Method subs() ineffective on tensor fields

[egourgoulhon]

As reported in this ​ask.sagemath question, tensor fields are endowed with a method subs() which is totally ineffective:

sage: E.<x,y> = EuclideanSpace()                                                                    
sage: a = var('a')                                                                                  
sage: v = E.vector_field(a*x, a^2 + y)                                                              
sage: v.display()                                                                                   
a*x e_x + (a^2 + y) e_y
sage: v.subs(a==1)                                                                                  
Vector field on the Euclidean plane E^2
sage: v.display()                                                                                   
a*x e_x + (a^2 + y) e_y

This is because subs() is inherited from the generic base class Element and the code of Element.subs() has

        parent = self._parent
        try:
            ngens = parent.ngens()
        except (AttributeError, NotImplementedError, TypeError):
            return self

Since v.parent().ngens() returns an AttributeError, this explains the silent failure.

Currently, the required substitution can be achieved by means of the method apply_map:

sage: v.apply_map(lambda comp: comp.subs(a==1))                                                     
sage: v.display()                                                                                   
x e_x + (y + 1) e_y

[gh-mjungmath]

We could simply overload subs and delegate this to apply_map? Or is there a more effective way?

[egourgoulhon]

Replying to gh-mjungmath:

We could simply overload subs and delegate this to apply_map?

Yes this is probably the route to go.

[egourgoulhon]

Also, in another ticket, we could question why Element.subs() treats the AttributeError with a return self

[tscrim]

Note that I would not expect v.subs(a==1) to do a substitution because it is passing in an expression a == 1, rather than setting a keyword a=1. Count the number of equals.

[gh-DaveWitteMorris]

The subs method of elements of SR does allow (and document) this syntax, so it would make sense to allow it here, too.

sage: var('t');
sage: cos(x).subs(x==sin(t))
cos(sin(t))

[mkoeppe]

Moving to 9.4, as 9.3 has been released.