@_Maxim_ 

Thanks. Could you also tell me how to remove the blue line in the graph? 

Yep,but that is a formula calculating directly from given p and n .My task is to reform my code in Ex 3 so that it could be used to cover a general case (p,n) rather than modifying my code everytime(Currently my code only works for p = 7 and n =3.If I want it for,say,p=8 and n =3,I would have to change my code to {seq( convert(a*v mod 8, list),a=0..7)}).

Sorry,I am not sure what you mean?

Sorry,I've just found out there is one more question...

If I want to transform the whole z-plane to a new domain of i*sqrt(z),what is the range of z? ( I tried 0..2Pi,but I guess maple regarded it as a real number)

@Rouben Rostamian  

Qmaple.mw

@Rouben Rostamian  

Hi,

I've tried fieldplot3d but it doesn't work for a system of differential equations ?

Question.mw


 

@tomleslie 

with(LinearAlgebra):
linearlise:=proc(s,u,x0,y0);
Sys:={s,u};
eq1:=rhs(Sys[1]);
eq2:=rhs(Sys[2]);
expansion1:=mtaylor(subs({x(t)=x,y(t)=y},eq1),[x=x0,y=y0],2);
expansion2:=mtaylor(subs({x(t)=x,y(t)=y},eq2),[x=x0,y=y0],2);
linsys:={diff(x(t),t)=subs({x=x(t),y=y(t)},expansion1),diff(y(t),t)=subs({x=x(t),y=y(t)},expansion2)};
end proc:

a:=(x,y)-> (x(t))*(y(t)-1);
b:=(x,y)->4-(y(t))^2-(x(t))^2;
linearlise(a,b,0,-2)
Warning, `Sys` is implicitly declared local to procedure `linearlise`
Warning, `eq1` is implicitly declared local to procedure `linearlise`
Warning, `eq2` is implicitly declared local to procedure `linearlise`
Warning, `expansion1` is implicitly declared local to procedure `linearlise`
Warning, `expansion2` is implicitly declared local to procedure `linearlise`
Warning, `linsys` is implicitly declared local to procedure `linearlise`
(x, y) -> x(t)*(y(t) - 1)
                      
(x, y) -> 4 - y(t)^2  - x(t)^2
Error, (in linearlise) invalid input: rhs received a, which is not valid for its 1st argument, expr

@Christopher2222 

?

Thanks all of you.I am pretty sure that the graph is correct since I've got a similar problem in my textbook,and thanks for the explanation of the meaning of function frac(t)