4 papers · 1 filter
Sparse Polynomial GCD Cannot Be Computed in Fixed-output Polynomial Time
Ruichen Qiu, Yichuan Cao, Qiao-Long Huang +2
This paper shows that, assuming , sparse univariate polynomial GCD cannot be computed in fixed-output polynomial time over any fixed computable field. Pre…
Sparse Polynomial Divisibility Test over Finite Field is CoNP-hard
Yichuan Cao, Ruichen Qiu, Qiao-Long Huang +2
In this paper, we show that deciding whether a sparse polynomial does not divide another sparse polynomial exactly over finite fields is NP-hard under BPP many-one reductions. Equi…
A Finite Certificate for the Positive Vasc Inequality
Dakai Guo, Ruichen Qiu, Yichuan Cao +1
We prove the positive-real case of the Vasc cyclic inequality. The proof was obtained with human-guided assistance from the AI agent MechMath Agent Team: the human-readable p…
Rational Solutions of First Order Algebraic Ordinary Differential Equations
Ruyong Feng, Shuang Feng
Let be a first order ordinary differential equation with polynomial coefficients. Eremenko in 1999 proved that there exists a constant …