#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## depend

[on sth; *see also*: base, rely, rest

However, the space Z depends crucially on the particular ambient algebra A chosen.

Note that O(g) depends on g only through its differential dg.

We have to keep track of how the constant K depends on the domain D.

The answer depends on how broadly or narrowly the term “matrix method” is
defined.

Up to equivalence it only depends on the pair (f,g).

We divide them into three classes depending on the width of k.

The proof of (2) is a matter of straightforward computation, and
depends on the relation ab-cd=1.

These functions are sometimes called elementary factors. Their utility depends on the fact that......

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