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How do I find the degree of a multivariable polynomial automatically?


I have a very simple question which appears not to have already been answered on this forum. Is there built-in functionality that returns the degree of a multivariable polynomial? For example if the polynomial is


s1 + s2^2 s3 + s3^2 s4^7

I want Mathematica to return 9. If there is no automatic solution, could somebody please suggest a simple (and fast) implementation?


EDIT: I removed my "solution" because it actually only works for simple examples. I tested out the four solutions presented so far on a degree 20 polynomial in 6 variables (ByteCount[poly] = 2006352). I used AbsoluteTiming to determine that the answer I chose is the fastest, with a run-time of 53.06 s for 1000 evaluations. This is quite a bit faster than the closest competitor's run-time of 283.76 s for 1000 evaluations.



UPDATE: I tested the improved version of the solution (the one with random reals) and found that the run-time is now slightly worse but still far better than the competition at 90.52 s for 1000 evaluations.



Answer



Perhaps


 Exponent[# /. Thread[Variables[#] -> \[FormalX]], \[FormalX]] &[s1 + s2^2 s3 + s3^2 s4^7]
 (* 9 *)

?


UPDATE: As noted by Daniel in the comments, the original function gives the wrong result if cancellations occur after all variables are replaced by the same symbol. To fix this issue, one can modify the function as


Exponent[# /. ((# -> \[FormalX] RandomReal[]) & /@ Variables[#]), \[FormalX]] &


(per Daniel's suggestion), or as


Max@Exponent[MonomialList[#] /.Thread[Variables[#] -> \[FormalX]], \[FormalX]]&

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