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- module kredelw;% Kredel Weispfenning algorithm .
- % Author: H . Melenk(ZIB Berlin).
- symbolic procedure gdimension_eval u;
- begin integer n,m;
- for each s in cdr gindependent_seteval u
- do if(m:=length cdr s) > n then n:=m;
- return n end;
- put('gdimension,'psopfn,'gdimension_eval);
-
- symbolic procedure gindependent_seteval pars;
- % Independent set algorithm(Kredel/Weispfenning).
- % Parameters:
- % 1 Groebner basis
- % 2 optional: list of variables.
- begin scalar a,u,v,vars,w,oldorder,!*factor,!*exp,!*gsugar,!*groebopt;!*exp:=t;
- u:=reval car pars;
- v:=if cdr pars then reval cadr pars else nil;
- w:=for each j in groerevlist u collect if eqexpr j then !*eqn2a j else j;
- if null w then rerror(groebnr2,3,"empty list");
- a:=if global!-dipvars!* and cdr global!-dipvars!* then cdr global!-dipvars!*
- else gvarlis w;
- vars:=if null v then for each j in a collect !*a2k j else groerevlist v;
- if not vars then return'(list);
- oldorder:=vdpinit vars;
- w:=for each j in w collect vdpevlmon a2vdp j;
- vars:=for each y in vars collect y.vdpevlmon a2vdp y;
- w:=groebkwprec(vars,nil,w,nil);
- return 'list.for each s in w collect
- 'list.reversip for each x in s collect car x end;
- put('gindependent_sets,'psopfn,'gindependent_seteval);
- symbolic procedure groebkwprec(vars,s,lt,m);
- % Recursive Kredel Weispfennig algorithm.
- % vars: unprocessed variables,
- % s: current subset of s,
- % lt: leading term basis,
- % m: collection of independent sets so far.
- % Returns : updated m .
- begin scalar x,s1,bool;
- s1:=for each y in s collect cdr y;
- while vars do
- <<x:=car vars;vars:= cdr vars;
- if groebkwprec1(cdr x.s1,lt) then m:=groebkwprec(vars,x.s,lt,m)>>;
- bool:=t;
- for each y in m do % bool and not subsetp(s,y);
- bool:=bool and not(length s=length intersection(s,y));
- return if bool then s.m else m end;
- symbolic procedure groebkwprec1(s,lt);
- % t if intersection of T(s) and lt is empty.
- if null lt then t else groebkwprec2(s,car lt)and groebkwprec1(s,cdr lt);
- symbolic procedure groebkwprec2(s,mon);
- % t if monomial not in T(s).
- <<for each m in s do mon:=vevcan0(m,mon);not vevzero!? mon>>;
- symbolic procedure vevcan0(m,mon);
- % Divide multiples of m1 out of mon.
- if vevzero!? m then mon else
- if vevzero!? mon then nil else
- (if car m neq 0 then 0 else car mon).vevcan0(cdr m,cdr mon);
- endmodule;;end;
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