In scientific writing my professor (not a native English speaker) sometimes uses "up to SOMETHING" with the intention of expressing that SOMETHING is neglected, ignored, or excluded (see the examples below). Is such usage ever correct? (It seems a bit contrary to the widespread use cases such as in "up to five" or "to be up to something".) Is there some other short expression that can be used to convey this intended meaning in general.
Here are the examples (First line: what is written. Second line: what is meant.)
A fulfills the condition B up to corrections of order x^4.
(A fulfills the condition B if we expand everything in x and neglect all terms of x^4 and higher.)
A equals B up to C-effects.
(A equals B if the effects of the phenomenon C are ignored.)
A is fixed up to a phase.
(We can determine the magnitude of A, but not the phase.)