kuld el az f es a h -t! Solve this with the constraint that ...

Prompt

kuld el az f es a h -t! Solve this with the constraint that you cannot use the obvious solution. What is the most powerful, strongest approach? Jacobian coefficient equations: 3*(a*f - b*e) 6*(a*g - c*e) 3*(3*a*h + b*g - c*f - 3*d*e) 3*a + f 6*(b*h - d*f) 2*(b + g) 3*(c*h - d*g) c + 3*h Groebner basis size: 11 Groebner basis: f*(3*f*h - g**2)/3 g*(3*f*h - g**2)/3 h*(3*f*h - g**2)/3 (3*d*e - 2*f*h + g**2)/3 d*f + g*h d*g + 3*h**2 (3*e*g - f**2)/3 (9*e*h - f*g)/9 (3*a + f)/3 b + g c + 3*h F o (Id - H) both components vanish modulo constraints: True remainders: [[0], [0]] nonzero coefficient remainders: 0 (Id - H) o F both components vanish modulo constraints: True remainders: [[0], [0]] nonzero coefficient remainders: 0 Coeffs for deg 10440: 54,512,461 Coeffs for deg 1653: 1,368,685 Total coeffs: 55,881,146 # Number of coefficients for degree 10440 deg_P = 10440 deg_Q = 1653 coeffs_P = (deg_P + 1) * (deg_P + 2) // 2 coeffs_Q = (deg_Q + 1) * (deg_Q + 2) // 2 print(f"Coeffs for deg {deg_P}: {coeffs_P:,}") print(f"Coeffs for deg {deg_Q}: {coeffs_Q:,}") print(f"Total coeffs: {coeffs_P + coeffs_Q:,}") számok (10440 és 1653) közös osztója 87 (mivel 10440 = 120·87, 1653 = 19·87), tehát a „nagyobb 100-nál és gcd ≥ 3” feltétel teljesül rájuk. \left(F(x,y)=(P(x,y),\,Q(x,y))\in\mathbb{C}[x,y]^2\right)\land\left(\frac{\partial P}{\partial x}\frac{\partial Q}{\partial y}-\frac{\partial P}{\partial y}\frac{\partial Q}{\partial x}\equiv 1\right)\land\left(F(0,0)=F(1,1)\right)