# Question:How do I iterate this function using the @@ operator?

## Question:How do I iterate this function using the @@ operator?

Maple

I can get the function to iterate as a recursive function by just reevaluating the x := evalf(x-(f1*j-i*g1)/(h*k-i*j), 25); y := evalf(y-(h*g1-f1*j)/(h*k-i*j), 25) portion of the function below but im trying beneath it to assign it as newt2d so that i can iterate it as newtons method in two variables like (newt2d@@10) and I can't seem to figure out what im doing wrong. Thanks for any help you can provide!

f := proc (x, y) options operator, arrow; x+y-cos(x)+sin(y-1) end proc; f1 := f(x, y)

(x, y) -> x + y - cos(x) + sin(y - 1)
x + y - cos(x) + sin(y - 1)

> g := proc (x, y) options operator, arrow; x^4+y^4-2*x*y end proc; g1 := g(x, y);

(x, y) -> x + y - 2 x y
x + y - 2 x y

> dh := D[1](f); h := dh(x, y);

(x, y) -> 1 + sin(x)
1 + sin(x)

> di := D[2](f); i := di(x, y);

(x, y) -> 1 + cos(y - 1)
1 + cos(y - 1)

> dj := D[1](g); j := dj(x, y);

(x, y) -> 4 x - 2 y
4 x - 2 y

> dk := D[2](g); k := dk(x, y);

(x, y) -> 4 y - 2 x
4 y - 2 x

x := .3; y := .8

0.3
0.8

> x := evalf(x-(f1*j-i*g1)/(h*k-i*j), 25); y := evalf(y-(h*g1-f1*j)/(h*k-i*j), 25);

0.2924403963319692595180140
0.8321243516906678979858730

> newt2d(.3, .8);

0.2577789764, 0.8333916830

> (newt2d@@5)(.3, .8);

Error, (in @@) invalid arguments

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