Is it more computationally expensive to call another contract's function than calling that function internally? If so, is it appreciably more expensive or is it fairly negligible?

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Yes it will cost more gas. By calling a function from another contract, you will need to use the CALL opcode. If you are calling a function within the same contract, it will simply do a JUMP. CALLs are a few hundred gas more expensive.

Edit for additional information: To be specific with gas amounts, CALLs are ~700 gas, whereas JUMPs are 1 gas.

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