论文标题
一种新颖的二元四分之一形式阳性的必要和充分条件
A novel necessary and sufficient condition for the positivity of a binary quartic form
论文作者
论文摘要
在本文中，通过考虑两个圆锥形的共同点而不是二元四分之一形式的根，我们使用圆锥形铅笔理论提出了一种新颖的必要条件，以实现二元四分之一形式的阳性。首先，我们根据两个碱基的共同点的不同出性来显示圆锥铅笔的退化成员。然后，根据退化锥体的特性获得了关于退化成员参数的不平等。最后，从不平等的情况下，我们得出了一个新的标准，用于在没有判别的情况下确定二元四分之一形式的阳性。
In this paper, by considering the common points of two conics instead of the roots of the binary quartic form, we propose a novel necessary and sufficient condition for the positivity of a binary quartic form using the theory of the pencil of conics. First, we show the degenerate members of the pencil of conics according to the distinct natures of the common points of two base conics. Then, the inequalities about the parameters of the degenerate members are obtained according to the properties of the degenerate conics. Last, from the inequalities we derive a novel criterion for determining the positivity of a binary quartic form without the discriminant.
