In this paper, we investigate the total coefficient size of Nullstellensatz proofs. We show that Nullstellensatz proofs of the pigeonhole principle on $n$ pigeons require total coefficient size $2^{\Omega(n)}$ and that there exist Nullstellensatz proofs of the ordering principle on $n$ elements with total coefficient size $2^n - n$.

翻译：在本文中,我们调查了Nullstelennsatz证据的总系数大小。我们表明,Nullstelennsatz证明鸽子洞原则对一美元鸽子的证明要求总系数大小为2美元Omega(n)美元,还有Nullstelennsatz证明对总系数大小为2美元的一美元元素的定购原则。