Fix kernel basis computation for polynomial matrix in corner case

src/sage/matrix/matrix_polynomial_dense.pyx

@@ -675,7 +675,7 @@ cdef class Matrix_polynomial_dense(Matrix_generic_dense):
             sage: M.reverse([2,3,-1])
             Traceback (most recent call last):
             ...
-            OverflowError: can't convert negative value to unsigned long
+            ValueError: degree argument must be a non-negative integer, got -1
 
         .. SEEALSO::
 
@@ -3980,6 +3980,13 @@ cdef class Matrix_polynomial_dense(Matrix_generic_dense):
             sage: Matrix(pR, 3, 2, [[x,0],[1,0],[x+1,0]]).minimal_kernel_basis()
             [6 x 0]
             [6 6 1]
+
+        TESTS:
+
+        We check that PR #37208 is fixed::
+
+            sage: Matrix(pR, 2, 0).minimal_kernel_basis().is_sparse()
+            False
         """
         from sage.matrix.constructor import matrix
 
@@ -4001,11 +4008,11 @@ cdef class Matrix_polynomial_dense(Matrix_generic_dense):
                 return matrix(self.base_ring(), 0, m)
 
             if n == 0: # early exit: kernel is identity
-                return matrix.identity(self.base_ring(), m, m)
+                return matrix.identity(self.base_ring(), m)
 
             d = self.degree() # well defined since m > 0 and n > 0
             if d == -1: # matrix is zero: kernel is identity
-                return matrix.identity(self.base_ring(), m, m)
+                return matrix.identity(self.base_ring(), m)
 
             # degree bounds on the kernel basis
             degree_bound = min(m,n)*d+max(shifts)
@@ -4040,11 +4047,11 @@ cdef class Matrix_polynomial_dense(Matrix_generic_dense):
                 return matrix(self.base_ring(), n, 0)
 
             if m == 0: # early exit: kernel is identity
-                return matrix.identity(self.base_ring(), n, n)
+                return matrix.identity(self.base_ring(), n)
 
             d = self.degree() # well defined since m > 0 and n > 0
             if d == -1: # matrix is zero
-                return matrix.identity(self.base_ring(), n, n)
+                return matrix.identity(self.base_ring(), n)
 
             # degree bounds on the kernel basis
             degree_bound = min(m,n)*d+max(shifts)

src/sage/rings/polynomial/polynomial_element.pyx

@@ -7667,9 +7667,11 @@ cdef class Polynomial(CommutativePolynomial):
 
         cdef unsigned long d
         if degree is not None:
+            if degree < 0:
+                raise ValueError("degree argument must be a non-negative integer, got %s" % (degree))
             d = degree
             if d != degree:
-                raise ValueError("degree argument must be a non-negative integer, got %s"%(degree))
+                raise ValueError("degree argument must be a non-negative integer, got %s" % (degree))
             if len(v) < degree+1:
                 v.reverse()
                 v = [self.base_ring().zero()]*(degree+1-len(v)) + v

src/sage/rings/polynomial/polynomial_integer_dense_flint.pyx

@@ -1827,9 +1827,11 @@ cdef class Polynomial_integer_dense_flint(Polynomial):
         cdef Polynomial_integer_dense_flint res = self._new()
         cdef unsigned long d
         if degree is not None:
+            if degree < 0:
+                raise ValueError("degree argument must be a non-negative integer, got %s" % (degree))
             d = degree
             if d != degree:
-                raise ValueError("degree argument must be a non-negative integer, got %s" % degree)
+                raise ValueError("degree argument must be a non-negative integer, got %s" % (degree))
             # FLINT expects length
             fmpz_poly_reverse(res._poly, self._poly, d+1)
         else:

src/sage/rings/polynomial/polynomial_zmod_flint.pyx

@@ -815,9 +815,11 @@ cdef class Polynomial_zmod_flint(Polynomial_template):
         cdef Polynomial_zmod_flint res = self._new()
         cdef unsigned long d
         if degree is not None:
+            if degree < 0:
+                raise ValueError("degree argument must be a non-negative integer, got %s" % (degree))
             d = degree
             if d != degree:
-                raise ValueError("degree argument must be a non-negative integer, got %s"%(degree))
+                raise ValueError("degree argument must be a non-negative integer, got %s" % (degree))
             nmod_poly_reverse(&res.x, &self.x, d+1) # FLINT expects length
         else:
             nmod_poly_reverse(&res.x, &self.x, nmod_poly_length(&self.x))

src/sage/rings/polynomial/polynomial_zz_pex.pyx

@@ -513,13 +513,18 @@ cdef class Polynomial_ZZ_pEX(Polynomial_template):
             sage: f.reverse(degree=200)
             2*x^200 + 3*x^199 + 5*x^198 + 7*x^197 + 11*x^196 + 13*x^195 + 17*x^194 + 19*x^193
             sage: f.reverse(degree=0)
-            Traceback (most recent call last):
-            ...
-            ValueError: degree argument must be a non-negative integer, got 0
+            2
             sage: f.reverse(degree=-5)
             Traceback (most recent call last):
             ...
             ValueError: degree argument must be a non-negative integer, got -5
+
+        Check that this implementation is compatible with the generic one::
+
+            sage: p = R([0,1,0,2])
+            sage: all(p.reverse(d) == Polynomial.reverse(p, d)
+            ....:     for d in [None, 0, 1, 2, 3, 4])
+            True
         """
         self._parent._modulus.restore()
 
@@ -533,11 +538,10 @@ cdef class Polynomial_ZZ_pEX(Polynomial_template):
         # When a degree has been supplied, ensure it is a valid input
         cdef unsigned long d
         if degree is not None:
-            if degree <= 0:
+            if degree < 0:
                 raise ValueError("degree argument must be a non-negative integer, got %s" % (degree))
-            try:
-                d = degree
-            except ValueError:
+            d = degree
+            if d != degree:
                 raise ValueError("degree argument must be a non-negative integer, got %s" % (degree))
             ZZ_pEX_reverse_hi(r.x, (<Polynomial_ZZ_pEX> self).x, d)
         else: