			}
+		}
+		else if (!target)
+			target = appendToRow(_targetRow, source->col, _factor * source->value);
+		else if (target->col > source->col)
+			target = prependInRow(target, source->col, _factor * source->value);
+
+		source = source->next_in_row;
+	}
+}
+
+
+void SparseMatrix::appendRow(LinearExpression const& _entries)
+{
+	Entry* prev = nullptr;
+	m_row_start.push(nullptr);
+	m_row_end.push(nullptr);
+	size_t row_nr = m_row_start.size() - 1;
+	for (auto&& [i, v]: _entries.enumerate()) {
+		if (!v)
+			continue;
+		prev = appendToRow(row_nr, i, move(v));
+
+		prev = curr;
+	}
+}
+
+void SparseMatrix::remove(Entry& _e)
+{
+	if (_e.prev_in_row)
+		_e.prev_in_row->next_in_row = _e.next_in_row;
+	else
+		m_row_start[_e.row] = _e.next_in_row;
+	if (_e.next_in_row)
+		_e.next_in_row->prev_in_row = _e.prev_in_row;
+	else
+		m_row_end[_e.row] = _e.prev_in_row;
+	if (_e.prev_in_col)
+		_e.prev_in_col->next_in_col = _e.next_in_col;
+	else
+		m_col_start[_e.col] = _e.next_in_col;
+	if (_e.next_in_col)
+		_e.next_in_col->prev_in_col = _e.prev_in_col;
+	else
+		m_col_end[_e.col] = _e.prev_in_col;
+}
+
+void SparseMatrix::appendToRow(size_t _row, size_t _column, rational _value)
+{
+	m_elements.emplace(make_unique<Element>(
+		move(_value),
+		_row,
+		_column,
+		m_row_end[_row],
+		nullptr,
+		m_column_end[i],
+		nullptr
+	));
+	Entry const* e = m_elements.back().get();
+	if (m_row_end[_row])
+		m_row_end[_row]->next_in_row = e;
+	if (!m_row_start[_row])
+		m_row_start[_row] = e;
+	if (i >= m_col_start.size())
+		m_col_start.resize(i + 1);
+	if (!m_col_start[i])
+		m_col_start[i] = e;
+	if (i >= m_col_end.size())
+		m_col_end.resize(i + 1);
+	if (!m_col_end[i])
+		m_col_end[i] = e;
+}
diff --git a/libsolutil/LinearExpression.h b/libsolutil/LinearExpression.h
index 0d5045421..75719e1ff 100644
--- a/libsolutil/LinearExpression.h
+++ b/libsolutil/LinearExpression.h
@@ -185,4 +185,41 @@ private:
 	std::vector<rational> factors;
 };
 
+class SparseMatrix
+{
+public:
+	struct Entry
+	{
+		rational value;
+		// TOOD make it 32 bit as well
+		size_t row;
+		size_t col;
+		// TODO maybe better to use 32-bit indices instead of 64-bit pointers
+		Entry* prev_in_row;
+		Entry* next_in_row;
+		Entry* prev_in_col;
+		Entry* next_in_col;
+	};
+	/// @returns (i, v) for all non-zero v in the column _column
+	void enumerateColumn(size_t _column) const;
+	/// @returns (i, v) for all non-zero v in the row _row
+	void enumerateRow(size_t _row) const;
+	void multiplyRowByFactor(size_t _row, rational const& _factor);
+	void addMultipleOfRow(size_t _sourceRow, size_t _targetRow, rational const& _factor);
+	rational entry(size_t _row, size_t _column) const;
+
+	void appendRow(LinearExpression const& _entries);
+
+private:
+
+	void remove(Entry& _entry);
+	Entry* appendToRow(size_t _row, size_t _column, rational _value);
+
+	std::vector<std::unique_ptr<Entry>> m_elements;
+	std::vector<Entry*> m_row_start;
+	std::vector<Entry*> m_col_start;
+	std::vector<Entry*> m_row_end;
+	std::vector<Entry*> m_col_end;
+};
+
 }