Generation of packing kernels

utils.py

@@ -111,6 +111,7 @@ class LinearEquationSystem:
         self._matrix = sp.zeros(size, size + 1)
         self.unknowns = unknowns
         self.next_zero_row = 0
+        self._reduced = True
 
     def copy(self):
         """Returns a copy of the equation system."""
@@ -135,6 +136,7 @@ class LinearEquationSystem:
         if rest.atoms(sp.Symbol):
             raise ValueError("Not a linear equation in the unknowns")
         self._matrix[zero_row_idx, -1] = -rest
+        self._reduced = False
 
     def add_equations(self, linear_equations):
         """Add a sequence of equations. For details see `add_equation`. """
@@ -148,18 +150,28 @@ class LinearEquationSystem:
         self._resize_if_necessary()
         self._matrix[self.next_zero_row, unknown_idx] = 1
         self.next_zero_row += 1
+        self._reduced = False
 
     def reduce(self):
         """Brings the system in reduced row echelon form."""
+        if self._reduced:
+            return
         self._matrix = self._matrix.rref()[0]
         self._update_next_zero_row()
+        self._reduced = True
 
     @property
     def matrix(self):
         """Return a matrix that represents the equation system.
         Has one column more than unknowns for the affine part."""
+        self.reduce()
         return self._matrix
 
+    @property
+    def rank(self):
+        self.reduce()
+        return self.next_zero_row
+
     def solution_structure(self):
         """Returns either 'multiple', 'none' or 'single' to indicate how many solutions the system has."""
         self.reduce()
@@ -198,4 +210,9 @@ class LinearEquationSystem:
             if any(e != 0 for e in self._matrix.row(row_to_check)):
                 break
             result -= 1
-        self.next_zero_row = result
+        self.next_zero_row = result
\ No newline at end of file
+
+
+def find_unique_solutions_with_zeros(system: LinearEquationSystem):
+    if not system.solution_structure() != 'multiple':
+        raise ValueError("Function works only for underdetermined systems")