With the most recent revision of FriCAS (Rev: 393) plus the patch that
I recently posted, FriCAS produces the following output:
(1) -> sqrt(2)::InputForm + 1::InputForm
(1) (+ (:: (** 2 (/ 1 2)) (AlgebraicNumber)) 1)
Type: InputForm
(2) -> unparse(%)
(2) "(2^(1/2))::AlgebraicNumber+1"
Type: String
(3) -> parse(%)$InputForm
(3) (+ (:: (^ 2 (/ 1 2)) AlgebraicNumber) 1)
Type: InputForm
(4) -> interpret(%)$InputForm
+-+
(4) \|2 + 1
Type: AlgebraicNumber
(5) -> %::InputForm
(5) (:: (+ (** 2 (/ 1 2)) 1) (AlgebraicNumber))
Type: InputForm
-----
I have a few questions about the InputForm values produced in different ways.
1) Use of coercions and types in InputForm. As far as I know, besides
it's use in
(6) -> integrate(sin(exp x),x)::InputForm
(6) (integral (sin (exp x)) (:: x Symbol))
Type: InputForm
(7) -> unparse %
(7) "integral(sin(exp(x)),x::Symbol)"
Type: String
this change introduces the first use of :: for representing explicit
type information in InputForm.
What do you think about this approach? Is there a better way?
One alternative would be to introduce a specific (non-overloaded)
operation exported by AlgebraicNumber such as 'algebraicNumber' that
does the same thing. That is how Float values are currently handled:
(8) -> 3.141592::InputForm
(8) (float 231808574432053350722 - 66 2)
Type: InputForm
(9) -> unparse %
(9) "float(231808574432053350722,-66,2)"
Type: String
Would doing something like this:
(algebraicNumber (** 2 (/ 1 2)))
be better?
One of the uses of unparse output will be to produce input for other
systems (usually used only internally in some interface program) such
as Sage. Will this use of :: cause any inconvenience for such use? How
will we/can we translate this into Sage coercions?
2) Notice that the InputForm value representing the same expression
occur with both ** and ^. Which one is currently the preferred form?
3) I would like to collect examples of coercions to InputForm fail in the sense
(10) -> test(interpret(parse(unparse(x::InputForm))$InputForm) = x)
(10) true
Type: Boolean
Any help appreciated.
Regards,
Bill Page.
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