gh-40173: Trac #40127: Pass factor_on_left in linear_combination
    
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Fixes [#40127](#40127).

Passes `factor_on_left` correctly to `iaxpy()` in `linear_combination`.

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URL: #40173
Reported by: Aolong Li
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/data_structures/blas_dict.pyx

@@ -340,6 +340,20 @@ cpdef dict linear_combination(dict_factor_iter, bint factor_on_left=True):
         {0: 10, 1: 10}
         sage: blas.linear_combination( [(D,1), (D,-1)] )
         {}
+
+    Check right multiplication with coefficients in a noncommutative ring::
+
+        sage: SGA = SymmetricGroupAlgebra(QQ, 3)
+        sage: s1 = SGA([2, 1, 3]) # (1 2)
+        sage: s2 = SGA([3, 1, 2]) # (1 3)
+        sage: D1 = {0: s1}
+        sage: blas.linear_combination([(D1, s2)], factor_on_left=False) # s1 * s2
+        {0: [1, 3, 2]} 
+
+    Check left multiplication with coefficients in a noncommutative ring::
+    
+        sage: blas.linear_combination([(D1, s2)], factor_on_left=True) # s2 * s1
+        {0: [3, 2, 1]} 
     """
     cdef dict result = {}
     cdef dict D
@@ -350,7 +364,8 @@ cpdef dict linear_combination(dict_factor_iter, bint factor_on_left=True):
         if not result and a == 1:
             result = D.copy()
         else:
-            iaxpy(a, D, result, remove_zeros=False)
+            iaxpy(a, D, result, remove_zeros=False, 
+                  factor_on_left=factor_on_left)
 
     return remove_zeros(result)