请问老师AS在此句英语的语法作用。Manyfirms,forinstance,havegreatdifficultyinobtainingtechnicalorscientificbooksfromlibrariesbecausetheyareunwillingtohavetheirnamesenteredashavingtakenoutsuchandsuchabook,

Question

请问老师AS在此句英语的语法作用。
Many firms, for instance, have great difficulty in obtaining technical or
scientific books from libraries because they are unwilling to have their names
entered as having taken out such and such a book, for fear the agents of other
firms should be able to trace the kind of research they are likely to be
undertaking.

其中 1.as having taken out 如何理解，
2.as在此处的语法功能，
3.为何having taken out 要用动名词的完成时态？

Answer 1

例如 很多公司向图书馆借阅科技书籍时感到很困难,因为它们不愿意因借阅某一本书让人家记下它们公司的名字,生怕别的公司的情报人员发现他们可能要从事的某项科研项目。

其中 as having taken out 可以看做 介词短语 ，也可以看做带连词的现在分词短语，可以看做是 原因 状语 修饰 不定式 to have their names entered 。因为 动作 在 不定式之前 所以 用 动名词或 现在分词 的完成形式。
（先借书， 后登记 某人借了什么书）