Side note: my recent discussion with Ralf should speed up
subtractIfCan of DirectProduct greatly.
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Your orignal problem is due to coerce. I think that
FullyRetractableTo is problematic because there are many different
reasonable definitions.
I agree, but also consider that the original authors explicitly mention
this in DirectProductCategory.
++ Description:
++ This category represents
I took a free minute to convert Ralf's example to something simpler.
Personally, I currently think (as Bill pointed out) that
?*? : (DirectProduct(ndim,R),%) - DirectProduct(ndim,R)
?*? : (%,DirectProduct(ndim,R)) - DirectProduct(ndim,R)
are wrong. Or, rather: once we think of DIRPROD as a
Gabriel Dos Reis g...@cs.tamu.edu writes:
[...]
| I am concerned with the operations defined by DirectProduct and their
| semantics. For the specific case at hand, I don't care about the
| default implementation in Algebra since DirectProduct explicitly
| overwrites it, saying that the scalar
By the way, this category membership assertion in DirectProductCategory
if R has CancellationAbelianMonoid then CancellationAbelianMonoid
is clearly wrong with the implementation of multiplication in DirectProduct.
In DirectProduct(2,INT), take
a := [1,0]
b := [0,1]
c
But note, my question was about looking for an appropriate operation *
(or rather an appropriate coercion) so that
R and SquareMatrix(2,Fraction R)
can be connected.
Why is there no automatic coercion when R = Polynomial(Complex
Integer))? Is this some limitation of Fraction?
Oh,
Ralf,
No. I asked why
*: (R, SquareMatrix(2, F) - something
is easy when R = Integer. But it is not easy when R =
Polynomial(Complex Integer))?
Regards,
Bill Page.
On Fri, Jun 11, 2010 at 2:04 AM, Ralf Hemmecke r...@hemmecke.de wrote:
But note, my question was about looking for an
Ralf,
Here is a test example:
(1) - )sys cat test-coerce1.input
-- test-coerce1.input
)cl co
R:=Integer
F:=Fraction R
M:=SquareMatrix(2,F)
m:M:=[[1,1],[1,1]]
f:F:=1
r:R:=1
f*m
r*m
--
)cl co
R:=Polynomial Integer
F:=Fraction R
M:=SquareMatrix(2,F)
m:M:=[[1,1],[1,1]]
f:F:=1
r:R:=1
f*m
r*m
--
(1)
On 06/11/2010 03:05 PM, Bill Page wrote:
Ralf,
No. I asked why
*: (R, SquareMatrix(2, F) - something
is easy when R = Integer. But it is not easy when R =
Polynomial(Complex Integer))?
Oh, your example reveals quite confusing behaviour. :-(
It seems that the interpreter treats
Ralf,
What does the following have to do with Monoid?
On Thu, Jun 10, 2010 at 1:06 PM, Ralf Hemmecke r...@hemmecke.de wrote:
On 06/10/2010 06:33 PM, Bill Page wrote:
Ralf,
I think that the map
coerce : Fraction Polynomial Complex Integer - %
which is apparently x+- [x,x]
in
)sh
On 06/10/2010 07:17 PM, Bill Page wrote:
Ralf,
What does the following have to do with Monoid?
On Thu, Jun 10, 2010 at 1:06 PM, Ralf Hemmecke r...@hemmecke.de wrote:
On 06/10/2010 06:33 PM, Bill Page wrote:
Ralf,
I think that the map
coerce : Fraction Polynomial Complex Integer -
Ralf,
In another thread Gaby observed that for a Field F SquareMatrix(n,F)
should satisfy VectorSpace(F), but unfortunately at present it does
not:
(1) - SquareMatrix(2,Fraction Integer) has VectorSpace(Fraction Integer)
(1) false
Or perhaps even better if every SquareMatrix(n,R) satisfied
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