Re: [Axiom-math] Assigning elements in a list of lists

[Ralf Hemmecke]

On 11/12/2008 11:42 AM, Fabio S. wrote:
> I can't understand why I am not able to assign an element in a list of 
> lists like in
>
> --------
> (35) -> A:=[[0,0,0,0]]
>   (35)  [[0,0,0,0]]       Type: List List NonNegativeInteger
>
> (36) -> A(1,1)
>    (36)  0               Type: NonNegativeInteger
>
> (37) -> A(1,1):=1
>
>    The form on the left hand side of an assignment must be a single 
> variable, a Tuple of variables or a reference to an entry in an object
> supporting the setelt operation.
> --------

I have not looked into the actual sources, but I'd guess, that there is 
no function of the form

    setelt: (%,Integer,Integer,R) -> R
      -- will become setelt_!
      ++ setelt(m,i,j,r) sets the element in the ith row and jth
      ++ column of m to r
      ++ error check to determine if indices are in proper ranges

(which you find in array2.spad (TwoDimensionalArrayCategory)) in exports 
of List. There is only

    if % has shallowlyMutable then
       setelt : (%, Dom, Im) -> Im
           ++ setelt(u,x,y) sets the image of x to be y under u,
           ++ assuming x is in the domain of u.
           ++ Error: if x is not in the domain of u.
           -- this function will soon be renamed as setelt!.

from aggcat.spad (EltableAggregate) that looks available to me.

> whereas if I declare A as a matrix it works:
>
> --------
> (43) -> A:=[[0,0,0,0]] :: Matrix INT
>    (43)  [0  0  0       Type: Matrix Integer
>
> (44) -> A(1,1):=1
>    (44)  1        Type: PositiveInteger
>
> (45) -> A
>    (45)  [1  0  0  0]    Type: Matrix Integer
> --------
>
> Can anybody please explain me what is wrong in the first esample?

The above explains, why it works for matrices, since there

    setelt: (%,Integer,Integer,R) -> R

is defined.


How to work around?

(2) -> A:=[[0,0,0,0]]

   (2)  [[0,0,0,0]]
                Type: List(List(NonNegativeInteger))
(3) -> B:=A.1

   (3)  [0,0,0,0]
                Type: List(NonNegativeInteger)
(4) -> B.1:=1

   (4)  1
                Type: PositiveInteger
(5) -> A

   (5)  [[1,0,0,0]]
                Type: List(List(NonNegativeInteger))
(6) -> setelt(A.1,2,3)

   (6)  3
                Type: PositiveInteger
(7) -> A

   (7)  [[1,3,0,0]]
                Type: List(List(NonNegativeInteger))

I somehow think, that this here...

(8) -> (A.1).3 :=4

   The form on the left hand side of an assignment must be a single
      variable, a Tuple of variables or a reference to an entry in an
      object supporting the setelt operation.

should also work. Even A.1.3 := 4 should be OK, since is should 
translate to setelt(elt(A, 1), 3, 4).

Ralf

>aldor -gloop
Aldor

Copyright (c) 1990-2007 Aldor Software Organization Ltd (Aldor.org).

Release: Aldor(C) version 1.1.0 (trunk-23 AXL_EDIT_1_1_13_18=0) for 
LINUX(glibc2.3)
Type "#int help" for more details.
Reading aldorinit.as...
...     ...     ...     ... 
   %3 >> import from MachineInteger
%4 >> import from Integer, List Integer, List List Integer
%5 >> A:=[[0,0,0,0]]
[[0,0,0,0]] @ List(List(AldorInteger))
%6 >> A.1.3 := 4
4 @ AldorInteger
%7 >> A
[[0,0,4,0]] @ List(List(AldorInteger))