Maxima Function
gradef (f(x_1, ..., x_n), g_1, ..., g_m)
gradef(a,x,expr)
Defines the partial derivatives (i.e., the components of the gradient) of the function f or variable a.
gradef (f(x_1, ..., x_n), g_1, ..., g_m)
defines df/dx_i
as g_i,
where g_i is an expression; g_i may be a function call, but not the name of a function.
The number of partial derivatives m may be less than the number of arguments n,
in which case derivatives are defined with respect to x_1 through x_m only.
gradef (a, x, expr)
defines the derivative of variable a
with respect to x as expr.
This also establishes the dependence of a on x (via depends (a, x)
).
The first argument f(x_1, ..., x_n)
or a is quoted,
but the remaining arguments g_1, ..., g_m are evaluated.
gradef
returns the function or variable for which the partial derivatives are defined.
gradef
can redefine the derivatives of Maxima's built-in functions.
For example, gradef (sin(x), sqrt (1 - sin(x)^2))
redefines the derivative of sin
.
gradef
cannot define partial derivatives for a subscripted function.
printprops ([f_1, ..., f_n], gradef)
displays the partial derivatives
of the functions f_1, ..., f_n, as defined by gradef
.
printprops ([a_n, ..., a_n], atomgrad)
displays the partial derivatives
of the variables a_n, ..., a_n, as defined by gradef
.
gradefs
is the list of the functions
for which partial derivatives have been defined by gradef
.
gradefs
does not include any variables
for which partial derivatives have been defined by gradef
.
Gradients are needed when, for example, a function is not known explicitly but its first derivatives are and it is desired to obtain higher order derivatives.