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I have 10 binary variables $x_0, ..,,x_4$ and $y_0,..,y_4$. I know $y_i=x_i+x_{(i+1)\bmod 5}$. I want to write $x_i$ in terms of $y$ variables. I know for this toy case we can use Gaussian elimination. But in actual case $y_i$s are nonlinear equations. I tried this idea:

n = 5

RING = PolynomialRing(GF(2),2*n,['x%d'%(i) for i in range(n)] + ['y%d'%(i) for i in range(n)])

RING.inject_variables()

Z = list(RING.gens())

E=[y0==x0+x1, y1==x1+x2, y2==x2+x3, y3==x3+x4, y4==x4+x0]

solve(E, x0,x1,x2,x3,x4)

It is not working.

I have 10 binary variables $x_0, ..,,x_4$ and $y_0,..,y_4$. I know $y_i=x_i+x_{(i+1)\bmod 5}$. I want to write $x_i$ in terms of $y$ variables. I know for this toy case we can use Gaussian elimination. But in actual case $y_i$s are nonlinear equations. I tried this idea:

n = 5

RING = PolynomialRing(GF(2),2*n,['x%d'%(i) for i in range(n)] + ['y%d'%(i) for i in range(n)])

RING.inject_variables()

Z = list(RING.gens())

E=[y0==x0+x1, y1==x1+x2, y2==x2+x3, y3==x3+x4, y4==x4+x0] E=[y0==x0x1+x2, y1==x1x2+x3, y2==x2x3+x4, y3==x3x4+x0, y4==x4*x0+x_1]

solve(E, x0,x1,x2,x3,x4)

It is not working. working.

I have 10 binary variables $x_0, ..,,x_4$ and $y_0,..,y_4$. I know $y_i=x_i+x_{(i+1)\bmod 5}$. I want to write $x_i$ in terms of $y$ variables. I know for this toy case we can use Gaussian elimination. But in actual case $y_i$s are nonlinear equations. I tried this idea:

n = 5

RING = PolynomialRing(GF(2),2*n,['x%d'%(i) for i in range(n)] + ['y%d'%(i) for i in range(n)])

RING.inject_variables()

Z = list(RING.gens())

E=[y0==x0E=[y0==x_0x1+x2, y1==x1x_1+x_2, y_1==x_1x2+x3, y2==x2x_2+x_3, y_2==x_2x3+x4, y3==x3x_3+x_4, y_3==x_3x4+x0, y4==x4*x0+x_1] x_4+x_0, y_4==x_4*x_0+x_1]

solve(E, x0,x1,x2,x3,x4)

It is not working.

I have 10 binary variables $x_0, ..,,x_4$ and $y_0,..,y_4$. I know $y_i=x_i+x_{(i+1)\bmod 5}$. I want to write $x_i$ in terms of $y$ variables. I know for this toy case we can use Gaussian elimination. But in actual case $y_i$s are nonlinear equations. I tried this idea:

n = 5

RING = PolynomialRing(GF(2),2*n,['x%d'%(i) for i in range(n)] + ['y%d'%(i) for i in range(n)])

RING.inject_variables()

Z = list(RING.gens())

E=[y0==x_0$E=[y_0==x_0x_1+x_2, y_1==x_1x_2+x_3, y_2==x_2x_3+x_4, y_3==x_3x_4+x_0, y_4==x_4*x_0+x_1] $

solve(E, x0,x1,x2,x3,x4)

It is not working.

I have 10 binary variables $x_0, ..,,x_4$ and $y_0,..,y_4$. I know $y_i=x_i+x_{(i+1)\bmod 5}$. I want to write $x_i$ in terms of $y$ variables. I know for this toy case we can use Gaussian elimination. But in actual case $y_i$s are nonlinear equations. I tried this idea:

n = 5

RING = PolynomialRing(GF(2),2*n,['x%d'%(i) for i in range(n)] + ['y%d'%(i) for i in range(n)])

RING.inject_variables()

Z = list(RING.gens())

$E=[y_0==x_0E=[y_0==x_0x_1+x_2, y_1==x_1x_2+x_3, y_2==x_2x_3+x_4, y_3==x_3x_4+x_0, y_4==x_4*x_0+x_1] $

solve(E, x0,x1,x2,x3,x4)

It is not working.

I have 10 binary variables $x_0, ..,,x_4$ $x_0$, ..., $x_4$ and $y_0,..,y_4$. $y_0$, ..., $y_4$. I know $y_i=x_i+x_{(i+1)\bmod 5}$. $y_i = x_i + x_{(i+1)\bmod 5}$.

I want to write $x_i$ in terms of $y$ variables. variables.

I know for this toy case we can use Gaussian elimination. elimination. But in actual case $y_i$s are nonlinear equations.

It is not working.