FriCAS/Axiom is a very rich system, so it is not so easy to extract the proper
information for all kind of users. Let me give you some hints.
Am 11.03.2011 um 15:26 schrieb Yrogirg:
>
>> (1) -> a:Float
>> Type: Void
>> (2) -> )display prop a
>> Properties of a :
>> Declared type or mode: Float
>
> It doesn't actually work:
> -> )display prop 5
> Properties of 5 :
> none
At that level 5 is not even interpreted what kind of mathematical object it
will be, so try the following
(8) -> j := 5
(8) 5
Type: PositiveInteger
(9) -> )display prop j
Properties of j :
Value (has type PositiveInteger): 5
(6) -> i : Integer := 5
(6) 5
Type: Integer
(7) -> )display prop i
Properties of i :
Declared type or mode: Integer
Value (has type Integer): 5
> -> )display prop integrate
> Properties of integrate :
> none
o.k. the right thing todo is
)wh op integrate
)d op integrate
the latter returns all 30 (!) different integrate functions in AXIOM, that is
what you propably as a starter not want to see.
So I suggest the following: do a concrete integral after switching on the
selection information as follows:
(9) -> )set messages selection on
(9) -> integrate(x^2, x)
Function Selection for ^
Arguments: (VARIABLE(x),PI)
Default target type: Polynomial(Integer)
[1] signature: (POLY(INT),NNI) -> POLY(INT)
implemented: slot $$(NonNegativeInteger) from POLY(INT)
[2] signature: (POLY(INT),PI) -> POLY(INT)
implemented: slot $$(PositiveInteger) from POLY(INT)
Function Selection for integrate
Arguments: (POLY(INT),VARIABLE(x))
[1] signature: (POLY(FRAC(INT)),SYMBOL) -> POLY(FRAC(INT))
implemented: slot $$(Symbol) from POLY(FRAC(INT))
Function Selection for map by coercion facility (map)
Arguments: ((INT -> FRAC(INT)),POLY(INT))
Target type: POLY(FRAC(INT))
[1] signature: ((INT -> FRAC(INT)),POLY(INT)) -> POLY(FRAC(INT))
implemented: slot (Polynomial (Fraction (Integer)))(Mapping (Fraction
(Integer)) (Integer))(Polynomial (Integer)) from POLY2(INT,FRAC(INT))
1 3
(9) - x
3
Type: Polynomial(Fraction(Integer))
and you get full infomation what function signature the Interpreter has
selected for you!
>
>> Why does not using it make you feel uncomfortable?
>
> It helps a lot while learning --- the first thing one would like to
> know about certain operation is what kind of arguments it accepts (if
> any) and what kind of output one should expect.
>
> For example, the fact that determinant is defined on square matrices
> and maps to the field the matrix is defined on in some sense is more
> basic than the properties of the determinant.
>
> I get used to this approach (always to bear in mind the types of
> objects you are working with) in Haskell, maybe it's not very
> applicable to FriCAS since the last deals heavily with symbolic
> computations. And I haven't studied yet what that mysterious thing
> "Expression" is, was going to move on it after the chapter about types.
>
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Mit freundlichen Grüßen
Johannes Grabmeier
Prof. Dr. Johannes Grabmeier
Köckstraße 1, D-94469 Deggendorf
Tel. +49-(0)-991-2979584, Tel. +49-(0)-171-5503789
Tel. +49-(0)-991-3615-100 (d), Fax: +49-(0)-1803-5518-17745
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