I've been using the capabilities in sympy.vector for generating MMS
solutions for verifying FEM in MOOSE. I'm curious whether sympy supports
calculation of the gradient of a vector field (e.g. with the result being a
tensor)? It doesn't appear to me that it does, but I'm hoping I overlooked
something. Below is the sample code I'd like to be able to execute and the
corresponding backtrace. If the ability to take the gradient of a vector
doesn't exist, I'm curious whether it would be difficult to add? If it's
not too much anticipated work, I'd be willing to take a stab at it.
from sympy.vector import gradient, CoordSys3D
R = CoordSys3D('R')
u = R.x*R.y * (R.i + R.j)
gradient(u)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-49-c095794df196> in <module>
5 u = R.x*R.y * (R.i + R.j)
6
----> 7 gradient(u)
~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/operators.py
in gradient(scalar_field, coord_sys, doit)
317
318 if doit:
--> 319 return (vx * i + vy * j + vz * k).doit()
320 return vx * i + vy * j + vz * k
321 else:
~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/basisdependent.py
in doit(self, **hints)
169 """Calls .doit() on each term in the Dyadic"""
170 doit_components = [self.components[x].doit(**hints) * x
--> 171 for x in self.components]
172 return self._add_func(*doit_components)
173
~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/basisdependent.py
in <listcomp>(.0)
169 """Calls .doit() on each term in the Dyadic"""
170 doit_components = [self.components[x].doit(**hints) * x
--> 171 for x in self.components]
172 return self._add_func(*doit_components)
173
~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/core/decorators.py
in __sympifyit_wrapper(a, b)
89 if not hasattr(b, '_op_priority'):
90 b = sympify(b, strict=True)
---> 91 return func(a, b)
92 except SympifyError:
93 return retval
~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/core/decorators.py
in binary_op_wrapper(self, other)
127 if f is not None:
128 return f(self)
--> 129 return func(self, other)
130 return binary_op_wrapper
131 return priority_decorator
~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/basisdependent.py
in __mul__(self, other)
34 @call_highest_priority('__rmul__')
35 def __mul__(self, other):
---> 36 return self._mul_func(self, other)
37
38 @_sympifyit('other', NotImplemented)
~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/vector.py
in __new__(cls, *args, **options)
412
413 def __new__(cls, *args, **options):
--> 414 obj = BasisDependentMul.__new__(cls, *args, **options)
415 return obj
416
~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/basisdependent.py
in __new__(cls, *args, **options)
257 # Make sure incompatible types weren't multiplied
258 if count > 1:
--> 259 raise ValueError("Invalid multiplication")
260 elif count == 0:
261 return Mul(*args, **options)
ValueError: Invalid multiplication
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