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h.lift(I) should do the job. See documentation for details.

h.lift(I) should do the job. See documentation for details.

B.<x,y> = BooleanPolynomialRing()
I = ideal(x+1,y+1)
pol = x+y
#print( pol.lift(I) )      # this is not implemented

#workaround:
nvars = len(B.gens())
F = PolynomialRing(GF(2),nvars,'z')
I2 = [F(g) for g in I.gens()] + [g^2+g for g in F.gens()]
print( F(pol).lift(I2)[:len(I.gens())] )

h.lift(I) should do the job. See documentation for details.

Since lift is not implemented for BooleanPolynomialRing, we can workaround by considering the ideal generated by $f,g$ and $x_i^2+x_i$ in $GF(2)[x_1,\dots,x_n]$. Here is a sample code:

B.<x,y> = BooleanPolynomialRing()
I = ideal(x+1,y+1)
pol = x+y
#print( pol.lift(I) )      # this is not implemented

#workaround:
nvars = len(B.gens())
F = PolynomialRing(GF(2),nvars,'z')
I2 = ideal( [F(g) for g in I.gens()] + [g^2+g for g in F.gens()]
F.gens()] )
print( F(pol).lift(I2)[:len(I.gens())] )

h.lift(I) should do the job. See documentation for details.

Since lift is not implemented for BooleanPolynomialRing, we can workaround by considering the ideal generated by $f,g$ and $x_i^2+x_i$ in $GF(2)[x_1,\dots,x_n]$. Here is a sample code:

B.<x,y> = BooleanPolynomialRing()
I = ideal(x+1,y+1)
pol = x+y
#print( pol.lift(I) )      # this is not implemented

#workaround:
nvars = len(B.gens())
F = PolynomialRing(GF(2),nvars,'z')
I2 = ideal( [F(g) for g in I.gens()] + [g^2+g for g in F.gens()] )
coefs = [c.substitute(dict(zip(F.gens(),B.gens()))) for c in F(pol).lift(I2)[:len(I.gens())]]    
print( F(pol).lift(I2)[:len(I.gens())] coefs )

h.lift(I) should do the job. See documentation for details.

Since lift is not implemented for BooleanPolynomialRing, we can workaround by considering the ideal generated by $f,g$ and $x_i^2+x_i$ in $GF(2)[x_1,\dots,x_n]$. Here is a sample code:

B.<x,y> = BooleanPolynomialRing()
I = ideal(x+1,y+1)
pol = x+y
x*y + 1
#print( pol.lift(I) )      # this is not implemented

#workaround:
nvars = len(B.gens())
F = PolynomialRing(GF(2),nvars,'z')
I2 = ideal( [F(g) for g in I.gens()] + [g^2+g for g in F.gens()] )
coefs = [c.substitute(dict(zip(F.gens(),B.gens()))) for c in F(pol).lift(I2)[:len(I.gens())]]    
print( coefs )

h.lift(I) should do the job. See documentation for details.

Since lift is not implemented for BooleanPolynomialRing, we can workaround by considering the ideal generated by $f,g$ and $x_i^2+x_i$ in $GF(2)[x_1,\dots,x_n]$. Here is a sample code:

B.<x,y> = BooleanPolynomialRing()
I = ideal(x+1,y+1)
pol = x*y + 1
#print( pol.lift(I) )      # this is not implemented

#workaround:
nvars = len(B.gens())
F = PolynomialRing(GF(2),nvars,'z')
GF(2)[B.gens()]
I2 = ideal( [F(g) for g in I.gens()] + [g^2+g for g in F.gens()] )
coefs = [c.substitute(dict(zip(F.gens(),B.gens()))) [B(c) for c in F(pol).lift(I2)[:len(I.gens())]]    
F(pol).lift(I2)[:len(I.gens())]]
print( coefs )