compose - Functional composition
Syntax
compose(f,g)
compose(f,g,z)
compose(f,g,x,z)
compose(f,g,x,y,z)
Description
compose(f,g) returns f(g(y)) where f
= f(x) and g = g(y). Here x is
the symbolic variable of f as defined by symvar and y is
the symbolic variable of g as defined by symvar.
compose(f,g,z) returns f(g(z)) where f
= f(x), g = g(y), and x and y are
the symbolic variables of f and g as
defined by symvar.
compose(f,g,x,z) returns f(g(z)) and
makes x the independent variable for f.
That is, if f = cos(x/t), then compose(f,g,x,z) returns cos(g(z)/t) whereas compose(f,g,t,z) returns cos(x/g(z)).
compose(f,g,x,y,z) returns f(g(z)) and
makes x the independent variable for f and y the
independent variable for g. For f = cos(x/t) and g
= sin(y/u), compose(f,g,x,y,z) returns cos(sin(z/u)/t) whereas compose(f,g,x,u,z) returns cos(sin(y/z)/t).
Examples
Suppose
syms x y z t u;
f = 1/(1 + x^2); g = sin(y); h = x^t; p = exp(-y/u);
Then
a = compose(f,g)
b = compose(f,g,t)
c = compose(h,g,x,z)
d = compose(h,g,t,z)
e = compose(h,p,x,y,z)
f = compose(h,p,t,u,z)
returns:
a =
1/(sin(y)^2 + 1)
b =
1/(sin(t)^2 + 1)
c =
sin(z)^t
d =
x^sin(z)
e =
(1/exp(z/u))^t
f =
x^(1/exp(y/z))
See Also
finverse, subs, syms
 | colspace | | conj (sym) |  |
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