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The following code illustrates the problem I'm having:

phi = M.scalar_field(function('phi')(*coord), name='phi')
print(phi)
V = function('V')(phi)

​

Scalar field phi on the 4-dimensional differentiable manifold R^4

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-61-7de84076176e> in <module>()
      1 phi = M.scalar_field(function('phi')(*coord), name='phi')
      2 print(phi)
----> 3 V = function('V')(phi)

/home/cduston/Programs/SageMath/local/lib/python2.7/site-packages/sage/symbolic/function.pyx in sage.symbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.cpp:6664)()
    473                     if callable(method):
    474                         return method()
--> 475                 raise TypeError("cannot coerce arguments: %s" % (err))
    476 
    477         else: # coerce == False

TypeError: cannot coerce arguments: no canonical coercion from Algebra of differentiable scalar fields on the 4-dimensional differentiable manifold R^4 to Symbolic Ring

I want to determine the equations of motion for a scalar field $\phi$ on a 4-manifold with potential $V(\phi)$. However, Sage can't seem to associate an algebra with those objects. This is a pretty standard thing to do in field theory / GR - study the inflaton field, or dark energy, for example.

Is there a correct way to write to get the behavior we expect?

The following code illustrates the problem I'm having:

phi = M.scalar_field(function('phi')(*coord), name='phi')
print(phi)
V = function('V')(phi)

​

Scalar field phi on the 4-dimensional differentiable manifold R^4

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-61-7de84076176e> in <module>()
      1 phi = M.scalar_field(function('phi')(*coord), name='phi')
      2 print(phi)
----> 3 V = function('V')(phi)

/home/cduston/Programs/SageMath/local/lib/python2.7/site-packages/sage/symbolic/function.pyx in sage.symbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.cpp:6664)()
    473                     if callable(method):
    474                         return method()
--> 475                 raise TypeError("cannot coerce arguments: %s" % (err))
    476 
    477         else: # coerce == False

TypeError: cannot coerce arguments: no canonical coercion from Algebra of differentiable scalar fields on the 4-dimensional differentiable manifold R^4 to Symbolic Ring

I want to determine the equations of motion for a scalar field $\phi$ on a 4-manifold with potential $V(\phi)$. However, Sage can't seem to associate an algebra with those objects. This is a pretty standard thing to do in field theory / GR - study the inflaton field, or dark energy, for example.

Is there a correct way to write to get the behavior we expect?

dphi=nab(phi)
T1=dphi['_a']*dphi['_b'] 
T2=g.inverse()['^ab']*T1['_ab']
T3=dphi*dphi + 1/2*g*(T2 - V)