# Revision history [back]

This kind of coercion is documented:

On the other hand, Sage has the notion of a coercion, which is a canonical morphism (occasionally up to a conventional choice made by developers) between parents. A coercion from one parent to another must be defined on the whole domain, and always succeeds. As it may be invoked implicitly, it should be obvious and natural (in both the mathematically rigorous and colloquial sense of the word).

Symbolic expressions can be coerced to symbolic matrices of a fixed size:

sage: B.parent().has_coerce_map_from(SR)
True
sage: cm = sage.structure.element.get_coercion_model()
Coercion on right operand via
Coercion map:
From: Symbolic Ring
To:   Full MatrixSpace of 3 by 3 dense matrices over Symbolic Ring
Arithmetic performed after coercions.
Result lives in Full MatrixSpace of 3 by 3 dense matrices over Symbolic Ring
Full MatrixSpace of 3 by 3 dense matrices over Symbolic Ring


It is because there is a canonical map, mapping $1$ to the identity matrix, which is a morphism of algebras with basis.

Symbolic expressions cannot be coerced to vectors of a fixed size:

sage: b.parent().has_coerce_map_from(SR)
False


It is because there is no canonical map which is a morphism of modules with basis. Of course there exist morphisms, like the $1 \mapsto (1,1,1)$ you suggest, but that is no better than $1 \mapsto (1,0,0)$ or $1 \mapsto (0,0,1)$. There is no obvious natural choice, so there is no coercion.