Re: Tensors in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg37634] Re: Tensors in Mathematica
- From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
- Date: Thu, 7 Nov 2002 06:41:18 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Earlier I tried to show how to define a function called TensorQ. However,
my earlier version would give the wrong answer if given a tensor when one or
more tensor element is not an atom. I have a much improved version below.
-------------------
In[5]:=
TensorQ[expr_List]:=
With[{rank=TensorRank[expr]},
FreeQ[ Head /@ Level[ expr, {rank},Heads->False ], List, {1},
Heads->False ]
];
TensorQ[_]=False;
TensorQ[expr_,test_]:=
TensorQ[expr] &&TrueQ[ And @@ test /@ Level[ expr, {3}, Heads®False ] ];
-----------
Here TensorQ knows t1 is a tensor even though (3+Pi) isn't an atom.
In[5]:=
t1={{{3,2},{3,3+Pi},{0,3}},{{0,3},{7,0},{5,2}},{{1,0},{2,0},{1,2}}};
TensorQ[t1]
Out[6]=
True
-----------
TensorQ knows t1 is a tensor and all elements of the tensor are numeric.
In[7]:=
TensorQ[t1,NumericQ]
Out[7]=
True
-----------
In the next line we get False because NumberQ[3+Pi] returns False.
In[8]:=
TensorQ[t1,NumberQ]
Out[8]=
False
-----------
TensorQ knows t2 below isn't a tensor.
In[9]:=
t2={{{3,2},{3,3+Pi},{0,3}},{{0,3},{7,0},{5,2}},{{1,0,0},{2,0},{1,2}}};
TensorQ[t2]
Out[9]=
False
----------
Regards,
Ted Ersek
Download my latest Mathematica Tips, Tricks from
http://www.verbeia.com/mathematica/tips/Tricks.html
or from
http://www.mathsource.com/Content/General/Tutorials/0212-331