On 10/08/2014 04:07 AM, Bill Page wrote:
> Something goes wrong with the display of a SquareMatrix with computed
> dependent size parameter that is passed as a parameter to a type.

> DifferentialGeometry(CoefRing, listIndVar : List Symbol, g:SMR) :
> Export == Implement where
>   CoefRing :  Join(IntegralDomain, Comparable)
>   DERHAM ==> DeRhamComplex(CoefRing, listIndVar)
>  ...
>   R       ==> Expression(CoefRing)
>   SMR     ==> SquareMatrix(#listIndVar,R

Not that I know a solution for this problem, but why not taking another
point of view, namely that everything is without variable names? In
other words, variable names are just used to achieve a nice looking
output. I don't think that variable names are important mathematically.

Unfortunately, that would mean some more deep change to Algebra, since
FriCAS, for example uses differentiate: (%, Symbol) -> % in
Expression(R) which is basically used in DERHAM (and, of course, it's
somehow convenient).

Of course that would lead to the question whether K[x] is the "same" as
K[y], but it would remove all of the problems where parameters in types
have to be *computed* in order to test whether the expression has a
correct type.

Suppose you have

Foo(l1: List Symbol, Bar(#l1)): ... == ...

And in a session you type

list1 := ['x, 'y]
list2 := ['x, 'y]
F1 := Foo(list1, Bar # list1)
F2 := Foo(list2, Bar # list1)

Should FriCAS already complain in the construction of F2?
Are F1 and F2 identical? I.e., can I have something like

f1: F1 := ...
f2: F2 := ...

f := f1 + f2 -- suppos Foo exports "+: (%,%)->".
What's the type of f? F1 or F2?

Now play the same game with initially setting list2 to ['u,'v].

You probably remember that DirectProct(5, Integer) and
DirectProduct(2+3, Integer) are different types (at least in Aldor).

Ralf

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