Functions - declaration of functions

Functions[f1f1[x1, x2, ..., xn], f2f2[y1, y2, ..., ym], ...,
fkfk[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).