Verrataan samalla tämän menetelmän ja Maplen oman extrema-funktion nopeutta:
> restart; > read `groebner.mpl`; > read `lagr.mpl`; > st:=time(): lagr(x^3+2*x*y*z-z^2, x^2+y^2+z^2-1); time()-st; 28 [{y = 0, x = 1, z = 0}, 1, {y = 1/3, x = -2/3, z = 2/3}, - ----] 27 3.283 > restart; > readlib(extrema); proc(fcn,cnstrnts,vars,candidates) ... end > st:=time(): extrema(x^3+2*x*y*z-z^2, x^2+y^2+z^2-1); time()-st; 28 {1, - ----} 27 2.917
Antamalla lagr:lle neljänneksi argumentiksi sana verbose saadaan näkyviin enemmän informaatiota:
> lagr(x^3+2*x*y*z-z^2, [x^2+y^2+z^2-1], [], verbose); The equations are: [2*x*z-2*lambda_[1]*y, 2*x*y-2*z-2*lambda_[1]*z, 3*x^2+2*y*z-2*lambda_[1]*x, -x ^2-y^2-z^2+1] The Groebner bases are: [[y+1, z, x, lambda_[1]], [y-1, z, x, lambda_[1]], [y, z-1, x, 1+lambda_[1]], [ y, z+1, x, 1+lambda_[1]], [3*y-1, 3*z-2, 2+3*x, 3*lambda_[1]+4], [3*y+1, 3*z+2 , 2+3*x, 3*lambda_[1]+4], [3*z+y, 128*z^2-11, 8*x+3, 8*lambda_[1]-1], [y, z, x- 1, -3+2*lambda_[1]], [y, z, x+1, 3+2*lambda_[1]], [y+1, z, x, lambda_[1]], [y-1 , z, x, lambda_[1]]] [[{x = 0, z = 0, lambda_[1] = 0, y = -1}, {x = 0, z = 0, lambda_[1] = 0, y = 1} , {z = 1, y = 0, x = 0, lambda_[1] = -1}, {y = 0, x = 0, z = -1, lambda_[1] = - 1}, {y = 1/3, x = -2/3, z = 2/3, lambda_[1] = -4/3}, {y = -1/3, x = -2/3, z = - 2/3, lambda_[1] = -4/3}, {x = -3/8, lambda_[1] = 1/8, y = -3/16*22^(1/2), z = 1 /16*22^(1/2)}, {y = 0, x = 1, z = 0, lambda_[1] = 3/2}, {y = 0, z = 0, x = -1, lambda_[1] = -3/2}, {x = 0, z = 0, lambda_[1] = 0, y = -1}, {x = 0, z = 0, lambda_[1] = 0, y = 1}], [{x = 0, z = 0, lambda_[1] = 0, y = -1}, {x = 0, z = 0 , lambda_[1] = 0, y = 1}, {z = 1, y = 0, x = 0, lambda_[1] = -1}, {y = 0, x = 0 , z = -1, lambda_[1] = -1}, {y = 1/3, x = -2/3, z = 2/3, lambda_[1] = -4/3}, {y = -1/3, x = -2/3, z = -2/3, lambda_[1] = -4/3}, {z = -1/16*22^(1/2), y = 3/16* 22^(1/2), x = -3/8, lambda_[1] = 1/8}, {y = 0, x = 1, z = 0, lambda_[1] = 3/2} , {y = 0, z = 0, x = -1, lambda_[1] = -3/2}, {x = 0, z = 0, lambda_[1] = 0, y = -1}, {x = 0, z = 0, lambda_[1] = 0, y = 1}]] The critical points are: {{z = -1/16*22^(1/2), y = 3/16*22^(1/2), x = -3/8}, {z = 1, y = 0, x = 0}, {y = 0, x = 0, z = -1}, {x = 0, z = 0, y = -1}, {x = 0, z = 0, y = 1}, {y = 0, x = 1, z = 0}, {y = 1/3, x = -2/3, z = 2/3}, {y = -1/3, x = -2/3, z = -2/3}, {x = -3/8, y = -3/16*22^(1/2), z = 1/16*22^(1/2)}, {y = 0, z = 0, x = -1}} Maximum point, maximum value, minimum point, minimum value: 28 [{y = 0, x = 1, z = 0}, 1, {y = 1/3, x = -2/3, z = 2/3}, - ----] 27