Here algebraic curve, for example.
Let c is algebraic curves, c_1, c_2, ..., c_n is c all irreducible branches.
We know that c can always be written as c = Σm_ic_i (m_i is a positive integer).
c is called irreducible if all m_i = 1.
From the perspective view of the equation: c is the local affine equation f (x, y) = 0 is defined, where f (x, y) is a polynomial.
f (x, y) can be factorized as:
f (x, y) = Π (p_i (x, y)) ^ (m_i), where m_i is a positive integer, p_i (x, y) is an irreducible polynomial.
f (x, y) is called irreducible if all m_i = 1.
p_i (x, y) = 0 defines the branch c irreducible c_i, so c = Σm_ic_i. |