Dear Bill, Ralf and Franz,
thank you for the pointers and the offered support. I will see if I
can understand
Table and if I can do something with it. Anyhow, at the moment, functionality
improvement still has priority over speed improvements, but on a longer
term basis such remember issues become vital.
Franz: I am stuck with 'dimGL(%,R) -> R' for Schur functions. Inbetween the
computations I get an integral polynomial in the parameter n:R (R =
CommutativeRing,
I think of Fraction Polynomial(Integer) and 'n' would be a (fraction)
q-polynomial) and
I would need to _divide_ that polynomial by an integer. It is
mathematically known
that the result is an integral polynomial again, but I cannot teach
FriCAS to do this.
Martin suggested to change R to IntegralDomain, but I am not jet sure about it.
This issue is much more pressing than the remember facility, since it
hinders me to
implement the plethysm for Schur functions. I will try to see if I can
implement
Axel Kohnert's algorithm, which is the fastes I know of.
Franz:
And, yes, plethysmRight is a general function if the following bits
of code are
properly coded using by dimGL(p,n). (see above remark)
line 6: return ((liy 1) c)^(#p1)*plethysm(p1,(liy 1) k)
=> return dimGL(p1, ((liy 1) c))*plethysm(p1,(liy 1) k)
line 11: res:=res+(mxm.c)*(ty1.c)^(#((mxm.k).1))*_
plethysm((mxm.k).1,ty1 k)*plethysmRight((mxm.k).2,resty)
=> res:=res+(mxm.c)*dimGL(((mxm.k).1),ty1.c)*_
plethysm((mxm.k).1,ty1 k)*plethysmRight((mxm.k).2,resty)
since in the power sum case dimGL(p,n) is just the exponentiation n^(#p)
I replaced it inside the code. This function is possibly heavily called, so
I found it better to inline the code, but if it could be remembered...
> I will come back to that soon,
> essentially I just overloaded Table.
Perhaps you just send me that part of code?
Greetings
BF.
--
% PD Dr Bertfried Fauser
% Research Fellow, School of Computer Science, Univ. of Birmingham
% Honorary Associate, University of Tasmania
% Privat Docent: University of Konstanz, Physics Dept
<http://www.uni-konstanz.de>
% contact |-> URL : http://clifford.physik.uni-konstanz.de/~fauser/
% Phone : +49 1520 9874517
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