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 vector, once as
a diagonal matrix. Right?
Martin
(1) -> m:SQMATRIX(2, POLY INT) := squareMatrix matrix [[a, b], [c, d]]
+a b+
(1) | |
+c d+
Type: SquareMatrix(2,Polynomial(Integer))
(2) -> im := inverse m
+ d b +
| --------- - ---------|
| a d - b c a d - b c|
(2) | |
| c a |
|- --------- --------- |
+ a d - b c a d - b c +
Type: Union(SquareMatrix(2,Fraction(Polynomial(Integer))),...)
(3) -> (r::FRAC POLY INT)*inverse m
+ d r b r +
| --------- - ---------|
| a d - b c a d - b c|
(3) | |
| c r a r |
|- --------- --------- |
+ a d - b c a d - b c +
Type: SquareMatrix(2,Fraction(Polynomial(Integer)))
(4) -> (r::POLY INT)*inverse m
(d - c)r (- b + a)r
(4) [---------,----------]
a d - b c a d - b c
Type: DirectProduct(2,Fraction(Polynomial(Integer)))
(5) -> )tr SQMATRIX )ma
Packages traced:
SquareMatrix(2,Fraction(Polynomial(Integer))), SquareMatrix
(2,Polynomial(Integer))
Parameterized constructors traced:
SQMATRIX
(5) -> )tr DIRPROD )ma
Packages traced:
SquareMatrix(2,Fraction(Polynomial(Integer))), SquareMatrix
(2,Polynomial(Integer)), DirectProduct(2,Fraction(
Polynomial(Integer))), DirectProduct(2,Polynomial(
Integer))
Parameterized constructors traced:
SQMATRIX, DIRPROD
(5) -> r*inverse m
1<enter SquareMatrix.inverse,67
:
+a b+
arg1= | |
+c d+
1>exit SquareMatrix.inverse,67
:
+ d b +
| --------- - ---------|
| a d - b c a d - b c|
| |
| c a |
|- --------- --------- |
+ a d - b c a d - b c +
1<enter DirectProduct.coerce,11
:
arg1= r
1>exit DirectProduct.coerce,11
:
[r,r]
1<enter SquareMatrix.*,46
:
arg1= [r,r]
+ d b +
| --------- - ---------|
| a d - b c a d - b c|
arg2= | |
| c a |
|- --------- --------- |
+ a d - b c a d - b c +
1<enter DirectProduct.coerce,10
:
arg1= [r,r]
1>exit DirectProduct.coerce,10
:
[r,r]
1<enter DirectProduct.directProduct,17
:
(d - c)r (- b + a)r
arg1= [---------,----------]
a d - b c a d - b c
1<enter DirectProduct.size?,16
:
(d - c)r (- b + a)r
arg1= [---------,----------]
a d - b c a d - b c
arg2= 2
1>exit DirectProduct.size?,16
:
true
1>exit DirectProduct.directProduct,17
:
(d - c)r (- b + a)r
[---------,----------]
a d - b c a d - b c
1>exit SquareMatrix.*,46
:
(d - c)r (- b + a)r
[---------,----------]
a d - b c a d - b c
1<enter DirectProduct.parts,13
:
(d - c)r (- b + a)r
arg1= [---------,----------]
a d - b c a d - b c
1>exit DirectProduct.parts,13
:
(d - c)r (- b + a)r
[---------,----------]
a d - b c a d - b c
(d - c)r (- b + a)r
(5) [---------,----------]
a d - b c a d - b c
Type: DirectProduct(2,Fraction(Polynomial(Integer)))
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