- Lie derivative
- Exterior product
- Tensor product
- Hodge operator
- Covariant derivative
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Data types in the atlas package
In the Atlas package any identifier is treated as 0-form i.e. as non-constant scalar (if it not declared as constant, p-form, tensor etc). To declare a variable as a constant, vector, tensor or p-form use Constants, Vectors, Tensors, Forms, respectively. To find out information about indexing facilities of the package see Indexing.
The Atlas package uses its own data types, called "Constant", scal, "Vector", tensor, form, func, domain, mapping, coframe, frame to represent corresponding objects. Use TypeQ to check the corresponding types.
The Atlas package uses its own data types, called "Constant", scal, "Vector", tensor, form, func, domain, mapping, coframe, frame to represent corresponding objects. Use TypeQ to check the corresponding types.
Examples:
| Kind[t] | t -any expression containing tensors, vectors, p-forms etc. |
| Constants[c1,c2,...,ci,...,cn] | c1, c2, ..., ci, ..., cn - constants identifiers. |
| 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 form's degree. |
| 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. |
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Verify that C is a constant using Kind (see Kind) and TypeQ procedures:
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is p-form using Kind and TypeQ procedures: | In[171]:= |
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| Domain[manifold] | manifold - string - a manifold name or a name of a manifold domain. |
| Coframe[idj,{j,1,n}] | id - identifier for indexed variable - the coframe 1-forms n - dimension of working manifold (a variable or integer) idi→ expri - rules where idi is indexed variable - coframe 1-form and expri is decomposition of the 1-form on exact 1-forms. |
| Mapping[f,m,n] | f - variable - the mapping identifier i.e. f : m → n m - variable - first domain identifier n - variable - second domain identifier |
| Who[] | returns information about all declarations made. |
| Who[l] | l -an identifier, list or set of identifies. |
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