CoCoA » CoCoA-5

I'm not sure how widespread this should be.

Perhaps the best approach would be to implement separately for a few functions, and then decide whether we want to (and can) automate the "coercion" from RINGELEM to INT or RAT.

I do have some doubts (=gut feeling) about automatic conversion for some "number theory" functions.
NOTE for instance gcd

I note that FloatStr used to be implemented in approx.cpkg5 and would accept a RINGELEM argument (which was presumably converted by AsRAT).

The problem arose when I tried running last year's examples for system solving...

Here are the fns which can be applied to RAT according to the C5 online help system:

? abs -- absolute value of a number
? AsINT -- convert into an INT
? AsRAT -- convert into a RAT
? ceil -- round rational up to integer
? CFApprox -- continued fraction approximation
? CFApproximants -- continued fraction approximants
? ContFrac -- continued fraction quotients
? floor -- round rational down to integer
? FloorLog2, FloorLogBase -- integer part of the logarithm
? IsZero -- test whether an object is zero
? max -- a maximum element of a sequence or list
? min -- a minimum element of a sequence or list
? num -- numerator
? product -- the product of the elements of a list
? round -- round to integer
? SimplestRatBetween -- find simplest rational in a closed interval
? sum -- the sum of the elements of a list
? TimeFrom -- time elapsed since a given moment

I think that abs, max, min, floor, ceil should not do auto conversion to RAT because they are operations defined on elements of ordered rings -- if the ring is not ordered, they should fail.

Similarly num and den should not do auto conversion because they are defined for elements of fraction fields.

sum and product would convert from INT|RAT to RINGELEM, and not the other way.

The only doubtful cases are: CFApprox, CFApproximants, ContFrac, ILogBase, round, SimplestRatBetween. At the moment I prefer not to have automatic conversion from RINGELEM to RAT for these functions.