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Ecuaţie algebrică

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O ecuaţie algebrică are forma:

NumberedEquation1.gif

f(x_1,x_2,...,x_n)=\sum_{e_1,...,e_n}c_{e_1,e_2,...,e_n}x_1^{e_1}x_2^{e_2}...x_n^{e_n}=0,

unde coeficienţii c_{e_1,e_2,...,e_n} sunt întregi, exponenţii e_i sunt pozitivi, iar suma este finită.

Exemple:

Curba Ecuaţia
Dreapta care trece prin punctele (1 , 0) şi (0 , 1) x+y-1=0
Sexticul lui Cayley  4(x^2+y^2-x)^3-27(x^2+y^2)^2=0
Octoida x^4 - (x^2 + y^2) = 0
Planul care trece prin punctele (1, 0, 0) x + y +z - 1 = 0
Cercul unitar x^2 + y^2 - 1 = 0
Sfera unitară x^2 + y^2  + z^2- 1 = 0


Sursa: Wolfram MathWord

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