with(FGb);
with(EXAGON);

vverb := 1;

## nonreached1
vars:=[x,y,z];
f:=(x*y-1)^2+y^2+z^2+42;
F:=[z];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;


## nonreached2
vars:=[x,y,z];
f := (x*y-1)^2+x^2+z^2*g+g^3*(x+1) + 42;
g := x^2-x*y+z*x*y+y+3:
F:=[g];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;


## isolated
vars:=[x,y];
f := (x^2+y^2-2)*(x^2+y^2);
F := [(x^2+y^2-1)*(x-3)];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;


## reachedasympt
vars:=[x,y,z];
f := (1/10*(x*y-1)^4 + x^6)*y^6 + 1/124*z^2 + 42;
F := [z];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;


## GGSZ2012
vars:=[x,y];
f := (x+1)^2+y^2;
F := [x^3 - y^2];
st := time():
Optimize(f, F,  vars, verbose = vverb);
time()-st;


## Nie 2010
vars:=[x,y,z];
f := x^6+y^6+z^6+3*x^2*y^2*z^2-x^2*(y^4+z^4)-y^2*(z^4+x^4)-z^2*(x^4+y^4);
F := [x + y + z - 1];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;


## laxlax
vars := [x1, x2, x3, x4];
f := x1*x2*x3*x4-x1*(x2-x1)*(x3-x1)*(x4-x1)-x2*(x1-x2)*(x3-x2)*(x4-x2)-x3*(x1-x3)*(x2-x3)*(x4-x3)-x4*(x1-x4)*(x2-x4)*(x3-x4);
F:=[x1, x2-x3, x3-x4];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;



## MaxCutPolynomial: computes the polynomial corresponding with the MaxCut problem
# input:
# - L: list of weights of the maxcut problem (L = [w_11, w_12,..., w_1n, w_23, w_24,...]
# - n: the number of vertices
# - vars: list of n variables
# output:
# - the polynomial defined as the sum of w_ij(1 - vars_i*vars_j) for i<j
MaxCutPolynomial := proc(L,n,vars)
local i, j, k, f;

    i := 1:
    k := 1:
    f := 0:
    while i < n do
        j := i+1:

        while j < n+1 do
            f := factor(f + L[k]*(1 - vars[i]*vars[j])):
            j := j+1:
            k := k+1:
        od:

        i := i+1:
    od:
    RETURN(-1/2*f):
end:

## maxcut 5-1
n := 5;
L := [23, 16, 18, 17, 25, 26, 23, 14, 24, 10];
vars := [seq(y[i], i = 1..n)];
f := MaxCutPolynomial(L,n,vars);
F :=[seq(y^2-1, y in vars)];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;


## maxcut 5-2
n := 5;
L := [6, 6, 8, 10, 5, 5, 6, 4, 6, 6];
vars := [seq(y[i], i = 1..n)];
f := MaxCutPolynomial(L,n,vars);
F :=[seq(y^2-1, y in vars)];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;


# Coleman5
M := 5;
vars := [seq(x[i],i=1..M-1),seq(y[i],i=1..M-1)];
f := 1/M*(sum(x[i]^2+y[i]^2,i=1..M-1));
F:=[y[1]-1,seq(y[i+1]-y[i]-1/M*(y[i]^2-x[i]),i=1..M-2)];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;


# Coleman6
M := 6;
vars := [seq(x[i],i=1..M-1),seq(y[i],i=1..M-1)];
f := 1/M*(sum(x[i]^2+y[i]^2,i=1..M-1));
F := [y[1]-1,seq(y[i+1]-y[i]-1/M*(y[i]^2-x[i]),i=1..M-2)];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;


## vor 1
f := 32*a^2*u^3*alpha^2+4*u*x^2*a^2-2*a*alpha*beta-2*x*beta*a^3+2*y*beta*a^2-16*a^3*u^3*alpha*beta+16*a^2*u^3*x*alpha+16*a^2*u^3*y*beta-16*a*u^3*alpha*beta-8*u^2*x*beta*a^3-24*u^2*a*alpha*beta+24*u^2*y*beta*a^2-24*u^2*alpha*beta*a^3-8*u^2*a*x*beta+24*u^2*x*alpha*a^2-8*u^2*y*a^3*alpha-8*u^2*a*y*alpha-12*u*alpha*beta*a^3-8*u*y*a^3*alpha+4*u*alpha*a^4*x+12*u*y*beta*a^2-4*u*y*a^3*x-8*u*a*x*beta+12*u*x*alpha*a^2-4*u*a*x*y-12*u*a*alpha*beta-8*u*a*y*alpha-8*u*x*beta*a^3+a^4*alpha^2+y^2*a^2+x^2*a^2+a^2*beta^2+a^2*alpha^2+32*a^2*u^3+4*u^2*beta^2+16*u^2*a^2+2*beta*y-2*alpha*beta*a^3-2*a*x*beta+2*x*alpha*a^2-2*y*a^3*alpha-2*a*y*alpha+beta^2+16*a^2*u^4+16*a^2*u^4*alpha^2+16*a^2*u^4*beta^2+32*a^2*u^3*beta^2+24*u^2*a^2*beta^2+24*u^2*a^2*alpha^2+4*u^2*a^4*alpha^2+4*u^2*y^2*a^2+4*u^2*x^2*a^2+2*alpha*a^4*x-2*y*a^3*x-2*a*x*y+4*u*a^4*alpha^2+4*u*y^2*a^2+8*u*a^2*alpha^2+8*u*a^2*beta^2+4*u*beta*y+4*u*beta^2+y^2+a^4*x^2:
vars:=[op(indets(f))];
F := [];
st := time():
Optimize(f, F, vars, verbose = vverb);
time()-st;