| 2539 | def _coerce_map_from_(self, TensorParent): |

| 2540 | r""" |

| 2541 | EXAMPLES:: |

| 2542 | |

| 2543 | sage: C = CombinatorialFreeModule(ZZ, Set([1,2])) |

| 2544 | sage: D = CombinatorialFreeModule(ZZ, Set([2,4])) |

| 2545 | sage: f = C.module_morphism(on_basis=lambda x: D.monomial(2*x), codomain=D) |

| 2546 | sage: f.register_as_coercion() |

| 2547 | sage: T = tensor((C,C)) |

| 2548 | sage: p = D.an_element() |

| 2549 | sage: T(tensor((p,p))) |

| 2550 | Traceback (most recent call last): |

| 2551 | ... |

| 2552 | AssertionError: do not know how to coerce Free module generated by {2, 4} over Integer Ring # Free module generated by {2, 4} over Integer Ring into Free module generated by {1, 2} over Integer Ring # Free module generated by {1, 2} over Integer Ring (there is no coercion map from Free module generated by {2, 4} over Integer Ring into Free module generated by {1, 2} over Integer Ring) |

| 2553 | sage: T = tensor((D,D)) |

| 2554 | sage: p = C.an_element() |

| 2555 | sage: T(tensor((p,p))) |

| 2556 | 4*B[2] # B[2] + 4*B[2] # B[4] + 4*B[4] # B[2] + 4*B[4] # B[4] |

| 2557 | """ |

| 2558 | assert(isinstance(TensorParent, CombinatorialFreeModule_Tensor)) |

| 2559 | modules = TensorParent._sets |

| 2560 | assert(module in ModulesWithBasis(self.base_ring()) for module in modules) |

| 2561 | for i, Parent_i in enumerate(modules): |

| 2562 | assert (self._sets[i]).has_coerce_map_from(Parent_i), "do not know how to coerce %s into %s (there is no coercion map from %s into %s)"%(TensorParent, self, Parent_i, self._sets[i]) |

| 2563 | vector_map = [(self._sets[i]).coerce_map_from(module) for i,module in enumerate(modules)] |

| 2564 | result = TensorParent.module_morphism(on_basis=lambda x: self._tensor_of_elements([vector_map[i](modules[i].monomial(x[i])) for i in range(len(modules))]), codomain=self) |

| 2565 | return result |

| 2566 | |

| 2567 | |