I have a set of multivariable polynomial equations. I want to show that each member of the solution set is a solution to the equations and that members of the solution set is unique. I want the result of verify to return one true, not many. Also the result of unique.

Is there a simpler way?

eq-soln-verify.mw

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);