- Lie derivative
- Exterior product
- Tensor product
- Hodge operator
- Covariant derivative
| Atlas Tutorial | Functions »|Tutorials »|More About » |
Dimension in the Atlas package
In the Atlas package the working dimension can be integer or symbolic. The corresponding variable is automatically assigned by Coframe procedure.
If the dimension is not an integer then all calculations are performed in terms of Sum operator (see examples below).
If the dimension is not an integer then all calculations are performed in terms of Sum operator (see examples below).
Examples:
| Functions[f1→f1[x1,x2,...,xn],f2→f2[y1,y2,...,ym],..., fk→fk[z1,z2,...,zj]] | fk=fk[z1, z2, ..., zj] - rules where fk-function identifier and zj - variables |
| Vectors[v1,v2,...,vi,...,vn] | vi - vector identivier |
| Forms[f1→n,f2→k,...,fi→p] | fi→p - rules where fi - form identifier and p is a variable or an integer - the s degree |
| Coframe[idj,{j,1,n}] | id - identifier for indexed variable - the coframe 1-forms n - dimension of working manifold (a variable or integer) |
| Frame[idj] | idj-indexed variable the frame vectors |
| Connection[id] | id-variable-connection identifier |
| In[7]:= |
| In[8]:= |
| Out[8]= |  |
| In[9]:= |
| Out[9]= |  |
| In[10]:= |
| Out[10]= |  |
| In[11]:= |
| Out[11]= |  |
| In[12]:= |
| Out[12]= |  |
| In[13]:= |
| Out[13]= |  |
| d[expr] | expr - any expression |
| ToBasis[t] | t - variable or expression of tensor type |
| div[expr] | expr - any vector expression |
Using d- procedure:
| In[14]:= |
| Out[14]= |  |
| In[15]:= |
| Out[15]= |  |
Using ToBasis- procedure:
| In[16]:= |
| Out[16]= |  |
Using div- procedure:
| In[17]:= |
| Out[17]= |  |
Using Lie derivative:
| In[18]:= |
| Out[18]= |  |
| In[19]:= |
| Out[19]= |  |
:| In[20]:= |
| Out[20]= |  |
| In[22]:= |
| Out[22]= |  |
| In[23]:= |
| Out[23]= |  |
| In[24]:= |
| Out[24]= |  |
| In[25]:= |
| Out[25]= |  |
| In[26]:= |
| Out[26]= |  |
| In[27]:= |
| Out[27]= |  |
