This is absolutely not a matter of English usage, but a matter of mathematical usage. I once said to a colleague of mine in the Anthropology Department that mathematicians often say, and write, “We have that $A=B$”, and his mouth dropped wide open. Now I have to admit that the Great and Blameless Serge Lang often wrote the offending words, but after all he was not a native speaker of English, and I think it’s wrong, wrong, wrong. Here’s my analysis of what’s going on:
The conjunction that is used to introduce a dependent noun clause of indirect statement: “I know that my Redeemer liveth”, “I’ve heard that you were sick.” My firm conviction is that such a clause can be introduced by, can be the object of, only verbs of sensing, thinking, or saying. Maybe a few other kinds of verbs. But it can’t be the object of the verb “have”. Syntactically it’s fine, “have” takes a noun as object, the clause of indirect statement is a noun clause, it all fits. It’s just that sensitive native speakers of English don’t complete that verb with that kind of clause.
And I agree with Knuth, that it’s perfectly all right to say “We have $A=B$.” Here the equation as written stands as a thing-in-itself, maybe you can explain the construction as a short form of “We have the relation $A=B$.” So the object of “have” is either the whole equation “$A=B$” or the noun “relation”, with the equation standing in apposition to the noun.
One more remark, before I get off my high horse: When refereeing a paper, I always say that I strongly urge the author to change the offending construction, but I do not insist. The usage is too well established to try singlehandedly to change things. But it’s still wrong, wrong, wrong.
Here endeth the sermon.