f /: lhs = rhs assigns rhs to be the value of lhs, and associates the assignment with the symbol f.

When you make a definition in the form f[args]=rhs or f[args]:=rhs, Mathematica associates your definition with the object f. This means, for example, that such definitions ...

Patterns stand for classes of expressions. They contain pattern objects that represent sets of possible expressions. Pattern objects. When several pattern objects with the ...

f /: lhs =. removes any rules defined for lhs, associated with the symbol f.

lhs ^= rhs assigns rhs to be the value of lhs, and associates the assignment with symbols that occur at level one in lhs.

Mathematica is to its core a fundamentally extensible system, in which efficient, modular, reusable packages of any size can readily be created. Mathematica's symbolic ...

Constants is an option for Dt which gives a list of objects to be taken as constants.

Dt[f, x] gives the total derivative d f/d x. Dt[f] gives the total differential d f. Dt[f, {x, n}] gives the multiple derivative d^n f/d x^n. Dt[f, x_1, x_2, ...] gives d/d ...

Mathematica's symbolic architecture supports a highly generalized notion of assignment, in which you can specify a transformation for any class of expressions defined by a ...

Mathematica uses various syntactic rules to interpret input that you give, and to convert strings and boxes into expressions. The version of these rules that is used for ...