Revision history [back]
 | 1 | initial version |
You'd better employ polynomial machinery here:
R.<b0, h, v_0, v_1, v_2, u_0, u_1, u_2, a1, a2> = PolynomialRing( QQ, order='lex' )
J = R.ideal( [-h*v_0+2*u_1-2*u_0 - a1, -2*(h*v_0-u_1+u_0) - a2] )
J.reduce( b0 - (16*h^2*v_0^2+(38*h*u_0-38*h*u_1)*v_0+25*u_1^2-50*u_0*u_1+25*u_0^2)/3 )
Notice that a0 and a1 comes last in the list of variables in R.<...> and so under the lexicographical order (order=lex') the other variables will be eliminated (by.reduce()function) in favor of usinga1anda2`.
| | 2 | No.2 Revision |
You'd better employ polynomial machinery here:
R.<b0, h, v_0, v_1, v_2, u_0, u_1, u_2, a1, a2> = PolynomialRing( QQ, order='lex' )
J = R.ideal( [-h*v_0+2*u_1-2*u_0 - a1, -2*(h*v_0-u_1+u_0) - a2] )
J.reduce( b0 - (16*h^2*v_0^2+(38*h*u_0-38*h*u_1)*v_0+25*u_1^2-50*u_0*u_1+25*u_0^2)/3 )
Notice that a0 and a1 comes last in the list of variables in R.<...> and so under the lexicographical order (order=order='lex'lex') the other variables will be eliminated (by(by .reduce().reduce() function) in favor of usingusing a1a1 and anda2a2`..
| | 3 | No.3 Revision |
You'd better employ polynomial machinery here:
R.<b0, h, v_0, v_1, v_2, u_0, u_1, u_2, a1, a2> = PolynomialRing( QQ, order='lex' )
J = R.ideal( [-h*v_0+2*u_1-2*u_0 - a1, -2*(h*v_0-u_1+u_0) - a2] )
J.reduce( b0 - ( (16*h^2*v_0^2+(38*h*u_0-38*h*u_1)*v_0+25*u_1^2-50*u_0*u_1+25*u_0^2)/3 ) )
Notice that a0 and a1 comes last in the list of variables in R.<...> and so under the lexicographical order (order='lex') the other variables will be eliminated (by .reduce() function) in favor of using a1 and a2.
| | 4 | No.4 Revision |
You'd better employ polynomial machinery here:
R.<b0, h, v_0, v_1, v_2, u_0, u_1, u_2, a1, a2> = PolynomialRing( QQ, order='lex' )
J = R.ideal( [-h*v_0+2*u_1-2*u_0 - a1, -2*(h*v_0-u_1+u_0) - a2] )
J.reduce( b0 - ( (16*h^2*v_0^2+(38*h*u_0-38*h*u_1)*v_0+25*u_1^2-50*u_0*u_1+25*u_0^2)/3 ) )
Notice that a0 and a1 comes last in the list of variables in R.<...> and so under the lexicographical order (order='lex') the other variables will be eliminated (by .reduce() function) in favor of using a1 and a2.. The result of .redice() function is
b0 - a1^2 - 13/12*a2^2
which you may interpret as b0 == a1^2 + 13/12*a2^2 if you like.
