I want to create the groups (Z/nZ)+ and (Z/nZ)*.

I can do this in python for n=7. I want to do this with other values of n.

(Z/7Z)+
   0 1 2 3 4 5 6
0 0 1 2 3 4 5 6
1 1 2 3 4 5 6 0
2 2 3 4 5 6 0 1
3 3 4 5 6 0 1 2
4 4 5 6 0 1 2 3
5 5 6 0 1 2 3 4
6 6 0 1 2 3 4 5
 
(Z/7Z)*
   1 2 3 4 5 6
1 1 2 3 4 5 6
2 2 4 6 1 3 5
3 3 6 2 5 1 4
4 4 1 5 2 6 3
5 5 3 1 6 4 2
6 6 5 4 3 2 1
 

I tried creating a Cayley table but can not get that right.

What is happening at f(0)?

Look at PlotProblem.mw

plot-problem.mw

I have done something but what?

I want to use maple notation for input and  output.

I have done something to mess this up.

How do I get rid of the typesetting messages?

How do I plot a volume of revolution? I can plot other volumes using Student[Calculus1]]:-VolumeOfRevolution, but not this one. I get a blank plot. I do get the correct volume from output=value..

How do I plot this using plot3d?

restart;
a := 0; b := 1;
f := (x) -> x^2+2;
g := (x) -> 1/2*x+1;
V := int(f(x)^2 - g(x)^2,x=a..b)*Pi;
Student[Calculus1]:-VolumeOfRevolution(f(x),g(x),x=a..b,output=value);
Student[Calculus1]:-VolumeOfRevolution(f(x),g(x),x=a..b,output=plot);
 

How do I characterize this equation set? I think it has 6 solutions, equal in pairs, or 3 distinct solutions.

restart;

eq1 := x = (((72*5^(3/2)+270)*a^2-1344*5^(3/2)*a)*w+(9*5^(5/2)-1485)*a^2-2016*5^(3/2)*a-12544*5^(5/2))/(((288*sqrt(5)+216)*a^2-5376*sqrt(5)*a)*w+(36*5^(3/2)-1188)*a^2-8064*sqrt(5)*a+6272*5^(3/2)):

eq2:= a^3 = -(128*5^(5/2)*w)/9+(1600*w)/3+(544*5^(3/2))/9+15200/27:

eq3:=1+w+w*w = 0:##   or w = (sqrt(3)*%i)/2-1/2;

for s1 in [solve(eq2,a)] do
    for s2 in [solve(eq3,w)] do
        subs(a=s1, eq1):
        subs(w=s2,%):
        lprint("sol",simplify(%));
    end do;
end do;