This question is one of English usage, but I'm sure only mathematicians can answer it for me.
I want to say in a technical report that an attribute is "ignored" or "forgotten" by an equivalence modulo that attribute. The specific example: the Hopf Map clumps all points on the 3-sphere $\mathbb{S}^3$ into equivalence classes of points $(z_1,\,z_2)$ that differ from one another by "phase only", i.e. modulo a common scaling by a point on the unit circle, i.e
$$(z_1,\,z_2) \sim (z_1^\prime,\,z_2^\prime) \Leftrightarrow \exists \phi\in\mathbb{R}\ni z_1^\prime=z_1\,e^{i\,\phi}, \,z_2^\prime=z_2\,e^{i\,\phi}$$
I'm seeking a sentence like the "Hopf map is modding away common phases", but that's my inner three year old coining a new verb from a noun - can people tell me similar phrase that has known usage? Surprisingly, I have not read the idea expressed in this way (a verb to describe an equivalence relation actively "forgetting" an attribute that is "modded away").
This is a report not meant for mathematicians, but rather for a mathematically literate audience whom I am trying to get across the the idea to of the Hopf map as the minimum complexity and precise tool for forgetting common phases.