[Learning algorithm] polynomial family bucket --3 (arbitrary modulus Series & strengthen series)

NTT any modulus

Topic links: Luo Gu P4245 arbitrary modulus NTT

Solution

https://www.luogu.com.cn/problemnew/solution/P4245

Any polynomial modulo inverse

Topic links: Luo Gu P4239 arbitrary modulus inverse polynomial multiplication

Solution

Any modulus exp

Topic links: Luo Gu T128649 arbitrary polynomial modulus exp

Solution

https://www.luogu.com.cn/blog/chuyanbuxun/solution-p4726

Open polynomial root (enhanced version)

Topic links: Luo Gu P5277 open polynomial root (enhanced version)

Solution

Polynomial power function (enhanced version)

Topic links: Luo Gu P5273 power polynomial function (enhanced version)

Solution

Trigonometric polynomial

Topic links: Luo Gu P5264 trigonometric polynomial

Solution

Inverse trigonometric polynomial

Topic links: Luo Gu P5265 inverse trigonometric polynomial

Description

Given a \ (n-1 \) Polynomial \ (A (X) \) , find one (mod \ x ^ n \) \ polynomial under \ (B (X) \) , satisfies \ (B ( x) \ equiv arcsin (A ( x)) \) or \ (B (X) \ equiv arctan (A (X)) \) .
All operations are die \ (998 244 353 \) be the sense, reading a \ (of the type \) , if \ (of the type = 0 \) , represents beg \ (arcsin \) , otherwise behalf seeking \ (arctan \) .
Data range \ (. 1 \ n-Le \ Le ^ 10. 5, a_i \ in [0, 998 244 353) ∩ the Z \) , to ensure data \ (a_0 = 0 \) .
Uniformly distributed half point satisfies \ (type = 0 \) , and the other half to meet \ (. 1 type = \) .