Write a function sop(ns, ps) which takes a group of tuples ns (i.e. [(a1,n1),...

Question

Write a function sop(ns, ps) which takes a group of tuples ns (i.e. [(a1,n1),...,(ak,nk)]) as its first argument, and a list of one or more primes ps (i.e., of the form [p1,...,pm]) as its second argument. The function returns the correct result of the sum of powers as long as the following is true (e.g., on a computer with unlimited memory and time):

0 <= a1^n1 + ... + ak^nk < p1 * ... * pm

You may assume the second list contains distinct prime numbers. You may not assume that the numbers in the first input list have any particular patterns or relationships; The implementation must work efficiently on very large inputs (e.g., with computations like 229999999999999999999999999999999996).

Explanation / Answer

A number of important SOP types are:

- Fundamental SOPs. These give instructions how to make SOPs of the other categories.
- Methodic SOPs. These describe a complete testing system or method of investigation.
- SOPs for safety precautions.
- Standard procedures for operating instruments, apparatus and other equipment.
- SOPs for analytical methods.
- SOPs for the preparation of reagents.
- SOPs for receiving and registration of samples.
- SOPs for Quality Assurance.
- SOPs for archiving and how to deal with complaints.

2.2 Initiating a SOP

As implied above, the initiative and further procedure for the preparation, implementation and management of the documents is a procedure in itself which should be described. These SOPs should at least mention:

a. who can or should make which type of SOP;
b. to whom proposals for a SOP should be submitted, and who adjudges the draft;
c. the procedure of approval;
d. who decides on the date of implementation, and who should be informed;
e. how revisions can be made or how a SOP can be withdrawn.

It should be established and recorded who is responsible for the proper distribution of the documents, the filing and administration (e.g. of the original and further copies). Finally, it should be indicated how frequently a valid SOP should be periodically evaluated (usually 2 years) and by whom. Only officially issued copies may be used, only then the use of the proper instruction is guaranteed.

In the laboratory the procedure for the preparation of a SOP should be as follows:

The Head of Laboratory (HoL) charges a staff member of the laboratory to draft a SOP (or the HoL does this himself or a staff member takes the initiative). In principle, the author is the person who will work with the SOP, but he or she should always keep in mind that the SOP needs to be understood by others. The author requests a new registration number from the SOP administrator or custodian (which in smaller institutes or laboratories will often be the HoL, see 2.4). The administrator verifies if the SOP already exists (or is drafted). If the SOP does not exist yet, the title and author are entered into the registration system. Once the writing of a SOP is undertaken, the management must actively support this effort and allow authors adequate preparation time.

In case of methodic or apparatus SOPs the author asks one or more qualified colleagues to try out the SOP. In case of execution procedures for investigations or protocols, the project leader or HoL could do the testing. In this phase the wording of the SOP is fine-tuned. When the test is passed, the SOP is submitted to the SOP administrator for acceptance. Revisions of SOPs follow the same procedure.

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