Hi,
I'm trying to write an example page of skew polynomial for hyperdoc, and
there are several questions:
1. How to construct an univariate skew polynomial domain with user defined
'sigma' and 'delta': for example:
a. if 'sigma' is an ring automorphism *other than* identity map; or,
b. if 'delta' is an inner derivation defined by using any fixed element
of coefficient ring?
I have no idea about both of them. Currently, for b, if I want to give a
OREUP over R:=SQMATRIX(2, INT), with sigma := 1 and delta(r:R):R == y*r-r*y,
where y : R is a fixed element, it says:
>> System error:
The function MAP is undefined.
Here is the code:
(1) -> )set expose add constructor SquareMatrix
SquareMatrix is now explicitly exposed in frame frame0
(1) -> R := SQMATRIX( 2 , INT )
(1) SquareMatrix(2,Integer)
Type: Domain
(2) -> y :R := matrix[[1,0],[1,1]]
+1 0+
(2) | |
+1 1+
Type: SquareMatrix(2,Integer)
(3) -> delta(r:R):R == y*r - r*y
Function declaration delta : SquareMatrix(2,Integer) ->
SquareMatrix(2,Integer) has been added to workspace.
Type: Void
(4) -> S := OREUP('x, R, 1, delta)
>> System error:
The function MAP is undefined.
As I said, how to define S correctly ?
2. I was able to construct OREUP over an univariate polynomial ring
R:=UP('t, INT), with sigma:=1 and delta be the usual derivation d/dt, like
this
(1) -> R:= UP('t, INT)
(1) UnivariatePolynomial(t,Integer)
Type: Domain
(2) -> W:= OREUP('x, R, 1, D)
(2) UnivariateSkewPolynomial(x,UnivariatePolynomial(t,Integer),R ->
R,theMap(DIFRING-;D;2S;1,723))
Type: Domain
(3) -> x: W := 'x
(3) x
(4) -> t: W:= 't
(4) t
(5) -> x*t
(5) t x + 1
Everything goes right. But HOW does the interpretor know that D is a
derivation ? I just want to know the mechanism behind this code :-)
3. I'm using REGSET.ht as a templete to write my example page for OREUP. How
to compile my .ht file so that I can see my page in hyperdoc system?
4. Can I write latex in .ht file?
PS: There is another problem about the hyperdoc system:
When I scroll mouse wheel on the example code, an xterm window comes out
and the code is pasted into this window, which is good. But when I close
xterm window, the whole fricas system quit, which is unexpected. How to quit
xterm ONLY? (I'm using debian with xfce desktop environment, recently fricas
svn running in an xfce-terminal.)
Best Regards,
Xiaojun
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