2. Canonic fraction
-------------------
For a mutually prime n, d : (D : IntegralDomain),
how to set fraction of n/d in Spad with avoiding gcd and also
obtaining a correct fraction?
Simplest answer is: use pretend.
Better answer is: without knowing the representation of Fraction(D) it's
impossible. And nobody, except the programmer of Fraction should know
the representation.
Recall that (2, -3) are mutually prime in Integer, as well as (-2, 3), or
(-2,-3).
Internally, Fraction uses a record, but it tries to keep the
representation normalized. So (2,-3) would be different from (-2,3).
There is desirable a function which can be applied like this:
fraction(NoGCD, n, d).
However, there is more. If you look into Fraction
https://github.com/hemmecke/fricas-svn/blob/master/src/algebra/fraction.spad.pamphlet#L314
you see that the argument type is only required to be IntegralDomain. So
one could form Fraction(X) for X being of type IntegralDomain, but not
of type GcdDomain. If X has not gcd function, it will of course not be
applied if you construct an element via n/d.
Anyway, you probably need it for X=Integer.
So the only way you can do what you want is "pretend" or provide a patch
that adds a function constructFractionWithoutCancelling:(S,S)->%.
But I will probably argue a lot that this function is basically like
pretend and should better be avoided.
[snip]
When DoCon puts a string to Axiom, fractions are in their canonical form
by "gi". And it is desirable to avoid gcd when parsing (by dParse)
of such a fraction to Axiom.
OK, this is a situation where your parsing framework should know about
the internal structure of FriCAS domains and Fraction in particular,
i.e. "pretend" should be the way to go.
You should, however, mark such "pretend" places in big bold red letters
so that maintenance does not become a nightmare. Whenever a FriCAS
domain changes its representation, your framework must be changed as
well. So keep producing lots of test cases so that such situations are
caught before a new release.
Ralf
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