I want to solve a system of 11^3 equations  (each equation is quite small) in 11^2 unknows. The equations are all viewed mod 2. I only want to know the possible solutions for 11 of those variables.

That is given variables a[i], 1 from 1 to 11 and b[n] for the remaining 11^2-11  variables.

I want to know all the  distinct consistent solutions for the a[i]'s. I dont care what the b's are as long as the solution to the a[i]s is consistent.

I am VERY sure that the equations will quickly show that there are no solutions but I am having difficulty comming up with how to code this. 

Hi i 2 questions. all pertaining to solving a systems of equations mod 2

First if i have a large set of equations, 11^3 equations in 11 unknowns and i want maple to give me ALL solutions mod 2 how can i do that? Maples msolve is loosing solutions.

Second suppose i want all unique solutions that say 6 of the variables can have but dont care what the solution to the other variables are as long as it is a solution. 

mini example:

say x=1,y=1,z=1 is a solution as well as x=1,y=1,z=0, i just want to know about x=1,y=1.

t := exp(2*(I*Pi*(1/11)))

u := t^10*a[10]+t^9*a[9]+t^8*a[8]+t^7*a[7]+t^6*a[6]+t^5*a[5]+t^4*a[4]+t^3*a[3]+t^2*a[2]+t*a[1]+a[0]

How can get maple to simplify expressions like u^3+u^2-1 so that the exponents are between 2*(I*Pi*(1/11)) and 1.

Essentially it keeps outputting things like exp(2*(I*Pi*(1/11)))^12 and not simplifying it as it is a root of unity

Ok so i have a matrix M filled with complex roots of unity. I want to execute the following code but it seems to be failing to do so correctly

t:=exp(2 Pi I/11);

m := (i, j) -> M[(i mod 11)+1, (j mod 11)+1] ;  

mu :=(i,j)->(add(add(add(a[k]*a[m]*a[n]*t^(m)*m((i+k-m),(j+n-m))),n=0..10),m=0..10),k=0..10));

Something is wrong with my indexing of the matrix . or when the mod procs.