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From a Baidu page about 拉丁矩 (Latin rectangles, a topic in combinatorial mathematics, and one of my research topics), we have the following sentence (listed as 定义1; I trim back some of the mathematics notation):

设A是一个m×s矩阵,若A的任一行是集{1,...,n}的一个s-排列,任一列是集{1,...,n}的一个m-排列,则称A是一个m×s拉丁矩。

I translate this to something like:

If A is an m×s matrix, such that every row is an s-permutation of {1,...,n} and every column is an m-permutation of {1,...,n}, then A is a Latin rectangle.

I'm confused about the grammar here, and in particular, the use of (what seems to be) the following:

设A是[a mathematical object], 若A的[conditions], 则称A是[a special type of that mathematical object].

I'm seeking a better overall idea of how this structure works, e.g., how frequently this is used, other examples, and what , , and are doing in the sentence.

Question: How does 设A是..., 若A的..., 则称A是... work for mathematical definitions?

  • see dictionaries, 设suppose, 若if, supposing, assuming, 则 then, 称 (call, name)is called, for more examples, find English original and Chinese translation of mathematical textbooks (available at university libraries) – user6065 Jul 5 '18 at 10:31
  • But I think there's more materials in English about Latin Squares hahaha. P.S. I was taught the term "Latin Square" 拉丁方 when I was learning discrete mathematics last year. : ) – Toosky Hierot Jul 5 '18 at 10:35
  • 则称是 is a little weird. I think it should be 则称A是. Then (we) call A [a special type of that mathematical object]. What's important is , I can't find your original sentence in the link, is it edited by anyoneone after you post this question? – user19549 Jul 5 '18 at 10:35
  • Oh I see the difference: A latin square has to be a square while a latin rectangle doesn't. – Toosky Hierot Jul 5 '18 at 10:37
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    @神秘德里克 Yeah, I find that the original sentence in the given link is actually “则称A是”. – Toosky Hierot Jul 5 '18 at 10:45
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  • 「設」is short for 假設 (Suppose that...)

  • 「若」means if

  • 「則稱」, literally then (it is) called, should just be taken as then.

設A是一個m×s矩陣,若A的任一行是集{1,...,n}的一個s-排列,任一列是集{1,...,n}的一個m-排列,則稱A是一個m×s拉丁矩。

「Suppose that」A is an m by s matrix.「If」every row of A is an s-permutation of {1, ..., n} and every column is an m-permutation of {1, ..., n},「then」A is an m by s Latin rectangle.

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