- Lie derivative
- Exterior product
- Tensor product
- Hodge operator
- Covariant derivative
| Functions[f1→f1[x1, x2, ..., xn], f2→f2[y1, y2, ..., ym], ..., fk→fk[z1, z2, ..., zj]] allows one to declare functions |
- fk=fk[z1, z2, ..., zj] - equations where fk-function identifier and zj - variables.
- 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. (see Types).
- The Functions procedure allows one to declare functions. In the Atlas package a function is non-constant 0-form which depends on other 0-forms.
- There are two different syntaxes for function declaration.
- - Use the first form f=f[x,y,z] to declare a function f depending on x, y, and z;
- - Use the second form F=F[xi] to declare a function F depending on xi if the working dimension is numeric or x1, x2, ..xn if the dimension is symbolic (see Dimension).
- The function identifiers can be either symbolic or indexed values (see examples below).
EXAMPLES
Basic Examples
Varify that f is a function using exterior derivative operator (see d):
And more - using exterior product operator (see Wedge):
Declare lambda as a constant (see Constants):
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j
