Thank you for your answer. Very well explained and extremely helpful. I've only been working on Maple for about 3 weeks now and it makes me wonder how on earth i'm actually going get my head around it all :).

Thank you for your answer. Very well explained and extremely helpful. I've only been working on Maple for about 3 weeks now and it makes me wonder how on earth i'm actually going get my head around it all :).

Thank you for your response. I have a second query:

If i want to modify NR1 above to NR2(f,x0,N,eps) where eps is a real number so that it returns the first iterate x_k for which |x[k]-x[k-1]|<eps and k<=N. However, if |x[k]-x[k-1]|>=eps for k=1,...,N, then an error message should be displayed.

If the procedure is correct then for f:= x-> x^5-1 i should get an answer when x₀=0.60+0.20i and the error message when x₀=0.60+0.16i.

The code i've written so far is incorrect but i'm not sure where i'm going wrong. Would you be able to give me some pointers?

NR2:=proc(f::mathfunc,x0::complex,N::posint,eps)
> local x,k:
> x := x0:
> for k to N do:
>   if abs(x[k]-x[k-1]) >= eps then
>   print("Convergence has not been achieved!"):
>   return :
> end if:
> x := x-f(x)/D(f)(x)
> end do:
>  evalf(x):
> end proc:f:= x-> x^5-1:
> NR2(f,0.6+I*0.16,10,0.00001);
Error, (in NR2) cannot determine if this expression is true or false: .1e-4 <= abs((.6+.16*I)[1]-(.6+.16*I)[0])

> NR2(f,0.6+I*0.20,10,0.00001);
Error, (in NR2) cannot determine if this expression is true or false: .1e-4 < abs((.6+.20*I)[1]-(.6+.20*I)[0])
 

Thanks in advance.

Thank you for your response. I have a second query:

If i want to modify NR1 above to NR2(f,x0,N,eps) where eps is a real number so that it returns the first iterate x_k for which |x[k]-x[k-1]|<eps and k<=N. However, if |x[k]-x[k-1]|>=eps for k=1,...,N, then an error message should be displayed.

If the procedure is correct then for f:= x-> x^5-1 i should get an answer when x₀=0.60+0.20i and the error message when x₀=0.60+0.16i.

The code i've written so far is incorrect but i'm not sure where i'm going wrong. Would you be able to give me some pointers?

NR2:=proc(f::mathfunc,x0::complex,N::posint,eps)
> local x,k:
> x := x0:
> for k to N do:
>   if abs(x[k]-x[k-1]) >= eps then
>   print("Convergence has not been achieved!"):
>   return :
> end if:
> x := x-f(x)/D(f)(x)
> end do:
>  evalf(x):
> end proc:f:= x-> x^5-1:
> NR2(f,0.6+I*0.16,10,0.00001);
Error, (in NR2) cannot determine if this expression is true or false: .1e-4 <= abs((.6+.16*I)[1]-(.6+.16*I)[0])

> NR2(f,0.6+I*0.20,10,0.00001);
Error, (in NR2) cannot determine if this expression is true or false: .1e-4 < abs((.6+.20*I)[1]-(.6+.20*I)[0])
 

Thanks in advance.

Ha ha, looks like i was heading completely in the wrong direction!

This opens up a whole new world. Thanks.

Ha ha, looks like i was heading completely in the wrong direction!

This opens up a whole new world. Thanks.

Brilliant! That is a much neater solution than the one i came up with. Thanks a million!

Brilliant! That is a much neater solution than the one i came up with. Thanks a million!

Interesting, your answer gave the opposite of what i needed. This what i came up with after a while of pulling my hair out before newton's apple struck me!

S:= {seq(i, i = 1 .. 66)};

> coprime66:= x-> igcd(x,66)=1;

> select(coprime66,S);

I've learnt from your response though; it shows there are so many diff ways to do the same thing. I'll probably asking another query fairly soon as i'm such a novice at Maple!

Thank you

Interesting, your answer gave the opposite of what i needed. This what i came up with after a while of pulling my hair out before newton's apple struck me!

S:= {seq(i, i = 1 .. 66)};

> coprime66:= x-> igcd(x,66)=1;

> select(coprime66,S);

I've learnt from your response though; it shows there are so many diff ways to do the same thing. I'll probably asking another query fairly soon as i'm such a novice at Maple!

Thank you