Given a pair of regular quadratic forms over $\mathbb{Q}$ which are in the same genus and a finite set of primes P, we show that there is an effective way to determine a rational equivalence between these two quadratic forms which are integral over every prime in P. This answers one of the principal questions posed by Conway and Sloane (1999) [3, page 402],.

中文翻译：

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避免素数的有理二次形式等价的显式结果

给定一对正则二次形式 $\mathbb{问}$它们属于相同的属，并且有素数P的有限集，我们证明存在一种有效的方法，可以确定在P的每个素数上都是不可或缺的这两个二次形式之间的有理等价。这回答了Conway和Sloane（1999）[3，第402页]提出的主要问题之一。