sagemathgh-40738: Fix ExteriorAlgebra multiplication over SR

Author: Hapsa21

src/sage/algebras/clifford_algebra_element.pyx

@@ -442,8 +442,21 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
             4*a*b*c*d + 4*a*b*c + 4*a*b*d + 4*a*c*d + 4*b*c*d
              + 2*a*b + 2*a*c + 2*a*d + 2*b*c + 2*b*d + 2*c*d
              + 2*a + 2*b + 2*c + 2*d + 1
+             
+             TESTS::
+
+            Check that multiplication with symbolic coefficients is handled correctly (gh-40738)::
+
+                sage: from sage.all import ExteriorAlgebra, SR, var
+                sage: L.<a, b> = ExteriorAlgebra(SR)
+                sage: x, y = var('x y')
+                sage: x * (y * b)
+                x*y*b
+                sage: (x * a) * (y * b)
+                x*y*a*b
         """
         cdef Parent P = self._parent
+        cdef R = P.base_ring()
         zero = P._base.zero()
         cdef dict d
         cdef ExteriorAlgebraElement rhs = <ExteriorAlgebraElement> other
@@ -514,7 +527,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
                     if tot_cross % 2:
                         cr = -cr
 
-                val = d.get(t, zero) + cl * cr
+                val = d.get(t, zero) + R(cl) * R(cr)
                 if not val:
                     del d[t]
                 else: