E = ExteriorAlgebra(QQ,['e'],2)
E.inject_variables()
bf = E.lifted_bilinear_form(matrix.identity(2))
bf(e0, e0)
----> 1/0
bf(e0*e1,e0*e1)
Flint exception (General error): Exception (fmpz_divexact). Division by 
zero.

But it does work with matrix(QQ,[[1,0],[0,1]])

--------------------------------------------------------------------------- 
RuntimeError Traceback (most recent call last) Cell In[51], line 1 ----> 1 
bf(e0*e1,e0*e1) File 
/data/Software/Sage/sage/src/sage/categories/poor_man_map.py:262, in 
PoorManMap.__call__(self, *args) 248 """ 249 EXAMPLES:: 250 (...) 259 260 
""" 261 for function in reversed(self._functions): --> 262 args = [function(
*args)] 263 return args[0] File 
/data/Software/Sage/sage/src/sage/algebras/clifford_algebra.py:2029, in 
ExteriorAlgebra.lifted_bilinear_form.<locals>.lifted_form(x, y) 2027 MA = 
MatrixArgs(R, n, matrix_list) 2028 del matrix_list -> 2029 result += cx * 
cy * MA.matrix(False).determinant() 2030 return result File 
/data/Software/Sage/sage/src/sage/matrix/matrix_rational_dense.pyx:842, in 
sage.matrix.matrix_rational_dense.Matrix_rational_dense.determinant() 840 
841 if algorithm is None or algorithm == "flint": --> 842 det = 
self._det_flint() 843 elif algorithm == "pari": 844 det = self._det_pari() 
File /data/Software/Sage/sage/src/sage/matrix/matrix_rational_dense.pyx:874, 
in sage.matrix.matrix_rational_dense.Matrix_rational_dense._det_flint() 872 
cdef fmpq_t e 873 fmpq_init(e) --> 874 sig_on() 875 fmpq_mat_det(e, 
self._matrix) 876 fmpq_get_mpq(d.value, e) RuntimeError: Aborted

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