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I have ceased to understand which article must be used there. On the one hand (suppose that the mentioned method exists and has no namesakes) it is the method. But on the other hand, there are many standard methods and this is one of them.

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In the absence of any further context, "A" implies that there are several standard methods of k-decomposition, and you are using one of them but not, at this point, specifying which; "the" implies that there is only one standard method of k-decomposition.

If you have previously identified the method being used, then "the" picks it out without implying that it is the only one.

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  • so, in neither case the sentence means that I use the (only existing) method of k-decomposition, which is one of standard methods?
    – Serguei
    Nov 6 '16 at 9:43
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    It could mean that with enough context, @Serguei; but I would not understand that to be the meaning otherwise.
    – Colin Fine
    Nov 7 '16 at 0:55

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