# When does one drop the article after "with"?

In a book on writing papers in english, one reads that the article is omitted "in some expressions describing a noun". The fact is illustrated by a few examples:

an algebra with unit e; an operator with domain H2; a solution with vanishing Cauchy data; a cube with sides parallel to the axes; a domain with smooth boundary; an equation with constant coefficients; a function with compact support; random variables with zero expectation

But

Let В be a Banach space with a weak symplectic form w. Two random variables with a common distribution.

What is the rule?

• It's a good question. In general, the rules for using articles are the same after with as they would be anywhere else (e.g. "A man with a dog"), but I think in this kind of technical writing the noun is used almost like a title or name. Also, in headlines, signs, and instructions, it's very common to leave out articles, like "Place wax paper on table" (even though paper and counter are countable and specific), and this may be a related phenomenon. Jan 6, 2017 at 16:16
• I don't believe you're going to find a rule that works for most situations, because whether you use the article really depends on what you are trying to communicate, and not on the word 'with'. Ok not happy with my examples. Let me think about it. Jan 9, 2017 at 17:24
• Note that the book mentioned by the OP and which the quoted text was taken from is Writing Mathematical Papers in English: A Practical Guide By Jerzy Trzeciak, page 26. (For your convenience, you can click this link to see the quoted text as printed in the book: i.stack.imgur.com/afe7w.jpg.) Jan 9, 2017 at 21:08
– Ben
Jul 21, 2021 at 14:41
• Ben, still no progress :( Jul 22, 2021 at 18:32

There is a specific explanation for each of the examples.

an algebra with unit e;

Every algebra had a unique unit which is a property of it; for this algebra the unit is e. It cannot be "a unit" because there is only one unit. This is perhaps a contraction of "with the unit being e".

an operator with domain H2;

Similar. Every operator has a domain, and only one domain.

a solution with vanishing Cauchy data;

"Data" is plural, so no article is needed.

a cube with sides parallel to the axes;

Plural, and all sides are parallel to the axes, so no article. If only one side is parallel, it would have to have an aritcle; "a side parallel" or "one side parallel".

a domain with smooth boundary;

As before, the boundary is referred to as a property of the domain, and not as just a curve; there is only one boundary, and it is smooth. Can be "with the boundary being smooth".

an equation with constant coefficients;

Plural.

a function with compact support;

Property of a function

random variables with zero expectation

The expectation is a property of the distribution, which is a property of the RV.

But

Let В be a Banach space with a weak symplectic form w.

W is some weak symplectic form, it is not determined, so use an indeterminate article.

Two random variables with a common distribution.

Some distribution, which is common to both, but otherwise not specified. If it was specified, the article would be omitted: "two random variables with common distribution N(0, 1)".

• This seems a roundabout way to say "there doesn't seem to be any overarching set of rules", which I already told OP in my own answer. I'm looking for something deeper. Jan 9, 2017 at 20:56
• What I'm saying is that these are separate examples and there is no "rule for article after with". There are article "rules" for plural, unique nouns, etc., which you can find in grammar books. I don't think there is anything deeper that applies to "with". Jan 12, 2017 at 15:50
• Hmm... what do you think about this example: Let X be a Banach space with weak symplectic form ω. Is it an error or is it an exception to the rule in the book? Jan 12, 2017 at 16:35
• Thanks for providing the source. Thus sentence was quoted in the OP, so it is definitely not an exception. As I explained above, the puzzle can be solved by noting that the "weak apoplectic form" is unique for a Banach space. Therefore the sentence needs no article. It is similar to "a house with red roof", in that there is only one roof, so no use of stating "with a red roof". Jan 13, 2017 at 7:35

As stangdon mentions in his comment, in technical writing the article is often omitted. So it's just as unnecessary in your second example,

"Let B be a Banach space with weak symplectic form w ..."

The only reason you would use an article is to clarify that, of the many flavors of "weak symplectic form" available, you one to focus on one specific iteration or type or whatever.

In the same way

Two random variables with common distribution

sounds fine. There's really no harm in using the article, though.

• Do you mean that the place after "with" is no different from any other? Jan 6, 2017 at 18:59
• @Serguei I'm not sure I understand the question? If you mean, can you always omit the article, the answer is "no". Rather, in technical writing, you can more often than with other kinds of writing. Jan 6, 2017 at 19:12
• " you can more often". This is my question: exactly when can I omit an article that would be mandatory in non-technical writing? Jan 6, 2017 at 19:54
• @Serguei this might help: ell.stackexchange.com/questions/33304/… Jan 6, 2017 at 20:00
• No, it doesn't :( Mathematical books bear no resemblance to the instruction cited by TRomano, which has no articles at all Jan 6, 2017 at 20:19