7.6. BasisValues

BasisValues        Values for the components of basis changes

Components of the basis changes

The components of the basis change matrices require separate treatment and are represented by the BasisValues head. Here we do not allow derivatives, because the derivatives of these objects are automatically replaced by Christoffel tensors.

In[363]:=

? BasisValues

In[364]:=

$CVVerbose = True ;

In[365]:=

ComponentValue[Basis[{1, polar}, {2, -cartesian}]]

Added independent rule e_ ( 2)^1 →e_ ( 2)^1 for tensor Basis

Out[365]=

e_ ( 2)^1 →e_ ( 2)^1

In[366]:=

AllComponentValues[Basis[{a, polar}, {-b, -cartesian}], Table[Random[], {3}, {3}]]

Added independent rule e_0 ^( 0) →0.6191 for tensor Basis

Added independent rule e_ ( 1)^0 →0.0145658 for tensor Basis

Added independent rule e_ ( 2)^0 →0.293863 for tensor Basis

Added independent rule e_0 ^( 1) →0.499612 for tensor Basis

Added independent rule e_1 ^( 1) →0.584013 for tensor Basis

Added independent value e_ ( 2)^1 →0.0644212 for tensor Basis

Added independent rule e_0 ^( 2) →0.172212 for tensor Basis

Added independent rule e_1 ^( 2) →0.813358 for tensor Basis

Added independent rule e_2 ^( 2) →0.635848 for tensor Basis

Out[366]=

In[367]:=

BasisValues[polar, -cartesian]

Out[367]=

The inverse basis change is not automatically computed, because it may take a very long time

In[368]:=

BasisValues[cartesian, -polar]

Out[368]=

FoldedRule[{}, {}]

Created by Mathematica  (May 16, 2008) Valid XHTML 1.1!