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 findsym and y is the symbolic variable of g as defined by findsym.
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 findsym.
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
compose(f,g) -> 1/(1+sin(x)^2)
compose(f,g,t) -> 1/(1+sin(t)^2)
compose(h,g,x,z) -> sin(z)^t
compose(h,g,t,z) -> x^sin(z)
compose(h,p,x,y,z) -> exp(-z/u)^t
compose(h,p,t,u,z) -> x^exp(-y/z)
See Also
finverse, subs, syms
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