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I'm looking for a term that describes "forcing into a particular form", "forcing into looking like something else", or even "forcefully fitting into a category"

Ex:

"We (word) the function/statement/etc. into this particular form so that we can make statements about it using what we already know"

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The metaphorical "shoehorning" might work. Pigeon-holing might be what you're looking for. Rubricate is a bit of a stretch, but it could work. How about circumscribe? –  rhetorician Apr 11 '13 at 1:09
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6 Answers

To borrow from programming terminology, to coerce or to cast might fit.

We can coerce an adjective into a noun by adding a -ness ending to it, which may be understood even if, technically, it isn't the correct noun form.

We cast expressions into variables to save our hands when writing equations.

Or simply even convert

We convert the function into this particular form so that we can make statements we already know.

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Refactor could also be useful in a programming context. –  Hannele Apr 10 '13 at 15:55
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I think the word mold would suffice in your sentence. As a verb, it means:

to work into a required shape or form; shape.

We mold the function into this particular form so that we can make statements about it using what we already know.

Works for me.

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Warp, twist, distort, transform, mutate, modify, bend.

When someone tries to modify the question so that the answer they have already chosen seems to work, we say, "Don't try to fit the question to the answer," or "Don't try to make the question fit the answer." Perhaps that will give you something to work with.

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The phrase Procrustean bed comes to mind. –  John Lawler Apr 10 '13 at 2:39
    
"Contort" maybe. Or "pervert". –  lessthanideal May 6 '13 at 1:53
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The previously-suggested words cast and manipulate are often used in contexts like your sample sentence; for example,

We cast the statement into form X so what we already know about X readily applies.”

Other words used in such a context include:
normalize, “To format in a standardized manner, to make consistent. [eg] We'll need to normalize these statements before we can compare them”
canonicalize, “To convert (data) into canonical form”, where canonical means “prototypical” or “according to recognised or orthodox rules” or “stated or used in the most basic and straightforwardly applicable manner [eg] the reduction of a linear substitution to its canonical form”. Note, canonicalize is a hyponym of normalize.

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manipulate: to change by artful or unfair means so as to serve one's purpose

"We manipulate the function/statement/etc. into this particular form so that we can make statements about it using what we already know."

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How about "put"?

"We put the statement into this particular form so that we can make statements about it using what we already know."

Doesn't work if by force you mean it isn't really a natural fit.

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