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### Defining families of function from p-1 to q using a function from p to q

Suppose that the function f : (x, y) f (x, y) is defined, and we want to define a family of functions g(t) such that g(t)(y) : = f (t, y) (i.e. t is viewed as a parameter). Since the expression after -> (or :=) is not evaluated, we should not define g(t) by g(t):=y->f(t,y), we have to use the unapply command.

For example, assuming that f : (x, y) x sin(y) and g(t) : y f (t, y), input :

f(x,y):=x*sin(y);g(t):=unapply(f(t,y),y)
Output :
((x,y)->x*sin(y), (t)->unapply(f(t,y),y))
Input
g(2)
Output :
y->2 . sin(y)
Input
g(2)(1)
Output :
2 . sin(1)

Next example, suppose that the function h : (x, y) [x*cos(y), x*sin(y)] is defined, and we want to define the family of functions k(t) having t as parameter such that k(t)(y) : = h(t, y). To define the function h(x, y), input :

h(x,y):=(x*cos(y),x*sin(y))
To define properly the function k(t), input :
k(t):=unapply(h(x,t),x)
Output :
(t)->unapply(h(x,t),x)
Input
k(2)
Output :
(x)->(x*cos(2),x*sin(2))
Input
k(2)(1)
Output :
(2*cos(1),2*sin(1))     suivant: Composition of two functions: monter: Defining algebraic functions précédent: Defining a function from   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse