module kernel; % Functions for operations on kernels.
% Author: Anthony C. Hearn.
% Copyright (c) 1990 The RAND Corporation. All rights reserved.
global '(exlist!* kprops!*);
symbolic procedure fkern u;
% Finds the unique "p-list" reference to the kernel U. The choice of
% the search and merge used here has a strong influence on some
% timings. The ordered list used here is also used by prepsq* to
% order factors in printed output, so cannot be unilaterally changed.
begin scalar x,y;
if atom u then return list(u,nil)
else if x := get(car u,'fkernfn) then return apply1(x,u);
y := if atom car u then get(car u,'klist) else exlist!*;
if not (x := assoc(u,y))
then <<x := list(u,nil);
y := ordad(x,y);
if atom car u
then <<kprops!* := union(list car u,kprops!*);
put(car u,'klist,y)>>
else exlist!* := y>>;
return x
end;
symbolic procedure kernels u;
% Returns list of kernels in standard form u.
kernels1(u,nil);
symbolic procedure kernels1(u,v);
% We append to end of list to put kernels in the right order, even
% though a cons on the front of the list would be faster.
if domainp u then v
else kernels1(lc u,
kernels1(red u,
if x memq v then v else append(v,list x)))
where x=mvar u;
symbolic procedure kernp u;
% True if U is standard quotient representation for a kernel.
denr u=1 and not domainp(u := numr u)
and null red u and lc u=1 and ldeg u=1; % onep
endmodule;
end;