An Upper Bound of the Bezout Number for Piecewise Algebraic Curves over a Rectangular Partition

Table 1

Comparisons of 𝐵𝑁 and 𝐵𝑁₂ (where 𝑎≥𝑏≥2 and 𝑁=𝑎𝑏).

	𝐵𝑁	𝐵𝑁2	𝐵𝑁2−𝐵𝑁
𝑎 and 𝑏 are both even	𝑁𝑚𝑛−𝑁𝑟	𝑁𝑚𝑛−𝑟(𝑁−𝑏)	𝑏𝑟≥0
(𝑎−𝑏) is odd	𝑁𝑚𝑛−(𝑁−1)𝑟	𝑁𝑚𝑛−𝑟(𝑁−𝑏)	(𝑏−1)𝑟≥0
𝑎 and 𝑏 are both odd	𝑁𝑚𝑛−(𝑁−2)𝑟	𝑁𝑚𝑛−𝑟(𝑁−𝑏)	(𝑏−2)𝑟≥0