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I know a Sledgehammer is a special type of hammer, but I still do not quite get the exact meaning of the word in such a paragraphs as:

The computational sledgehammer par excellence is the spectral sequence; these are essential in the Cartan-Eilenberg and Tohoku approaches where they are needed, for instance, to compute the derived functors of a composition of two functors. Spectral sequences are less essential in the derived category approach, but still play a role whenever concrete computations are necessary.

Does it mean something like the key to decipher a problem, to facilitate or easy up computation, or does it mean something like the nemesis in this context, a fatal flaw which makes everything crash?

Ivo Terek
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Javier Arias
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    It means that the technique is a great computational tool- a heavy tool for smashing many problems. "Hulk Smash" – voldemort Jan 20 '15 at 15:13
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    It means that one is using a a very powerful tool where a much lower-powered tool would suffice to do the job, like using a sledgehammer to pound a nail when a carpenter hammer would suffice, or using a nuclear bomb to kill a mosquito, etc. – Bill Dubuque Jan 20 '15 at 15:55
  • @Bill: In this context I think that voldemort is right: it’s simply a very powerful computational tool. Using it is sometimes necessary and sometimes overkill. – Brian M. Scott Jan 20 '15 at 19:08
  • @Brian Right, but one wouldn't call it a sledgehammer in specific cases where there is no simpler way. An analogous remark might be made about the use of the Euclidean algorithm, Grobner bases, etc. – Bill Dubuque Jan 20 '15 at 19:19
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    @Bill: But the quoted passage does call it a sledgehammer in cases in which it is essential. – Brian M. Scott Jan 20 '15 at 19:24

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A sledgehammer is not just a special hammer, but a very large and heavy hammer. Normally one uses it for demolition, to break big things. You wouldn't want to use it to drive a nail, much less a small nail.

vadim123
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  • Well, but is it to be taken in the paragraph above as a key allowing some computation, or, on the contrary, as something smashing it and making it impossible? – Javier Arias Jan 20 '15 at 15:34
  • Smashing in this case means smashing the problem, the difficulties. For example, one can sum the harmonic series by a simple formula, or use the sledgehammer of approximating with an integral, then calculating the accuracy of that the approximation. – vadim123 Jan 20 '15 at 15:50
  • Ok,so it is a problem-solving device, so to speak.... – Javier Arias Jan 20 '15 at 15:59