module cvit; % Header module for CVIT package.
% Authors: A.Kryukov, A.Rodionov, A.Taranov.
% Copyright (C) 1988,1990, Institute of Nuclear Physics, Moscow State
% University.
% VERSION 2.1
% RELEASE 11-MAR-90
% 07.06.90 all MAP replaced by MAP_ RT
% 08.06.90 SOME MACROS FROM CVITMAP FILE ADDED to section IV RT
% 10.06.90 SOME MACROS FROM CVITMAP FILE ADDED RT
% Modifications for Reduce 3.4.1 by John Fitch.
create!-package('(cvit red2cvit map2strn evalmaps intfierz cvitmap),
'(contrib physics));
% The High Energy Physics package must be loaded first.
load_package hephys;
% These fluids and globals have been moved here for cleaner compilation.
fluid '(!*msg ndims!* dindices!*)$
global '(windices!* indices!* !*cvit gamma5!* !*g5cvit)$
if null windices!*
then windices!*:=
'(nil !_f0 !_f1 !_f2 !_f3 !_f4 !_f5 !_f6 !_f7 !_f8 !_f9)$
if null gamma5!*
then gamma5!*:=
'(nil !_a0 !_a1 !_a2 !_a3 !_a4 !_a5 !_a6 !_a7 !_a8 !_a9)$
%GGGGGGGGGGGGGGGGGGGGGGGGG GLOBALS & FLUIDS FFFFFFFFFFFFFFFFFFFFFFFFF$
global '( !_0edge)$
fluid '( new_edge_list old_edge_list )$
% NEW_EDGE_LIST - LIST OF CREATED EDGES$
% OLD_EDGE_LIST - LIST OF INITIAL EDGES$
fluid '(n_edge)$
% N_EDGE - NUMBER OF CREATED EDGES$
% The following smacros need only be present during compilation.
%************ SECTION I ************************************
smacro procedure hvectorp x$
get(x,'rtype) eq 'hvector$
smacro procedure windexp x$
x memq car windices!*$
smacro procedure replace_by_indexp v$
get(v,'replace_by_index)$
smacro procedure indexp i$
i memq indices!*$
smacro procedure replace_by_vectorp i$
get(i,'replace_by_vector)$
smacro procedure replace_by_vector i$
get(i,'replace_by_vector) or i$
smacro procedure gamma5p x$
memq(x,car gamma5!*)$
smacro procedure nospurp x$
flagp(x,'nospur)$
smacro procedure clear_gamma5()$
gamma5!* := nil . append(reverse car gamma5!*,cdr gamma5!*)$
%********************* SECTION II **************************
symbolic smacro procedure p_empty_map_ map_$
% IS MAP_ EMPTY ? $
null map_$
symbolic smacro procedure p_empty_vertex vertex$
% IS VERTEX EMPTY ? $
null vertex$
%++++++++++++++++++++++++++ SELECTORS +++++++++++++++++++++++++++++++$
symbolic smacro procedure s_vertex_first map_$
% SELECT FIRST VERTEX IN MAP_ $
car map_$
symbolic smacro procedure s_map__rest map_$
% SELECT TAIL OF MAP_ $
cdr map_$
symbolic smacro procedure s_vertex_second map_$
% SELECT SECOND VERTEX IN MAP_ $
s_vertex_first s_map__rest map_$
symbolic smacro procedure first_edge vertex$
% SELECT FIRST EDGE IN VERTEX $
car vertex$
symbolic smacro procedure s_vertex_rest vertex$
% SELECT TAIL OF VERTEX $
cdr vertex$
symbolic smacro procedure second_edge vertex$
% SELECT SECOND EDGE IN VERTEX $
first_edge s_vertex_rest vertex$
symbolic smacro procedure s_edge_name edge$
% SELECT EDGE'S NAME $
car edge$
symbolic smacro procedure s_edge_prop_ edge$
% SELECT PROP_ERTY OF AN EDGE (NAMES OF PARENTS OR NUMBERS)$
cadr edge$
symbolic smacro procedure s_edge_type edge$
% SELEC TYPE (PARITY) OF AN EDGE$
caddr edge$
%?????????????????????? CONSTRUCTORS ??????????????????????????????$
symbolic smacro procedure add_vertex (vertex,map_)$
% ADD VERTEX TO MAP_ $
vertex . map_ $
symbolic smacro procedure add_edge (edge,vertex)$
% ADD EDGE TO VERTEX$
edge . vertex$
symbolic smacro procedure append_map_s (map_1,map_2)$
% APPEND TWO MAP_S $
append(map_1,map_2)$
symbolic smacro procedure conc_map_s (map_1,map_2)$
% APPEND TWO MAP_S $
nconc(map_1,map_2)$
symbolic smacro procedure conc_vertex (vertex1,vertex2)$
% APPEND TWO VERTICES
nconc(vertex1,vertex2)$
symbolic smacro procedure mk_name1 name$
explode name$
symbolic smacro procedure mk_edge_prop_ (prop_1,prop_2)$
prop_1 . prop_2 $
symbolic smacro procedure mk_edge_type (typ1,typ2)$
% DEFINED EDGE <=> TYPE T,
% UNDEFINED EDGE <=> TYPE NIL$
typ1 and typ2 $
symbolic smacro procedure mk_edge (name,prop_,type)$
% MAKE UP NEW EDGE $
list(name,prop_,type)$
symbolic smacro procedure mk_edge3_vertex (edge1,edge2,edge3)$
% MAKES PRIMITIVE VERTEX $
list(edge1,edge2,edge3)$
symbolic smacro procedure mk_empty_map_ ()$
% GENERATE EMPTY MAP_ $
nil $
symbolic smacro procedure mk_empty_vertex ()$
% GENERATE EMPTY VERTEX $
nil $
symbolic smacro procedure mk_vertex1_map_ vertex1$
% MAKE MAP_ OF ONE VERTEX $
list(vertex1)$
symbolic smacro procedure mk_vertex2_map_ (vertex1,vertex2)$
% MAKE MAP_ OF TWO VERTICES $
list(vertex1,vertex2)$
symbolic smacro procedure mk_edge2_vertex (edge1,edge2)$
%MAKES VERTEX FROM TWO EDGES$
list(edge1,edge2)$
symbolic smacro procedure conc_vertex (vertex1,vertex2)$
nconc(vertex1,vertex2)$
symbolic smacro procedure cycl_map_ map_$
% MAKES CYCLIC PERMUTATION OF MAP_$
append(cdr map_,list car map_)$
symbolic smacro procedure cycl_vertex vertex$
% MAKES CYCLIC PERMUTATION OF VERTEX$
append(cdr vertex,list car vertex)$
symbolic smacro procedure mk_world (actedges,world1)$
list(actedges,list nil,world1)$
%====================== PREDICATES (CONTINUE) =====================$
symbolic smacro procedure p_member_edge (edge,vertex)$
% IS EDGE (WITH THE SAME NAME) CONTAINS IN VERTEX ?$
assoc(s_edge_name edge,vertex)$
symbolic smacro procedure equal_edges (edge1,edge2)$
% IF EDGES HAVE THE SAME NAMES ? $
eq ( s_edge_name edge1, s_edge_name edge2)$
symbolic smacro procedure single_no_parents edges$
length edges = 1 $
symbolic smacro procedure resto_map__order map_$
% REVERSE (BETTER REVERSIP) MAP_ $
reverse map_$
symbolic smacro procedure map__length map_$
% NUMBER OF VERTICES IN MAP_$$
length map_$
symbolic smacro procedure vertex_length vertex$
% NUMBER OF EDGES IN VERTEX $
length vertex$
symbolic smacro procedure prepare_map_ map_$
for each x in map_
collect mk_old_edge x$
symbolic smacro procedure p_vertex_prim vertex$
% IS VERTEX PRIMITIVE ? $
vertex_length (vertex) <= 3 $
%************ SECTION III ************************************
symbolic smacro procedure s!-edge!-name edge$ car edge$
symbolic smacro procedure sappend(x,y)$ append(x,y)$
symbolic smacro procedure sreverse y $ reverse y$
symbolic smacro procedure getedge(x,y)$ cdr assoc(x,y)$
symbolic smacro procedure mk!-road!-name(x,y,n)$
list(car x . n,car y . n)$
symbolic smacro procedure mk!-external!-leg edge$
%< FLAG(LIST EDGE,'EXTRNL)$
list( edge . 0) $
symbolic smacro procedure index!-in(ind,l)$
if atom ind then nil
else member(ind,l)$
%************ SECTION IV ************************************
symbolic smacro procedure reverse_map_ map_$
reverse map_$
symbolic smacro procedure mk_edge1_vertex edge$
list edge$
symbolic smacro procedure mk_edges_vertex edges$
edges$
symbolic smacro procedure reversip_vertex vertex$
reversip vertex$
symbolic smacro procedure append_vertex (vertex1,vertex2)$
append(vertex1,vertex2)$
%symbolic smacro procedure conc_vertex (vertex1,vertex2)$
% nconc(vertex1,vertex2)$
symbolic smacro procedure mk_edge4_vertex (edge1,edge2,edge3,edge4)$
list(edge1,edge2,edge3,edge4)$
symbolic smacro procedure p_old_edge edge$
assoc(s_edge_name edge,old_edge_list )$
symbolic smacro procedure s_atlas_map_ atlas$
car atlas$
symbolic smacro procedure s_atlas_coeff atlas$
cadr atlas$
symbolic smacro procedure s_atlas_den_om atlas$
caddr atlas$
symbolic smacro procedure mk_atlas (map_,atlases,den_om)$
list(map_,atlases,den_om)$
symbolic smacro procedure vertex_edges edge$
edge$
symbolic smacro procedure s_coeff_world1 world1$
cadr world1 $
symbolic smacro procedure s_edgelist_world world$
car world$
symbolic smacro procedure s_world1 world$
caddr world $
symbolic smacro procedure s_world_var world$
cadr world$
symbolic smacro procedure s_world_atlas world$
caddr world$
symbolic smacro procedure s_world_edges world$
car world$
endmodule;
module red2cvit;
% COPYRIGHT (C) 1988,1990,INSTITUTE OF NUCLEAR PHYSICS,MOSCOW STATE
% UNIV.
% PURPOSE INTERFACE BETWEEN REDUCE AND CVITANOVICH ALGORITHM.
% AUTHOR A.KRYUKOV
% VERSION 2.1
% RELEASE 11-MAR-90
exports isimp1,replace_by_vector,replace_by_vectorp,gamma5p$
imports calc_spur,isimp2$
switch cvit$ % CVITANOVICH ALGORITHM SWITCH
!*cvit := t$ % DEFAULT ON
%************ ISIMP1 REDEFINITION ************************
remflag('(isimp1),'lose)$
symbolic procedure isimp1(u,i,v,w,x)$
if null u then nil
else if domainp u
then if x then multd(u,if !*cvit
then calc_spurx (i,v,w,x)
else spur0 (car x,i,v,w,cdr x)
)
else if v then multd(u,index_simp (1,i,v,w))
else if w then multfs(emult w,isimp1(u,i,v,nil,nil))
else u
else addfs(isimp2(car u,i,v,w,x),isimp1(cdr u,i,v,w,x))$
flag('(isimp1),'lose)$
%************* INDEX_SIMP *******************************
symbolic procedure index_simp (u,i,v,w)$
if v then index_simp (multf(mksprod(caar v,cdar v),u),
update_index (i,car v),cdr v,w)
else isimp1(u,i,nil,w,nil)$
symbolic procedure mksprod(x,y)$
mkdot(if indexp x then replace_by_vector x else x,
if indexp y then replace_by_vector y else y)$
symbolic procedure update_index (i,v)$
% I - LIST OF UNMATCH INDICES
% V - PAIR: (I/V . I/V)
% VALUE - UPDATE LIST OF INDICES
delete(cdr v,delete(car v,i))$
%************ CALC_SPURX - MAIN PROCEDURE ***************
symbolic procedure calc_spurx (i,v,w,x)$
% I - LIST OF INDICES
% V - LIST OF SCALAR PRODUCT:(<I/V> . <I/V>)
% W - EPS-EXPR
% X - LIST OF SPURS
% VALUE - CALCULATED SPUR(S.F.)
begin scalar u, % SPUR: (LNAME G5SWITCH I/V I/V ... )
x1, % (UN ... U1)
dindices!*,% A-LIST OF DUMMY INDICES: (I . NIL/T)
c$ % COEFFICIENT GENERATIED BY GX*GX
if numberp ndims!* and null evenp ndims!*
then cviterr list('calc_spur,":",ndims!*,
"is not even dimension of G-matrix space")$
c := 1$ % INITIAL VALUE
while x
do << if nospurp caar x
then cviterr list "Nospur not yet implemented"$
u := cdar x$
x := cdr x$
if car u
then if evenp ndims!*
then u := next_gamma5() . reverse cdr u
else cviterr
{"G5 invalid for non even dimension"}
else u := reverse cdr u$
if null u then nil % SP()
else if null evenp
length(if gamma5p car u and cdr u then cdr u
else u)
then x := c := nil % ODD - VALUE=0
else << u := remove_gx!*gx u$
c := multf(car u,c)$
u := replace_vector(cdr u,i,v,w)$
i := cadr u$
v := caddr u$
w := cadddr u$
if u then x1 := car u . x1
>>
>>$
x1 := if null c then nil ./ 1 % ZERO
else if x1 then multsq(c ./ 1,calc_spur x1)
else c ./ 1$
if denr x1 neq 1 then cviterr list('calc_spurx,":",x1,
"has non unit denominator")$
clear_windices ()$
clear_gamma5 ()$
return isimp1(numr x1,i,v,w,nil)
end$
symbolic procedure third_eq_indexp i$
begin scalar z$
if null(z := assoc(i,dindices!*))
then dindices!* := (i . nil) . dindices!*
else if null cdr z
then dindices!* := (i . t) . delete(z,dindices!*)$
return if z then cdr z else nil
end$
symbolic procedure replace_vector(u,i,v,w)$
% U - SPUR (INVERSE)
% I - LIST OF UNMATCH INDICES
% V - A-LIST OF SCALAR PRODUCT
% W - EPS-EXPRESION
% VALUE - LIST(U,UPDATE I,UPDATE V,UPDATE W)
begin scalar z,y,x, % WORK VARIABLES
u1$ % SPUR WITHOUT VECTOR
while u
do << z := car u$
u := cdr u$
if indexp z
then << % REMOVE DUMMY INDICES
while (y := bassoc(z,v))
do << i := delete(z,i)$
v := delete(y,v)$
% W := ....
x := if z eq car y then cdr y
else car y$
if indexp x then z := x
else if gamma5p x
then cviterr
list "G5 bad structure"
else replace_by_index (x,z)
>>$
u1 := z . u1
>>
else if gamma5p z then u1 := z . u1
else << z := replace_by_index (z,next_windex())$
u1 := z . u1
>>
>>$
return list(reverse u1,i,v,w)
end$
symbolic procedure replace_by_index (v,y)$
begin scalar z$
if (z := replace_by_vectorp y) eq v
then cviterr list('replace_by_index,":",y,
"is already defined for vector",z)$
put(y,'replace_by_vector ,v)$
return y
end$
symbolic procedure remove_gx!*gx u$
begin scalar x,c$
integer l,l1$
c := 1$
l1 := l := length u$
u := for each z in u % MAKE COPY
collect << if indexp z then
if third_eq_indexp z
then cviterr
list("Three indices have name",z)
else nil
else if null hvectorp z then
if cvitdeclp(z,'vector)
then vector1 list z
else cviterr nil
else nil$
z
>>$
if l < 2 then return u$
x := u$
while cdr x do x := cdr x$
rplacd(x,u)$ % MAKE CYCLE
while l1 > 0
do if car u eq cadr u % EQUAL ?
then << c := multf(if indexp car u then ndims!*
else mkdot(car u,car u)
,c)$
rplaca(u,caddr u)$ % YES - DELETE
rplacd(u,cdddr u)$
l1 := l := l - 2
>>
else << u := cdr u$ % NO - CHECK NEXT PAIR
l1 := l1 - 1
>>$
x := cdr u$
rplacd(u,nil)$ % CUT CYCLE
return (c . if cdr x and car x eq cadr x then nil else x)
end$
%************* ERROR,MESSAGE *****************************
symbolic procedure cviterr u$
<< clear_windices()$
clear_gamma5()$
if u then rederr u else error(0,nil) >>$
symbolic procedure cvitdeclp(u,v)$
if null !*msg then nil
else if terminalp()
then yesp list("Declare",u,v,"?")
else << lprim list(u,"Declare",v)$ t >>$
%*********** WORK INDICES & VECTOR ***********************
symbolic procedure clear_windices ()$
while car windices!*
do begin scalar z$
z := caar windices!*$
windices!* := cdar windices!* . z . cdr windices!*$
remprop(z,'replace_by_vector)$
indices!* := delete(z,indices!*)$
end$
symbolic procedure next_windex()$
begin scalar i$
windices!* := if null cdr windices!*
then (intern gensym() . car windices!*) .
cdr windices!*
else (cadr windices!* . car windices!*) .
cddr windices!*$
i := caar windices!*$
vector1 list i$
indices!* := i . indices!*$
return i
end$
symbolic procedure next_gamma5()$
begin scalar v$
cviterr list "GAMMA5 is not yet implemented. use OFF CVIT";
gamma5!* := if null cdr gamma5!*
then (intern gensym() . car gamma5!*) .
cdr gamma5!*
else (cadr gamma5!* . car gamma5!*) .
cddr gamma5!*$
v := list caar gamma5!*$
vector1 v$
return car v
end$
%************ END ****************************************
%prin2t "_Cvitanovich_algorithm_is_ready"$
endmodule;
module map2strn;
%************* TRANSFORMATION OF MAP TO STRAND **********************$
% $
% 25.11.87 $
% $
%********************************************************************$
exports color!-strand,contract!-strand $
imports nil$
%---------------- utility added 09.06.90 ---------------------------
symbolic procedure constimes u;
% u=list of terms
% inspect u, delete all 1's
% and form smar product $
cstimes(u,nil)$
symbolic procedure cstimes(u,s);
if null u then
if null s then 1
else if null cdr s then car s
else 'times . s
else if car u = 1 then cstimes(cdr u,s)
else cstimes(cdr u,car u . s)$
symbolic procedure consrecip u;
% do same as consTimes
if or(car u = 1,car u = -1) then car u
else 'recip . u$
symbolic procedure listquotient(u,v)$
% the same !!!
if v=1 then u
else
if v = u then 1
else list('quotient,u,v)$
symbolic procedure consplus u;
% u=list of terms
% inspect u, delete all 0's
% and form smar sum $
csplus(u,nil)$
symbolic procedure csplus(u,s);
if null u then
if null s then 0
else if null cdr s then car s
else 'plus . s
else if car u = 0 then csplus(cdr u,s)
else csplus(cdr u,car u . s)$
%--------------------------------------------------------------------
%---------------- CONVERTING OF MAP TO STRAND DIAGRAM ---------------$
symbolic procedure map_!-to!-strand(edges,map_)$
%.....................................................................
% ACTION: CONVERTS "MAP_" WITH "EDGES" INTO STRAND DIAGRAM.
% STRAND ::= <LIST OF STRAND VERTICES>,
% STRAND VERTEX ::= <SVERTEX NAME> . (<LIST1 OF ROADS> <LIST2 ...>),
% ROAD ::= <ATOM> . <NUMBER>.
% LIST1,2 CORRESPOND TO OPPOSITE SIDES OF STRAND VERTEX.
% ROADS LISTED CLOCKWISE.
%....................................................................$
if null edges then nil
else mk!-strand!-vertex(car edges,map_) .
map_!-to!-strand(cdr edges,map_)$
%YMBOLIC PROCEDURE MAP_!-TO!-STRAND(EDGES,MAP_)$
%F NULL EDGES THEN NIL
%LSE (LAMBDA SVERT$ IF SVERT THEN SVERT .
% MAP_!-TO!-STRAND(CDR EDGES,MAP_)
% ELSE MAP_!-TO!-STRAND(CDR EDGES,MAP_) )
% MK!-STRAND!-VERTEX(CAR EDGES,MAP_)$
symbolic procedure mk!-strand!-vertex(edge,map_)$
begin
scalar vert1,vert2,tail$
tail:=incident(edge,map_,1)$
vert1:=car tail$
tail:=incident(edge,cdr tail,add1 cdar vert1)$
vert2:= if null tail then mk!-external!-leg edge
else car tail$
return %F NULL VERT2 THEN NIL
mk!-strand!-vertex2(edge,vert1,vert2)
end$
symbolic procedure incident(edge,map_,vertno)$
if null map_ then nil
else (lambda z$ if z then z . cdr map_
else incident(edge,cdr map_,add1 vertno) )
incident1( edge,car map_,vertno)$
symbolic procedure incident1(edname,vertex,vertno)$
if eq(edname,s!-edge!-name car vertex) then
mk!-road!-name(cadr vertex,caddr vertex,vertno)
else if eq(edname,s!-edge!-name cadr vertex) then
mk!-road!-name(caddr vertex,car vertex,vertno)
else if eq(edname,s!-edge!-name caddr vertex) then
mk!-road!-name(car vertex,cadr vertex,vertno)
else nil$
symbolic procedure mk!-strand!-vertex2(edge,vert1,vert2)$
list(edge, vert1, vert2)$
%------------------ COLOURING OF ROADS IN STRAND --------------------$
symbolic procedure color!-strand(alst,map_,count)$
%.....................................................................
% ACTION: GENERATE REC. ALIST COLORING STRAND, CORRESPONDING TO "MAP_".
% COLORING OF STRAND INDUCED BY "MAP_" COLORING, DEFINED BY ALIST
% "ALST". "COUNT" COUNTS MAP_ VERTICES. INITIALLY IS 1.
% REC.ALIST::= ( ... <(ATOM1 . COL1 ATOM2 . COL2 ...) . NUMBER> ... )
% WHERE COL1 IS COLOR OF ROAD=ATOM1 . NUMBER.
%....................................................................$
if null map_ then nil
else (color!-roads(alst,car map_) . count) .
color!-strand(alst,cdr map_,add1 count)$
symbolic procedure color!-roads(alst,vertex)$
begin
scalar e1,e2,e3,lines$
e1:=getedge(s!-edge!-name car vertex,alst)$
e2:=getedge(s!-edge!-name cadr vertex,alst)$
e3:=getedge(s!-edge!-name caddr vertex,alst)$
lines:=(e1+e2+e3)/2$
e1:=lines-e1$
e2:=lines-e2$
e3:=lines-e3$
return list(
s!-edge!-name car vertex . e1,
s!-edge!-name cadr vertex . e2,
s!-edge!-name caddr vertex . e3)
end$
symbolic procedure zero!-roads l$
%---------------------------------------------------------------------
% L IS OUTPUT OF COLOR!-STRAND
%--------------------------------------------------------------------$
if null l then nil
else (lambda z$ if z then z . zero!-roads cdr l
else zero!-roads cdr l)
z!-roads car l$
symbolic procedure z!-roads y$
(lambda w$ w and (car w . cdr y))
( if (0=cdr caar y)then caar y
else if (0=cdr cadar y) then cadar y
else if (0=cdr caddar y) then caddar y
else nil)$
%------------------- CONTRACTION OF STRAND --------------------------$
symbolic procedure deletez1(strand,alst)$
%.....................................................................
% ACTION: DELETES FROM "STRAND" VERTICES WITH NAMES HAVING 0-COLOR
% VIA MAP_-COLORING ALIST "ALST".
%....................................................................$
if null strand then nil
else if 0 = cdr assoc(caar strand,alst) then
deletez1(cdr strand,alst)
else car strand . deletez1(cdr strand,alst)$
symbolic procedure contract!-strand(strand,slst)$
%.....................................................................
% ACTION: CONTRACTS "STRAND".
% "SLST" IS REC. ALIST COLORING "STRAND"
%....................................................................$
contr!-strand(strand,zero!-roads slst)$
symbolic procedure contr!-strand(strand,zlst)$
if null zlst then strand
else contr!-strand(contr1!-strand(strand,car zlst),cdr zlst)$
symbolic procedure contr1!-strand(strand,rname)$
contr2!-strand(strand,rname,nil,nil)$
symbolic procedure contr2!-strand(st,rname,rand,flag_)$
if null st then rand
else (lambda z$
if z then
if member(car z,cdr z) then sappend(st,rand) % 16.12 ****$
else
if null flag_ then
contr2!-strand(contr2(z,cdr st,rand),rname,nil,t)
else contr2(z,cdr st,rand)
else contr2!-strand(cdr st,rname,car st . rand,nil) )
contrsp(car st,rname)$
symbolic procedure contrsp(svertex,rname)$
contrsp2(cadr svertex,caddr svertex,rname)
or
contrsp2(caddr svertex,cadr svertex,rname)$
symbolic procedure contrsp2(l1,l2,rname)$
if 2 = length l1 then
if rname = car l1 then (cadr l1) . l2
else if rname = cadr l1 then (car l1) . l2
else nil$
symbolic procedure contr2(single,st,rand)$
if null st then contr(single,rand)
else if null rand then contr(single,st)
else split!-road(single,car st) . contr2(single,cdr st,rand)$
symbolic procedure contr(single,strand)$
if null strand then nil
else split!-road(single,car strand) . contr(single,cdr strand)$
symbolic procedure split!-road(single,svertex)$
list(car svertex,
sroad(car single,cdr single,cadr svertex),
sroad(car single,cdr single,caddr svertex))$
symbolic procedure sroad(line_,lines,lst)$
if null lst then nil
else if line_ = car lst then sappend(lines,cdr lst)
else car lst . sroad(line_,lines,cdr lst)$
endmodule;
module evalmaps; % Interaction with alg mode: variant without nonlocs;
exports strand!-alg!-top $
imports color!-strand,contract!-strand $
%------------------ AUXILIARY ROUTINES -----------------------------$
symbolic procedure permpl(u,v)$
if null u then t
else if car u = car v then permpl(cdr u,cdr v)
else not permpl(cdr u,l!-subst1(car v,car u,cdr v))$
symbolic procedure repeatsp u$
if null u then nil
else (member(car u,cdr u) or repeatsp cdr u )$
symbolic procedure l!-subst1(new,old,l)$
if null l then nil
else if old = car l then new . cdr l
else (car l) . l!-subst1(new,old,cdr l)$
%-------------------FORMING ANTISYMMETRIHERS -----------------------$
symbolic procedure propagator(u,v)$
if null u then 1
else if (repeatsp u) or (repeatsp v) then 0
else 'plus . propag(u,permutations v,v)$
symbolic procedure propag(u,l,v)$
if null l then nil
else (if permpl(v,car l) then 'times . prpg(u,car l)
else list('minus,'times . prpg(u,car l) ) ) . propag(u,cdr l,v)$
symbolic procedure prpg(u,v)$
if null u then nil
else list('cons,car u,car v) . prpg(cdr u,cdr v)$
symbolic procedure line(x,y)$
propagator(cdr x,cdr y)$
%------------------ INTERFACE WITH CVIT3 ---------------------------$
symbolic procedure strand!-alg!-top(strand,map_,edlst)$
begin
scalar rlst$
strand:=deletez1(strand,edlst)$
rlst:=color!-strand(edlst,map_,1)$
strand:=contract!-strand(strand,rlst) $
%RINT STRAND$ TERPRI()$
%RINT RLST$ TERPRI()$
%RINT EDLST$ TERPRI()$
return dstr!-to!-alg(strand,rlst,nil)
%ATHPRINT REVAL(W)$ RETURN W
end$
symbolic procedure mktails(side,rlst,dump)$
begin
scalar pntr,newdump,w,z$
if null side then return nil . dump$
pntr:=side$
newdump:=dump$
while pntr do << w:=mktails1(car pntr,rlst,newdump)$
newdump:=cdr w$
z:=sappend(car w,z)$
pntr:=cdr pntr >>$
return z . newdump
end$
symbolic procedure mktails1(rname,rlst,dump)$
begin
scalar color,prename,z$
color:=getroad(rname,rlst)$
if 0 = color then return nil . dump$
if 0 = cdr rname then
return (list replace_by_vector car rname) . dump$
% IF FREEIND CAR RNAME THEN RETURN (LIST CAR RNAME) . DUMP$
z:=assoc(rname,dump)$
if z then return
if null cddr z then cdr z . dump
else (sreverse cdr z) . dump$
% PRENAME:=APPEND(EXPLODE CAR RNAME,EXPLODE CDR RNAME)$
prename:=rname$
z:= mkinds(prename,color)$
return z . ((rname . z) . dump)
end$
symbolic procedure mkinds(prename,color)$
if color = 0 then nil
else
begin
scalar indx$
% INDX:=INTERN COMPRESS APPEND(PRENAME,EXPLODE COLOR)$
indx:= prename . color $
return indx . mkinds(prename,sub1 color)
end$
symbolic procedure getroad(rname,rlst)$
if null rlst then 1 % ******EXT LEG IS ALWAYS SUPPOSET TO BE SIMPLE $
else if cdr rname = cdar rlst then
cdr qassoc(car rname,caar rlst)
else getroad(rname,cdr rlst) $
symbolic procedure qassoc(atm,alst)$
if null alst then nil
else if eq(atm,caar alst) then car alst
else qassoc(atm,cdr alst)$
%------------- INTERACTION WITH RODIONOV ---------------------------$
symbolic procedure from!-rodionov x$
begin scalar strand,edges,edgelsts,map_,w$
edges:=car x$
map_:=cadr x$
edgelsts:=cddr x$
strand := map_!-to!-strand(edges,map_)$
w:= for each edlst in edgelsts collect
strand!-alg!-top(strand,map_,edlst)$
return reval('plus . w )
end$
symbolic procedure top1 x$
mathprint from!-rodionov to_taranov x$
%----------------------- COMBINATORIAL COEFFITIENTS -----------------$
symbolic procedure f!^(n,m)$
if n<m then cviterr "Incorrect args of f!^"
else if n = m then 1
else n*f!^(sub1 n,m)$
%% This exists in basic REDUCE these days -- JPff
%%symbolic procedure factorial n$
%%f!^(n,0)$
symbolic procedure mk!-coeff1(alist,rlst)$
if null alist then 1
else
eval ('times .
for each x in alist collect factorial getroad(car x,rlst) )$
%--------------- CONTRACTION OF DELTA'S -----------------------------$
symbolic procedure prop!-simp(l1,l2)$
prop!-simp1(l1,l2,nil,0,1)$
symbolic procedure prop!-simp1(l1,l2,s,lngth,sgn)$
if null l2 then list(lngth,sgn) . (l1 . sreverse s)
else
(lambda z$ if null z then
prop!-simp1(l1,cdr l2,car l2 . s,lngth,sgn)
else prop!-simp1(cdr z,cdr l2,s,add1 lngth,
(car z)*sgn*(-1)**(length s)) )
prop!-simp2(l1,car l2)$
symbolic procedure prop!-simp2(l,ind)$
begin
scalar sign$
if sign:=index!-in(ind,l) then
return ((-1)**(length(l)-length(sign))) . delete(ind,l)
else return nil
end$
symbolic procedure mk!-contract!-coeff u$
if caar u = 0 then 1
else
begin
scalar numr,denr,pk,k$
pk:=caar u$
k:=length cadr u$
numr:=constimes ((cadar u) .mk!-numr(ndim!*,k,k+pk))$
% denr:=f!^(pk+k,k)*(cadar u)$
return numr
end$
symbolic procedure mk!-numr(n,k,p)$
if k=p then nil
else (if k=0 then n else list('difference,n,k)) . mk!-numr(n,add1 k,p)$
symbolic procedure mod!-index(term,dump)$
%-------------------------------------------------------------------
% MODYFIES INDECES OF "DUMP" VIA DELTAS IN "TERM"
% DELETES UTILIZED DELTAS FROM "TERM"
% RETURNS "TERM" . "DUMP"
%------------------------------------------------------------------$
begin
scalar coeff,sign$
coeff:=list 1$
term:= if sign:= eq(car term,'minus) then cdadr term
else cdr term$
while term do << if free car term then
coeff:=(car term) . coeff
else dump:=mod!-dump(cdar term,dump)$
term:=cdr term >>$
return
( if sign then
if null cdr coeff then (-1)
else 'minus . list(constimes coeff)
else if null cdr coeff then 1
else constimes coeff ) . dump
end$
symbolic procedure dpropagator(l1,l2,dump)$
(lambda z$
if z=0 then z
else if z=1 then nil . dump
else for each trm in cdr z collect
mod!-index(trm,dump) )
propagator(l1,l2)$
symbolic procedure dvertex!-to!-projector(svert,rlst,dump)$
begin
scalar l1,l2,coeff,w$
l1:=mktails(cadr svert,rlst,dump)$
if repeatsp car l1 then return 0$
l2:= mktails(caddr svert,rlst,cdr l1)$
if repeatsp car l2 then return 0$
dump:=cdr l2$
w:=prop!-simp(car l1,sreverse car l2)$
coeff:=mk!-contract!-coeff w$
return coeff . dpropagator(cadr w,cddr w,dump)
end$
%SYMBOLIC PROCEDURE DSTR!-TO!-ALG(STRAND,RLST,DUMP)$
%IF NULL STRAND THEN LIST('RECIP,MK!-COEFF1(DUMP,RLST))
%ELSE
% BEGIN
% SCALAR VRTX$
% VRTX:=DVERTEX!-TO!-PROJECTOR(CAR STRAND,RLST,DUMP)$
% IF 0=VRTX THEN RETURN 0$
% IF NULL CADR VRTX THEN RETURN
% LIST('TIMES,CAR VRTX,DSTR!-TO!-ALG(CDR STRAND,RLST,CDDR VRTX))$
%
% RETURN LIST('TIMES,CAR VRTX,
% 'PLUS . (FOR EACH TRM IN CDR VRTX COLLECT
% LIST('TIMES,CAR TRM,DSTR!-TO!-ALG(CDR STRAND,RLST,CDR TRM))) )
%===MODYFIED 4.07.89
remflag('(dstr!-to!-alg),'lose)$
symbolic procedure dstr!-to!-alg(strand,rlst,dump)$
%IF NULL STRAND THEN LIST('RECIP,MK!-COEFF1(DUMP,RLST))
if null strand then consrecip list(mk!-coeff1(dump,rlst))
else
begin
scalar vrtx$
vrtx:=dvertex!-to!-projector(car strand,rlst,dump)$
if 0=vrtx then return 0$
if null cadr vrtx then return
if 1 = car(vrtx) then
dstr!-to!-alg(cdr strand,rlst,cddr vrtx)
else
cvitimes2(car vrtx,
dstr!-to!-alg(cdr strand,rlst,cddr vrtx))$
return
cvitimes2(car vrtx,
consplus (for each trm in cdr vrtx collect
cvitimes2(car trm,
dstr!-to!-alg(cdr strand,rlst,
cdr trm))))$
end$
flag('(dstr!-to!-alg),'lose)$
symbolic procedure cvitimes2(x,y)$
if (x=0) or (y=0) then 0
else if x = 1 then y
else if y = 1 then x
else list('times,x,y)$
symbolic procedure free dlt$
(freeind cadr dlt) and (freeind caddr dlt)$
symbolic procedure freeind ind$
atom ind $
% AND
%LAGP(IND,'EXTRNL)$
symbolic procedure mod!-dump(l,dump)$
if not freeind car l then mod!-dump1(cadr l,car l,dump)
else mod!-dump1(car l,cadr l,dump)$
symbolic procedure mod!-dump1(new,old,dump)$
if null dump then nil
else ( (caar dump) . l!-subst(new,old,cdar dump) ) .
mod!-dump1(new,old,cdr dump)$
symbolic procedure l!-subst(new,old,l)$
if null l then nil
else if old = car l then new . l!-subst(new,old,cdr l)
else car l . l!-subst(new,old,cdr l) $
endmodule;
module intfierz; % Interface with Rodionov-Fierzing Routine.
exports calc_map_tar,calc_den_tar,pre!-calc!-map_ $
imports mk!-numr,map_!-to!-strand $
lisp$
%----------- DELETING VERTS WITH _0'S ------------------------------$
%symbolic procedure sort!-map_(map_,tadepoles,deltas,s)$
%if null map_ then list(s,tadepoles,deltas)
%else
% begin
% scalar vert,edges$
% vert:=incident1('!_0,car map_,'ll)$
% return
% if null vert then sort!-map_(cdr map_,tadepoles,deltas,
% car map_ . s)
% else if car vert = cadr vert then
% sort!-map_(cdr map_,caar vert . tadepoles,deltas,s)
% else sort!-map_(cdr map_,tadepoles,list('cons,caar vert,
% caadr vert) . deltas,s)
% end$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% modified 17.09.90 A.Taranov %%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
symbolic procedure sort!-map_(map_,tadepoles,deltas,poles,s)$
% tadepoles are verts with 1 0_ edge and contracted others
% deltas are verts with 1 0_ edge
% poles are verts with at list 2 0_ edges
if null map_ then list(s,tadepoles,deltas,poles)
else
begin
scalar vert,tdp$
vert:=incident1('!_0,car map_,'ll)$
if null vert then tdp:=tadepolep car map_
else %%%% vertex contain !_0 edge
return
if (caar vert = '!_0) then
sort!-map_(cdr map_,tadepoles,deltas,caadr vert . poles,s)
else if (caadr vert = '!_0) then
sort!-map_(cdr map_,tadepoles,deltas,caar vert . poles,s)
else if car vert = cadr vert then
sort!-map_(cdr map_,caar vert . tadepoles,deltas,
poles,s)
else sort!-map_(cdr map_,tadepoles,list('cons,
caar vert,caadr vert) . deltas,poles,
s)$
%%%%% here car Map_ was checked to be a real tadpole
return
if null tdp then sort!-map_(cdr map_,tadepoles,deltas,
poles,car map_ . s)
else sort!-map_(cdr map_,cadr tdp . tadepoles,deltas,
caar tdp . poles,s)
end$
symbolic procedure tadepolep vrt; %%%%%% 17.09.90
% return edge1 . edge2 if vrt is tadpole,
% NIL otherwise.
% edge1 correspond to 'pole', edge2 - to 'loop' of a tadpole.
if car vrt = cadr vrt then caddr vrt . car vrt
else if car vrt = caddr vrt then cadr vrt . car vrt
else if cadr vrt = caddr vrt then car vrt . cadr vrt
else nil;
symbolic procedure del!-tades(tades,edges)$
if null tades then edges
else del!-tades(cdr tades,delete(car tades,edges))$
symbolic procedure del!-deltas(deltas,edges)$
if null cdr deltas then edges
else del!-deltas(cdr deltas,del!-tades(cdar deltas,edges))$
%--------------- EVALUATING MAP_S -----------------------------------$
symbolic procedure pre!-calc!-map_(map_,edges)$
% : (STRAND NEWMAP_ TADEPOLES DELTAS)$
begin
scalar strand,w$
w:=sort!-map_(map_,nil,list 1,nil,nil)$
% delete from edge list deltas,poles and tades
edges:=del!-deltas(caddr w,
del!-tades(cadr w,delete('!_0,edges)))$
strand:= if car w then map_!-to!-strand(edges,car w)
else nil$
return strand . w
end$
symbolic procedure calc_map_tar(gstrand,alst)$
% THIRD VERSION.$
begin
scalar poles,edges,strand,deltas,tades,map_$
strand:=car gstrand$
map_:=cadr gstrand$
tades:=caddr gstrand $
deltas:=car cdddr gstrand $
poles:= car cddddr gstrand $
if ev!-poles(poles,alst) then return 0; %%%%% result is zero
return constimes list(constimes deltas,
constimes ev!-tades(tades,alst),
(if null map_ then 1
else strand!-alg!-top(strand,map_,alst)))
end$
symbolic procedure ev!-poles(poles,alst)$ %%% 10.09.90
if null poles then nil
else if getedge(car poles,alst) = 0 then ev!-poles(cdr poles,alst)
else poles$
symbolic procedure ev!-deltas(deltas)$
if null deltas then list 1
else ('cons . car deltas) . ev!-deltas(cdr deltas)$
symbolic procedure ev!-tades(tades,alst)$
if null tades then list 1
else binc(ndim!*,getedge(car tades,alst))
. ev!-tades(cdr tades,alst)$
%------------------------ DENOMINATOR CALCULATION -------------------$
symbolic procedure ev!-edgeloop(edge,alst)$
% EVALUATES LOOP OF 'EDGE' COLORED VIA 'ALST'$
binc(ndim!*,getedge(s!-edge!-name edge,alst) )$
symbolic procedure ev!-denom2(vert,alst)$
% EVALUATES DENOM FOR PROPAGATOR$
ev!-edgeloop(car vert,alst)$
symbolic procedure ev!-denom3(vert,alst)$
% EVALUATES DENOM FOR 3 - VERTEX$
begin
scalar e1,e2,e3,lines,sign,!3j,numr$
e1:=getedge(s!-edge!-name car vert,alst)$
e2:=getedge(s!-edge!-name cadr vert,alst)$
e3:=getedge(s!-edge!-name caddr vert,alst)$
lines:=(e1+e2+e3)/2$
e1:=lines-e1$
e2:=lines-e2$
e3:=lines-e3$
sign:=(-1)**(e1*e2+e1*e3+e2*e3)$
numr:=mk!-numr(ndim!*,0,lines)$
numr:=(if numr then (constimes numr)
else 1)$
!3j:=listquotient(numr,
factorial(e1)*factorial(e2)*factorial(e3)*sign)$
return !3j
end$
symbolic procedure binc(n,p)$
% BINOMIAL COEFF C(N,P)$
if 0 = p then 1 else
listquotient(constimes mk!-numr(n,0,p),factorial p)$
symbolic procedure calc_den_tar(den_,alst)$
(lambda u$ if null u then 1
else if null cdr u then car u
else constimes u )
denlist(den_,alst)$
symbolic procedure denlist(den_,alst)$
if null den_ then nil
else if length car den_ = 2 then
ev!-denom2(car den_,alst) . denlist(cdr den_,alst)
else ev!-denom3(car den_,alst) . denlist(cdr den_,alst)$
endmodule;
module cvitmap;
exports calc_spur$
imports simp!*,reval,calc_map_tar ,calc_den_tar,spaces$
% SIMP!* AND REVAL REDUCE SYSTEM GENERAL FUNCTIONS FOR
% EVALUATING ALGEBRAIC EXPRESSIONS.
%*********************************************************************
% *
% FOR CVITANOVIC GAMMA MATRICES *
% CALCULATIONS *
% *
% *
% 18.03.88 10.06.90 15.06.90 31.08.90 *
% 01.09.90 11.09.90 14.09.90 *
%********************************************************************$
lisp$
% 07.06.90 all MAP was replaced by MAP_
% 07.06.90 all DEN was replaced by DEN_
% 07.06.90 all PROP was replaced by PROP_
% SOME FUNCTIONS WAS MOVED TO SMACRO SECTION 08.06.90 10.06.90
%**********************************************************************
% *
% _DATA_STRUCTURE *
% *
% WORLD::=(EDGELIST,VARIANTS,WORLD1) *
% WORLD1::=(MAP_2,COEFF,DEN_OM) *
% MAP_2::=(MAP_S,VARIANTS,PLAN) *
% MAP_S::=(EDGEPAIR . GSTRAND) *
% MAP_1::=(EDGEPAIR . MAP_) *
% EDGEPAIR::=(OLDEDGELIST . NEWEDGELIST) *
% COEFF::=LIST OF WORLDS (UNORDERED) *
% ATLAS::=(MAP_,COEFF,DEN_OM) *
% MAP_::=LIST OF VERTICES (UNORDERED) *
% VERTEX::=LIST OF EDGES (CYCLIC ORDER) *
% VERTEX::=(NAME,PROP_ERTY,TYPE) *
% NAME::=ATOM *
% PROP_ERTY::= (FIRSTPARENT . SECONDPARENT) *
% TYPE::=T OR NIL *
% *
%*********************************************************************$
%========================== PREDICATES =============================$
symbolic procedure is_indexp x$ % 01.09.90 RT
(lambda z$
z and cdr z)
assoc(s_edge_name x,dindices!*)$
symbolic procedure mk_edge_name (name1,name2)$
% GENERATE NEW EDGE NAME $
<< n_edge := n_edge +1$
%INTERN COMPRESS APPEND(MK_NAME1 NAME1,
compress append(mk_name1 name1,
append ( mk_name1 n_edge ,
mk_name1 name2)) >> $
symbolic procedure new_edge (fedge,sedge)$
% GENERATE NEW EDGE $
begin
scalar s$
s:=
mk_edge ( mk_edge_name ( s_edge_name fedge,
s_edge_name sedge),
mk_edge_prop_ ( s_edge_name fedge,
s_edge_name sedge),
mk_edge_type ( nil,
nil))$
% MK_EDGE_TYPE ( S_EDGE_TYPE FEDGE,
% S_EDGE_TYPE SEDGE))$
new_edge_list := s . new_edge_list $
return s
end$
symbolic procedure delete_vertex (vertex,map_)$
%DELETS VERTEX FROM MAP_$
if p_empty_map_ map_ then mk_empty_map_ ()
else
if p_eq_vertex (vertex,s_vertex_first map_)
then s_map__rest map_
else
add_vertex (s_vertex_first map_,
delete_vertex (vertex,s_map__rest map_))$
%====================== PREDICATES (CONTINUE) =====================$
symbolic procedure p_eq_vertex (vertex1,vertex2)$
% VERTICES ARE EQ IF THEY HAVE EQUAL NUMBER OF EDGES
% IN THE SAME ORDER WITH EQUAL _NAMES $
if p_empty_vertex vertex1 then p_empty_vertex vertex2
else
if p_empty_vertex vertex2 then nil
else
if equal_edges (first_edge vertex1,
first_edge vertex2)
then p_eq_vertex (s_vertex_rest vertex1,
s_vertex_rest vertex2)
else nil$
%::::::::::::::::::::::: SOME ROUTINES :::::::::::::::::::::::::::::$
symbolic procedure mk_old_edge x$
begin
scalar s$
s:=assoc(x,old_edge_list )$
if s then return s$
s:=mk_edge ( x,
if not gamma5p x
then mk_edge_prop_ (1,1) %10.06.90 RT
else mk_edge_prop_ (ndim!*,ndim!*),
mk_edge_type (t,t))$
old_edge_list :=cons(s,old_edge_list )$
return s
end$
symbolic procedure change_name (name,edge)$
% CHANGES EDGE'S NAME $
mk_edge (name,
s_edge_prop_ edge,
s_edge_type edge )$
%======================= PREDICATES (CONTINUE) ================== $
symbolic procedure is_tadpole vertex$ %11.09.90 RT
% RETURNS T IF THERE IS ONLY ONE EXTERNAL LEG
is_tadpolen(vertex) < 2$
symbolic procedure is_tadpolen vertex$ %11.09.90 RT
% RETURNS NUMBER OF EXTERNAL LEGS
vertex_length diff_legs(vertex,mk_empty_vertex())$
symbolic procedure diff_legs(vertex,vertex1)$ %11.09.90 RT
% RETURNS LIST OF EXTERNAL LEGS
if p_empty_vertex vertex then vertex1
else if p_member_edge(first_edge vertex,
s_vertex_rest vertex)
or
p_member_edge(first_edge vertex,
vertex1)
then diff_legs(s_vertex_rest vertex,vertex1)
else diff_legs(s_vertex_rest vertex,
add_edge(first_edge vertex,vertex1))$
symbolic procedure is_buble (vertex1,vertex2)$
% RETURNS NIL IF VERTEX1 AND VERTEX2 DOES NOT FORMED A BUBLE,
% OR N . MAP_ ,WHERE N IS A NUMBER OF EXTERNAL LINES ( 0 OR 2 ),
% MAP_ IS A MAP_ CONTAINING THIS BUBLE $
%NOT(IS_TADPOLE VERTEX1) AND NOT(IS_TADPOLE VERTEX2) AND %14.09.90 RT
(lambda z$ if z >= 2 then nil
else (2*z) . mk_vertex2_map_ (vertex1,vertex2))
vertex_length ( diff_vertex (vertex1,vertex2))$
%^^^^^^^^^^^^^^^^^^^^^^^ MAIN PROGRAM ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^$
symbolic procedure transform_map_ map_$
% GENERATE SIMPLE MAP_ (ONLY PRIMITIVE VERTICES) FROM INITIAL ONE$
begin
scalar n_edge$
n_edge := 0$
new_edge_list :=nil$
old_edge_list :=nil$
return
mk_simple_map_
(for each vertex in map_ collect
prepare_map_ vertex)$
end$
%,,,,,,,,,,,,,,,,,,,,,RODIONOV & TARANOV INTERFACE ,,,,,,,,,,,,,,,$
global '(bubltr freemap_)$
symbolic procedure to_taranov map_$
% MAP_ IS INITIAL MAP_,
% RETURNS (FULL LIST OF EDGES (INITIAL AND GENERATED) .
% (MAP_ OF PRIMITIVE VERTICES ) .
% (LIST OF ALL POSSIBLE ENUMERATION OF MAP_'S EDGES) $
begin
scalar new_edge_list ,old_edge_list ,full_edge_list ,
new_map_ ,free_map_ ,marks ,variants ,alst ,bubles$
new_map_ :=transform_map_ map_$
free_map_ :=find_bubltr new_map_ $
bubles:=car free_map_ $
bubltr:=bubles $
free_map_ := cdr free_map_ $
freemap_:=free_map_ $
full_edge_list := for each edge in old_edge_list collect
s_edge_name edge $
alst:=nconc(for each x in full_edge_list collect (x . 1) ,
list('!_0 . 0) ) $ %ADD EMPTY EDGE $
marks:=set_mark (new_edge_list ,
nil,
buble_proves bubles,
new_map_ ,
add_tadpoles (bubles,alst))$
variants:=edge_bind (marks,alst)$
full_edge_list :=nconc (for each edge in new_edge_list collect
s_edge_name edge,
full_edge_list )$
return full_edge_list .
new_map_ .
variants
end$
% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST $
% TO_TARANOV '((A B C C B A)) $
%END$ %cvit2.red
%********************************************************************
% NOW WE MARKED THE MAP_ *
%*******************************************************************$
% 09.03.88 $
lisp$
global '(ndim!* )$
%ERROERRORERRORERRORERROR ERROR ROUTINES ERRORERRORERRORERRORERROR $
global '(!*cviterror)$
flag('(cviterror),'switch)$
!*cviterror:=t$ % IF T THEN ERROR MESSAGES WILL BE PRINTED$
% The FEXPR for set_error has been re-written by JPff
%%% symbolic fexpr procedure set_error u$
%%% if !*cviterror then set_error0 (u,alst)
%%% else
%%% error(55,"ERROR IN MAP_ CREATING ROUTINES") $
symbolic macro procedure set_error u$
list('set_error_real,mkquote cadr u,cons('list,cddr u))$
symbolic procedure set_error_real (u,v)$
<<
if !*cviterror then <<
prin2 "Function: "$
prin2 car u$
prin2 " Arguments: "$
if v then for each x in v do <<
prin2 x$ prin2 " IS " $
prin2 x$
terpri() >>;
>>;
error(55,"Error in MAP_ creating routines")
>>$
%ERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERE$
symbolic procedure mark_edges (newedges,oldedges,map_)$
mk_proves (map_,oldedges) .
set_mark (newedges,nil,nil,map_,
for each x in oldedges collect (s_edge_name x .
car s_edge_prop_ x ) ) $
symbolic procedure mk_proves (map_,oldedges)$
if p_empty_map_ map_ then nil
else
if defined_vertex (s_vertex_first map_,oldedges) then
s_vertex_first map_ .
mk_proves (s_map__rest map_,oldedges)
else
mk_proves (s_map__rest map_,oldedges)$
symbolic procedure defined_vertex (vertex,oldedges)$
if p_empty_vertex vertex then t
else
memq_edgelist (first_edge vertex,oldedges)
and
defined_vertex (s_vertex_rest vertex,oldedges)$
symbolic procedure set_mark (edges,notdef,toprove,map_,blst)$
% EDGES - LIST OF NEW EDGES CREATED WHILE MAKING A MAP_,
% NOTDEF - LIST OF EDGES WHICH CANNOT BE FULLY IDEN_TIFY,
% TOPROVE - LIST OF VERTICES FOR CHECKING TRIANGLE RULE,
% MAP_ - MAP_ CREATED EARLIER,
% BLST - ALIST OF BINDED EDGES$
if null edges then
if notdef or toprove then % 15.06.90 RT
set_error_real('set_mark,
list(edges,notdef,toprove,map_,blst))
else nil
else
(lambda z$
if z then %THE EDGE IS FULLY DEFINED$
set_prove (append(notdef, %RESTOR LIST OF EDGES$
cdr edges),
car edges,
append(new_prove (car edges, %ADD CHECKS$
map_),
toprove),
map_,
(s_edge_name car edges . 0) .
blst)
else
set_mark (cdr edges, %TRY NEXT$
car edges . notdef, % ADD NOT DEF. LIST$
toprove,
map_,
blst))
( assoc(caadar edges,blst) %CHECK IF BOTH PARENT IS $
and %ALREADY DEFINED $
assoc(cdadar edges,blst) ) $
symbolic procedure new_prove (edge,map_)$
% RETURNS NEW VERTEX FOR TRIANGLE RULE CHECKING LIST$
if null map_ then nil
else
(lambda z$ if z then list z
else new_prove (edge,cdr map_))
new_provev (edge,car map_) $
symbolic procedure new_provev (edge,vertex)$
% CAN THIS VERTEX BE UTILIZED FOR CHECKING ? $
if not member(edge,vertex) then nil
else
if (assoc(caadr edge,vertex)
and
assoc(cdadr edge,vertex))
then nil
else vertex $
symbolic procedure is_son (edge,vertex)$
assoc(car s_edge_prop_ edge,vertex)$
symbolic procedure not_parents (edge,proves)$
if null proves then nil
else
if is_son (edge,car proves)
then cdr proves
else car proves . not_parents (edge,cdr proves)$
symbolic procedure set_prove (edges,edge,toprove,map_,blst)$
% RETURNS A PAIR (EDGE . (LIST FOF VERICES FOR TRIANGLE RULE TEST))$
(lambda z$
(edge . not_parents (edge,car z)) .
set_mark (edges,nil,cdr z,map_,blst))
find_proved (toprove,nil,nil,blst)$
symbolic procedure find_proved (toprove,proved,unproved,blst)$
% RETURNS A PAIR ((LIST OF ALREADY DEFINED VERTICES) .
% (LIST OF NOT YET DEFINED EDGES) ) $
if null toprove then proved . unproved
else
if is_proved (car toprove,blst) then
find_proved (cdr toprove,
car toprove . proved,
unproved,
blst)
else find_proved (cdr toprove,
proved,
car toprove . unproved,
blst) $
symbolic procedure is_proved (vertex,blst)$
if null vertex then t
else if assoc(caar vertex,blst) then is_proved (cdr vertex,blst)
else nil $
%@@@@@@@@@@@@@@@@@@@@@@@ NOW GENERATES ALL POSSIBLE NUMBERS @@@@@@@@$
symbolic procedure mk_binding (provedge,blst)$
can_be_proved (car provedge,blst)
and
edge_bind (cdr provedge,blst)$
symbolic procedure edge_bind (edgelist,blst)$
if null edgelist then list blst
else
begin
scalar defedge,prop_,p,emin,emax,s,proves,i$
% DEFEDGE - EDGE WITH DEFINED RANG,
% PROP_ - ITS PROP_ERTY: (NUM1 . NUM2),
% P - ITS NAME,
% EMIN AND EMAX - RANGE OF P,
% S - TO STORE RESULTS,
% PROVES - CHECKS OF TRIANGLE LAW$
defedge:=car edgelist$
proves:=cdr defedge$
defedge:=car defedge$
edgelist:=cdr edgelist$
p:=s_edge_name defedge$
prop_:=s_edge_prop_ defedge$
emin:=assoc(car prop_,blst)$
emax:=assoc(cdr prop_,blst)$
if null emin or null emax
then set_error_real ('edge_bind,list(prop_,blst))$
prop_:=(cdr emin) . (cdr emax)$
emin:=abs((car prop_)-(cdr prop_))$
emax:=(car prop_)+(cdr prop_)$
if numberp ndim!* then %NUMERICAL DIMENSIONAL$
<< emax:=min(emax,ndim!*)$
if emin > ndim!* then return nil >> $
i:=emin$
loop:
if i > emax then return s$
if can_be_proved (proves,(p . i) . blst)
then s:=append(edge_bind (edgelist,
(p . i) . blst),
s) $
i:=i+2$
go loop
end$
symbolic procedure can_be_proved (proves,blst)$
if null proves then t
else if can_be_p (car proves,blst) then
can_be_proved (cdr proves,blst)
else nil$
symbolic procedure can_be_p (vertex,blst)$
%CHECKS TRIANGLE RULE$
begin
scalar i,j,k$
i:=assoc(car car vertex,blst)$
j:=assoc(car cadr vertex,blst)$
k:=assoc(car caddr vertex,blst)$
if null i or null j or null k then set_error_real('can_be_proved,
list(vertex,%%edge,
blst))$
i:=cdr i$
j:=cdr j$
k:=cdr k$
if numberp ndim!* and (i+j+k) > (2*ndim!*) then
return nil $ %SINCE S+T+U<NDIM!* $
% ======== NOW CHECK TRIANGLE RULE ======= $
return
if not evenp(i+j+k) or
k < abs(i-j) or
k > (i+j)
then nil
else t
end$
%END$ %cvit4.red
%OOOOOOOOOOOOOOOOOOOOOOOOO ROUTINES TO SELECT BUBLES OOOOOOOOOOOOOOOO$
lisp$ %24.05.88$
symbolic procedure find_bubles atlas$
find_bubles1 (atlas,old_edge_list )$
symbolic procedure find_bubles_coeff (atlaslist,edgelist,bubles)$
%F NULL BUBLES THEN NIL . ATLASLIST
%LSE
find_bubles1_coeff (atlaslist,nil,edgelist,bubles)$
symbolic procedure find_bubles1_coeff (atlaslist,passed,edgelist,
bubles)$
if null atlaslist then bubles . passed
else
(lambda z$ %Z - PAIR = (BUBLES . REDUCED MAP_)
find_bubles1_coeff (cdr atlaslist,
cdr z . passed,
edgelist,
if null car z then bubles else
car z . bubles) )
find_bubles1 (car atlaslist,edgelist) $
symbolic procedure mk_atlaslist (map_,coeff,den_om)$
list mk_atlas (map_,coeff,den_om)$
symbolic procedure find_bubles1 (atlas,edgelist)$
select_bubles (nil,
s_atlas_map_ atlas,
nil,
s_atlas_coeff atlas,
s_atlas_den_om atlas,
edgelist)$
symbolic procedure select_bubles(bubles,map_,passed,coeff,den_om,al)$
% RETURNS (LIST OF BUBLES ) . ATLAS,
% WHERE BUBLES ARE TWO OR ONE VERTICES MAP_S $
if p_empty_map_ map_ then
(lambda x$
car x .
mk_atlas (passed,cdr x,den_om))
find_bubles_coeff (coeff,
union_edges (map__edges passed,
al),
bubles)
else
if (map__length map_ + map__length passed) < 3 then
select_bubles (bubles,
mk_empty_map_ (),
append_map_s(map_,
passed),
coeff,
den_om,
al)
else
(lambda z$ % Z IS NIL OR A PAIR
% N . MAP_ ,WHERE
% N - NUMBER OF FREE EDGES$
if z then %A BUBLE IS FIND$
(lambda d$
(lambda bool$ %BOOL=T IFF ALL EDGES CAN BE DEFINED$
if car z = 0 then %NO EXTERNAL LINES$
if bool then
select_bubles ( z . bubles,
mk_empty_map_ (),
cdr z,
mk_atlaslist ( conc_map_s (passed,
delete_vertex (
s_vertex_second
cdr z,
s_map__rest
map_)),
coeff,
den_om),
nil,
al)
else
select_bubles ( z . bubles, %ADD BUBLE$
delete_vertex (s_vertex_second cdr z,
s_map__rest map_),
passed,
try_sub_atlas (mk_atlas (cdr z,
nil,
nil),
coeff),
den_om,
al)
else
if not p_old_vertex d then
if bool then
select_bubles (z . bubles,
mk_empty_map_ (),
cdr z,
mk_atlaslist (conc_map_s (passed,
buble_vertex (
cdr z,
delete_vertex (
s_vertex_second
cdr z,
s_map__rest
map_ ),
al)),
coeff,
den_om),
list d,
al)
else
select_bubles ( z . bubles, %ADD NEW BUBLE$
buble_vertex (cdr z, %RENAME EDGES $
conc_map_s (passed,
delete_vertex (s_vertex_second cdr z,
s_map__rest map_)),
al),
mk_empty_map_ (),
try_sub_atlas (mk_atlas (cdr z,nil,list d),
coeff),
den_om,
al)
else
if bool then
select_bubles (z . bubles,
mk_empty_map_ (),
ren_vertmap_ (d,cdr z),
mk_atlaslist (
conc_map_s (
passed,
add_vertex (add_edge (!_0edge ,d),
delete_vertex (
s_vertex_second cdr z,
s_map__rest map_ ))),
coeff,
den_om),
list ren_vertices (d,d),
al)
else
select_bubles (z . bubles,
add_vertex (add_edge (!_0edge ,d),
delete_vertex(s_vertex_second cdr z,
s_map__rest map_)
),
passed,
try_sub_atlas (mk_atlas (ren_vertmap_
(d,cdr z),
nil,
list
ren_vertices (d,d)
),
coeff),
den_om,
al )
)
% ALL_DEFINED (CDR Z,AL))
t )
delta_edges cdr z
else
select_bubles (bubles,
s_map__rest map_,
add_vertex (s_vertex_first map_,passed),
coeff,
den_om,
al )
)
find_buble (s_vertex_first map_,
s_map__rest map_ ) $
symbolic procedure p_old_vertex vertex$
% RETURNS T IFF ALL EDGES OF VERTEX ARE OLD OR VERTEX IS EMPTY ONE$
if p_empty_vertex vertex then t
else p_old_edge first_edge vertex
and
p_old_vertex s_vertex_rest vertex$
symbolic procedure renames_edges (vertex,al)$
rename_edges_par (first_edge vertex,
second_edge vertex,
al)$
symbolic procedure rename_edges_par (vertex1,vertex2,al)$
% Here VERTEX1 and VERTEX2 are edges!
if defined_edge (vertex1,al)
and not p_old_edge(vertex2) then % 14.09.90 RT
replace_edge (vertex2,vertex1,new_edge_list )
else
if defined_edge (vertex2,al)
and not p_old_edge(vertex1) then % 14.09.90 RT
replace_edge (vertex1,vertex2,new_edge_list )
else
if p_old_edge (vertex1)
and not p_old_edge(vertex2) then % 14.09.90 RT
replace_edge (vertex2,vertex1,new_edge_list )
else
if p_old_edge (vertex2)
and not p_old_edge(vertex1) then % 14.09.90 RT
replace_edge (vertex1,vertex2,new_edge_list )
else rename_edges (vertex1,vertex2)$
symbolic procedure buble_vertex (map_2,map_,al)$
if p_empty_map_ map_2 then mk_empty_map_ ()
else
<< renames_edges (delta_edges map_2,al)$
map_ >> $
symbolic procedure delta_edges map_2$
% MAP_2 - MAP_ OF TWO VERTICES $
mk_edge2_vertex (
first_edge
diff_vertex (s_vertex_first map_2,
s_vertex_second map_2),
first_edge
diff_vertex (s_vertex_second map_2,
s_vertex_first map_2 )
)$
symbolic procedure delta_names map_2$
% MAP_2 - MAP_ OF TWO VERTICES $
(lambda z$
s_edge_name first_edge car z .
s_edge_name first_edge cdr z )
(diff_vertex (s_vertex_first map_2,
s_vertex_second map_2) .
diff_vertex (s_vertex_second map_2,
s_vertex_first map_2) ) $
symbolic procedure old_rename_edges (names,map_)$
if p_empty_map_ map_ then mk_empty_map_ ()
else add_vertex (ren_edge (names,s_vertex_first map_),
old_rename_edges (names,
s_map__rest map_) ) $
symbolic procedure ren_vertmap_ (vertex1,map_)$
% VERTEX1 MUST BE TWO EDGE VERTEX,
% EDGES OF VERTEX2 TO BE RENAME$
if vertex_length vertex1 neq 2 then set_error_real ('ren_vertmap_ ,
list(vertex1,map_))
else old_rename_edges (s_edge_name first_edge vertex1 .
s_edge_name second_edge vertex1,
map_)$
symbolic procedure ren_vertices (vertex1,vertex2)$
% VERTEX1 MUST BE TWO EDGE VERTEX,
% EDGES OF VERTEX2 TO BE RENAME$
if vertex_length vertex1 neq 2
then set_error_real ('ren_vertices,list(vertex1,vertex2))
else ren_edge (s_edge_name first_edge vertex1 .
s_edge_name second_edge vertex1,
vertex2)$
symbolic procedure ren_edge (names,vertex)$
% NAMES IS NAME1 . NAME2,
% CHANGE NAME1 TO NAME2$
if null assoc(car names,vertex) then vertex %NO SUCH EDGES IN VERTEX$
else ren_edge1 (names,vertex)$
symbolic procedure ren_edge1 (names,vertex)$
if p_empty_vertex vertex then mk_empty_vertex ()
else if car names =s_edge_name first_edge vertex then
add_edge ( change_name (cdr names,first_edge vertex),
ren_edge1 (names ,s_vertex_rest vertex))
else
add_edge ( first_edge vertex,
ren_edge1 (names,s_vertex_rest vertex))$
symbolic procedure find_buble (vertex,map_)$
if p_empty_map_ map_ then mk_empty_map_ ()
else
is_buble (vertex,s_vertex_first map_)
or
find_buble (vertex,s_map__rest map_) $
symbolic procedure diff_vertex (vertex1,vertex2)$
if p_empty_vertex vertex1 then mk_empty_vertex ()
else
if p_member_edge (first_edge vertex1,vertex2)
and
not equal_edges (first_edge vertex1,!_0edge )
then diff_vertex (s_vertex_rest vertex1,vertex2)
else
add_edge (first_edge vertex1,
diff_vertex (s_vertex_rest vertex1,vertex2)) $
%SSSSSSSSSSSSSSSSSSSSSSSSSS NOW MAKES PROVES FROM BUBLE PPPPPPPPPPPPPP$
global '(!_0edge )$
!_0edge :=mk_edge ('!_0 ,
mk_edge_prop_ (0,0),
mk_edge_type (t,t)) $
symbolic procedure buble_proves bubles$
if null bubles then nil
else
if caar bubles = 0 %NO EXTERNAL LINES $
then buble_proves cdr bubles
else if caar bubles = 2 then
mk_edge3_vertex (
first_edge diff_vertex (
s_vertex_first cdar bubles,
s_vertex_second cdar bubles),
first_edge diff_vertex (
s_vertex_second cdar bubles,
s_vertex_first cdar bubles),
!_0edge ) .
buble_proves cdr bubles
else
if caar bubles = 3 then
car cdar bubles .
buble_proves cdr bubles
else buble_proves cdr bubles $
symbolic procedure try_sub_atlas (atlas,atlaslist)$
if null atlaslist then list atlas
else
if sub_map__p (s_atlas_map_ atlas,
s_atlas_den_om car atlaslist)
then try_sub_atlas (mk_sub_atlas (atlas,car atlaslist),
% THEN TRY_SUB_ATLAS (MK_SUB_ATLAS (CAR ATLASLIST,
% ATLAS ),
cdr atlaslist)
else car atlaslist .
try_sub_atlas (atlas,cdr atlaslist)$
symbolic procedure sub_map__p (map_1,den_)$
%MAP_1 AND DEN_ HAVE COMMON VERTEX (DEN_ - DEN_OMINATOR)$
if p_empty_map_ map_1 then nil
else sub_vertex_map_ (s_vertex_first map_1,den_)
or
sub_map__p (s_map__rest map_1,den_)$
symbolic procedure sub_vertex_map_ (vertex,den_)$
if null den_ then nil
else p_common_den_ (vertex,car den_)
or
sub_vertex_map_ (vertex,cdr den_)$
symbolic procedure p_common_den_ (vertex,vertexd)$
(lambda n$
if n = 3 then %TRIANGLE
p_eq_vertex (vertex,vertexd)
else
if n = 2 then %KRONEKER
p_member_edge (first_edge vertexd,vertex)
else nil )
vertex_length vertexd $
symbolic procedure mk_sub_atlas (atlas1,atlas2)$
mk_atlas (s_atlas_map_ atlas1,
atlas2 . s_atlas_coeff atlas1,
s_atlas_den_om atlas1)$
symbolic procedure all_defined (map_,al)$
all_defined_map_ (map_,
defined_append(map__edges map_,al))$
symbolic procedure all_defined_map_ (map_,al)$
al1_defined_map_ (map_,mk_empty_map_ (),al)$
symbolic procedure al1_defined_map_ (map_,passed,al)$
% T IF ALL EDGES IN MAP_ CAN BE DEFINED $
if p_empty_map_ map_ then
if p_empty_map_ passed then t
else nil
else
if all_defined_vertex (s_vertex_first map_,al) then
al1_defined_map_ (conc_map_s(passed,s_map__rest map_),
mk_empty_map_ (),
append(vertex_edges s_vertex_first map_ ,al))
else
al1_defined_map_ (s_map__rest map_,
add_vertex (s_vertex_first map_,passed),
al)$
symbolic procedure all_defined_vertex (vertex,al)$
al1_defined_vertex (vertex,mk_empty_vertex (),
mk_empty_vertex (),al)$
symbolic procedure al1_defined_vertex (vertex,passed,defined,al)$
% T IF ALL EDGES IN VERTEX CAN BE DEFINED $
if p_empty_vertex vertex then
if p_empty_vertex passed then t
else re_parents (passed,defined)
else
if defined_edge (first_edge vertex,al)
then
al1_defined_vertex (conc_vertex(passed,s_vertex_rest vertex),
mk_empty_vertex (),
add_edge (first_edge vertex,defined),
first_edge vertex . al)
else
al1_defined_vertex (s_vertex_rest vertex,
add_vertex (first_edge vertex,passed),
defined,
al)$
symbolic procedure re_parents (passed,defined)$
%TRY TO MAKE NEW PARENTS
if vertex_length passed = 1 and vertex_length defined = 2
then make_new_parents (first_edge passed,defined)
else nil$
symbolic procedure make_new_parents (edge,vertex)$
%VERTEX CONSISTS OF TWO EDGES
add_parents0 (edge,
s_edge_name first_edge vertex .
s_edge_name second_edge vertex ,
t)$
%^.^.^.^.^.^.^.^.^.^.^.^.^.^.^..^.^.^.^.^.^.^.^.^.^.^.^.^.^.^.^.^.^.^
% 13.05.88
symbolic procedure p_def_edge edge$
s_edge_type edge$
%P_OLD_EDGE EDGE$
symbolic procedure defined_edge (edge,al)$
p_old_edge edge
or
defined_all_edge (all_edge (s_edge_name edge,new_edge_list ),
nil,
al) $
symbolic procedure all_edge (edgename,edgelist)$
if null edgelist then nil
else
if edgename eq s_edge_name car edgelist then
car edgelist . all_edge (edgename,cdr edgelist)
else all_edge (edgename,cdr edgelist)$
symbolic procedure def_edge (edge,al)$
(lambda z$
assoc(car z,al) and assoc(cdr z,al))
s_edge_prop_ edge$
symbolic procedure defined_all_edge (edgelist,passed,al)$
if null edgelist then nil
else
if def_edge (car edgelist,al) then
if p_def_edge car edgelist then t %REPLACE WAS ALREADY DONE
else rep_edge_prop_ (nconc(passed,edgelist),
s_edge_prop_ car edgelist . list t)
else defined_all_edge (cdr edgelist,
car edgelist . passed,
al)$
symbolic procedure rep_edge_prop_ (edgelist,prop_)$
if null edgelist then t
else << rplacd(car edgelist,prop_)$ %CHANGE EDGE PARENTS
rep_edge_prop_ (cdr edgelist,prop_) >> $
%END$ %cvit6.red
%<><><><><><><><><><><> ROUTINES FOR SELECTING TRIANGLES <><><><><><>$
%24.05.88$
global '(!*cvitbtr !*cviterror)$
flag('(cvitbtr),'switch)$
!*cvitbtr:=t$ %IF T THEN BUBLES AND TRIANGLES WILL BE
% FACTORIZED
!*cviterror:=t$ %IF T THEN ERROR MESSAGES WILL BE PRINTED
symbolic procedure find_triangles atlas$
find_triangles1 (atlas,old_edge_list)$
symbolic procedure find_triangles1 (atlas,al)$
select_triangles (nil,
s_atlas_map_ atlas,
nil,
s_atlas_coeff atlas,
s_atlas_den_om atlas,
al)$
symbolic procedure find_triangl_coeff (atlaslist,edgelist,triangles)$
find_triangle_coeff (atlaslist,nil,edgelist,triangles)$
symbolic procedure find_triangle_coeff(atlaslist,passed,edgelist,
triangles)$
if null atlaslist then triangles . passed
else
(lambda z$ % Z - PAIR= (TRIANGLES . REDUCED MAP_)
find_triangle_coeff (cdr atlaslist,
cdr z . passed,
edgelist,
if null car z then triangles
else car z . triangles))
find_triangles1 (car atlaslist,edgelist)$
symbolic procedure select_triangles (triangles,map_,passed,
coeff,den_om,al)$
%RETURNS A PAIR OF THE FORM ( (LIST OF TRIANGLES) . (ATL.WITHOUT TR.))$
if p_empty_map_ map_ then %No triangles found.
(lambda x$
car x .
mk_atlas (passed,cdr x,den_om))
find_triangl_coeff (coeff,
union_edges (map__edges passed,al),
triangles)
else
if (map__length map_ + map__length passed) < 4 then
select_triangles (triangles,
mk_empty_map_ (),
append_map_s (map_,passed),
coeff,
den_om,
al)
else
(lambda z$
if z then %TRIANGLE IS FOUND$
(lambda trn$ %TRN - NEW VERTEX $
%IF ALL_DEFINED (CDDR Z,AL) THEN
if t then
select_triangles (
z . triangles,
mk_empty_map_ (),
add_vertex (trn,cddr z),
mk_atlaslist (
conc_map_s (
mk_vertex1_map_ trn,
conc_map_s (passed,delete_map_s (cddr z,map_))
),
coeff,
% TRN . DEN_OM ),
den_om ),
% NIL,
list trn,
al )
else
select_triangles ( z . triangles, %ADD NEW TRIANGLE $
% SELECT_TRIANGLES ( CDDR Z . TRIANGLES, %ADD NEW TRIANGLE$
conc_map_s (mk_vertex1_map_
trn, %ADD NEW VERTEX$
conc_map_s (passed,
delete_map_s(cddr z,
map_)
)
),
mk_empty_map_ (),
try_sub_atlas (
mk_atlas (add_vertex (trn,cddr z),
nil,
list trn),
coeff ),
den_om,
al
)
)
sk_vertextr z
else
select_triangles (triangles,
s_map__rest map_,
add_vertex (s_vertex_first map_,passed),
coeff,
den_om,
al
) )
reduce_triangle
find_triangle (s_vertex_first map_,
s_map__rest map_) $
symbolic procedure vertex_neighbour (vertex,map_)$
%RETURNS A MAP_ OF VERTEX NEIGHBOURS $
if p_empty_vertex vertex
or
p_empty_map_ map_ then mk_empty_map_ ()
else
(lambda z$ %Z - NIL OR A PAIR (EDGE . ADJACENT EDGE )$
if z then
add_vertex (cdr z,
vertex_neighbour (delete_edge (car z,vertex),
delete_vertex (cdr z,map_)))
else
vertex_neighbour (vertex,s_map__rest map_))
is_neighbour (vertex,
s_vertex_first map_)$
symbolic procedure delete_map_s (map_1,map_2)$
if p_empty_map_ map_1 then map_2
else delete_map_s (s_map__rest map_1,
delete_vertex (s_vertex_first map_1,map_2) ) $
symbolic procedure delete_edge (edge,vertex)$
%DELETES EDGE FROM VERTEX $
if p_empty_vertex vertex then mk_empty_vertex ()
else
if equal_edges (edge,first_edge vertex)
then s_vertex_rest vertex
else
add_edge (first_edge vertex,
delete_edge (edge,
s_vertex_rest vertex ) ) $
symbolic procedure is_neighbourp (vertex1,vertex2)$
% ARE VERTEX1 AND VERTEX2 NEIGHBOURS ?
if p_empty_vertex vertex1 then nil % NIL IF NOT NEIGHBOURS$
else
p_member_edge (first_edge vertex1,vertex2)
or
is_neighbourp (s_vertex_rest vertex1,vertex2)$
symbolic procedure is_neighbour (vertex1,vertex2)$
% ARE VERTEX1 AND VERTEX2 NEIGHBOURS ?
% IF THEY ARE THEN RETURN A PAIR: (ADJ.EDGE . VERTEX2)$
if p_empty_vertex vertex1 then nil % NIL IF NOT NEIGHBOURS$
else
(lambda z$
if z then %FIRTS VERTEX IS ADJACENT TO VERTEX2$
first_edge vertex1 . vertex2
else is_neighbour (s_vertex_rest vertex1,
vertex2 ) )
p_member_edge (first_edge vertex1,
vertex2)$
symbolic procedure find_triangle (vertex,map_)$
%FINDS TRIANGLE WICH INCLUDES THE VERTEX.
%RETURNS MAP_ OF THREE VERTICES (TRIANGLE) OR NIL $
(lambda z$ %Z - MAP_ OF VERTICES WICH ARE NEIGHBOURS
% OF VERTEX OR (IF NO NEIGHBOURS) EMPTY MAP_$
if map__length z neq 2 then nil
else add_vertex (vertex,z) )
is_closed vertex_neighbour (vertex,map_)$
symbolic procedure is_closed map_$
if p_empty_map_ map_ or
p_empty_map_ s_map__rest map_ then mk_empty_map_ ()
else
two_neighbour (s_vertex_first map_,
s_map__rest map_)
or
is_closed s_map__rest map_$
symbolic procedure two_neighbour (vertex,map_)$
% HAS VERTEX A NEIGHBOUR IN THE MAP_ ? $
if p_empty_map_ map_ then nil
else
if is_neighbourp (vertex,s_vertex_first map_)
then mk_vertex2_map_ (vertex,s_vertex_first map_)
else two_neighbour (vertex,s_map__rest map_)$
symbolic procedure mk_vertextr map_$
%MAKES VERTEX FROM TRIANGLE MAP_$
if map__length map_ neq 3 then set_error_real ('mk_vertextr ,list(map_))
else
mk_vertextr3 (map_,3)$
symbolic procedure add_edge1(edge,vertex)$ % 14.09.90 RT
if null edge then vertex
else add_edge(edge,vertex)$
symbolic procedure mk_vertextr3 (map_,n)$
if n <= 0 then mk_empty_map_ ()
else
add_edge1 (take_edge (s_vertex_first map_,
s_map__rest map_),
mk_vertextr3 (cycl_map_ map_,n-1)) $
symbolic procedure take_edge (vertex,map_)$
if p_empty_vertex vertex then nil %14.09.90 RT
% SET_ERROR ('TAKE_EDGE ,VERTEX,MAP_) % 14.09.90 RT
else
% IF P_EMPTY_VERTEX S_VERTEX_REST VERTEX THEN FIRST_EDGE VERTEX
% ELSE % 14.09.90 RT
if contain_edge (first_edge vertex,map_)
and
not equal_edges (first_edge vertex,!_0edge )
then take_edge (s_vertex_rest vertex,map_)
else first_edge vertex$
symbolic procedure contain_edge (edge,map_)$
% IS THERE A VERTEX IN THE MAP_ CONTAINING THE EDGE? $
if p_empty_map_ map_ then nil
else
p_member_edge (edge,s_vertex_first map_)
or
contain_edge (edge,s_map__rest map_) $
% ,,,,,,,,,,,,,,,,,,,,,,,,,,,,SORTING AFTER FACTORIZATION ,,,,,,,,,,,$
% 19.05.88 $
symbolic procedure find_bubltr atlas$
if null !*cvitbtr then atlas else
begin
scalar s$
s:=errorset(list('find_bubltr0 ,mkquote atlas),
!*cviterror,
!*backtrace)$
return
if atom s then atlas
else car s
end$
symbolic procedure find_bubltr0 atlas$
%(LAMBDA Z$
% IF CAR Z THEN SORT_ATLAS CDR Z %FACTORIZATION HAPPENED
% ELSE CDR Z)
sort_atlas cdr
find_bubltr1 (atlas,old_edge_list )$
% ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,$
symbolic procedure find_bubltr1 (atlas,al)$
%FINDS BOTH BUBLES AND TRIANGLES IN ATLAS$
begin
scalar s,c,bubles$
s:=find_bubles1 (atlas,al)$
c:=car s$
atlas:=cdr s$
bubles:=append(c,bubles)$
loop:
s:=find_triangles1 (atlas,al)$
c:=car s$
atlas:=cdr s$
bubles:=append(c,bubles)$
if null c then return bubles . atlas$
s:=find_bubles1 (atlas,al)$
c:=car s$
atlas:=cdr s$
bubles:=append(c,bubles)$
if null c then return bubles . atlas$
go loop
end$
symbolic procedure reduce_triangle triangle$
% RETURN (N . VERTEX . TRIANGLE) OR NIL,
% N - NUMBER OF EXTERNAL EDGES$
if null triangle then nil
else
begin
scalar extedges,vertex,n$
%EXTEDGES - LIST OF EXTERNAL EDGES,
% N - NUMBER OF EXTERNAL EDGES,
%VERTEX - NEW VERTEX,MADE FROM TRIANGLE$
vertex:=mk_vertextr triangle$
extedges:=ext_edges vertex$
n:=length extedges$
return
if n = 1 then nil % 14.09.90 RT
else % 14.09.90 RT
n . vertex . triangle
end$
symbolic procedure sk_vertextr z$
% Z IS (N . VERTEX . TRIANGLE) $
if car z = 1 then mk_empty_vertex ()
else
if car z = 3 then cadr z
else set_error_real ('sk_vertextr,list z) $
symbolic procedure ext_edges vertex$
%SELECT EXTERNAL EDGES IN VERTEX $
if p_empty_vertex vertex then nil
else
if p_member_edge (first_edge vertex,s_vertex_rest vertex)
or
equal_edges (first_edge vertex,!_0edge )
then ext_edges delete_edge (first_edge vertex,
s_vertex_rest vertex)
else first_edge vertex .
ext_edges s_vertex_rest vertex $
symbolic procedure ext_edges_map_ map_$
%SELECT EXTERNAL EDGES OF MAP_$
if p_empty_map_ map_ then nil
else
ext_map__ver (ext_edges s_vertex_first map_,
ext_edges_map_ s_map__rest map_)$
symbolic procedure ext_map__ver (vlist,mlist)$
if null vlist then mlist
else
if memq(car vlist,mlist) then
ext_map__ver (cdr vlist,
delete(car vlist,mlist))
else ext_map__ver (cdr vlist,car vlist . mlist)$
symbolic procedure add_tadpoles (bubles,alst)$
if null bubles then alst
else
if caar bubles = 1 then
add_tadpoles (cdr bubles,
cons(cons(car mk_vertextr cadr car bubles,
0),
alst))
else add_tadpoles (cdr bubles,alst)$
%END$ %cvit8.red
%::::::::::::::::::::::: ATLAS SORTING ROUTINES ********************** $
% 13.06.88$
lisp$
global '(!*cvitrace)$
!*cvitrace:=nil$ %IF T THEN TRACE BACTRAKING WHILE ATLAS SORTING$
flag('(cvitrace),'switch)$
symbolic procedure sort_atlas atlas$
%TOP LEVEL PROCEDURE
if null atlas then atlas
else
(lambda z$
if z then z %ATLAS FULLY SORTED
else set_error_real ('sort_atlas ,list atlas))
sort_atlas1 atlas $
symbolic procedure sort_atlas1 atlas$
(lambda z$
if z then z %ATLAS FULLY SORTED
else
if !*cviterror then print_atlas_sort (atlas,nil)
else nil )
atlas_sort (atlas,old_edge_list )$
symbolic procedure print_atlas_sort (atlas,edgelist)$
<< print "Atlas not sorted "$
print_atlas atlas$
if edgelist then
<< print "Defined edges: "$
for each edge in edgelist do print edge >> $
nil >> $
symbolic procedure atlas_sort (atlas,edgelist)$
begin
scalar z,newedges$
newedges:=store_edges new_edge_list$
z:=
errorset(list('atlas_sort1 ,mkquote atlas,mkquote edgelist),
!*cvitrace,
!*backtrace)$
return
if atom z then %ATLAS NOT SORTED
<< restor_edges (newedges,new_edge_list)$ %RESTORE EDGES PARENTS
if !*cvitrace then print_atlas_sort (atlas,edgelist)
else nil >>
else car z
end$
symbolic procedure store_edges edgelist$
for each edge in edgelist collect
(car edge . cdr edge)$
symbolic procedure restor_edges (edgelist,newedgelist)$
if null edgelist then
if newedgelist
then set_error_real ('restor_edges ,list(edgelist,newedgelist))
else nil
else
if null newedgelist then
set_error_real ('restor_edges ,list(edgelist,newedgelist))
else
if s_edge_name car edgelist = s_edge_name car newedgelist then
<< rplacd(car newedgelist,cdar edgelist)$
car newedgelist . restor_edges (cdr edgelist,
cdr newedgelist) >>
else
set_error_real ('restor_edges ,list(edgelist,newedgelist))$
symbolic procedure defined_atlas (atlas,edgelist)$
(lambda edges$
defined_edges (edges,
% DEFINED_APPEND(EDGES,EDGELIST)))
edgelist))
atlas_edges atlas$
symbolic procedure defined_append (edges,edgelist)$
if null edges then edgelist
else if defined_edge (car edges,edgelist) then
car edges . defined_append (cdr edges,edgelist)
else defined_append (cdr edges,edgelist) $
symbolic procedure defined_edges (edges,edgelist)$
if null edges then t
else
if defined_edge (car edges,edgelist)
then
defined_edges (cdr edges,car edges . edgelist)
else definedl_edges (cdr edges,list car edges,edgelist)$
symbolic procedure definedl_edges (edges,passed,edgelist)$
if null edges then null passed
else
if defined_edge (car edges,edgelist) then
defined_edges (nconc(passed,cdr edges),car edges . edgelist)
else definedl_edges (cdr edges,car edges . passed,edgelist)$
symbolic procedure atlas_sort1 (atlas,edgelist)$
if all_defined (s_atlas_map_ atlas,edgelist) then
mk_atlas (s_atlas_map_ atlas,
coeff_sortl( s_atlas_coeff atlas,
nil,
nconc( map__edges s_atlas_map_ atlas,
edgelist)),
s_atlas_den_om atlas)
else coeff_sort (coeff_ordn (s_atlas_coeff atlas,edgelist),
%LSE COEFF_SORT (S_ATLAS_COEFF ATLAS,
mk_atlaslist (s_atlas_map_ atlas,
nil,
s_atlas_den_om atlas),
edgelist)$
symbolic procedure coeff_sortl (atlaslist,passed,edgelist)$
coeff_sortl1 (coeff_ordn (atlaslist,edgelist),passed,edgelist)$
symbolic procedure coeff_sort (atlaslist,passed,edgelist)$
if atlaslist then
(lambda z$ %Z - NIL OR SORDET ATLAS
if z then %FIRST ATLAS ALREADY DEFINED
mk_atlas (s_atlas_map_ z,
coeff_sortl (append(s_atlas_coeff z,
append(cdr atlaslist,passed)),
nil,
nconc(map__edges s_atlas_map_ z,
edgelist)),
s_atlas_den_om z)
else
coeff_sort (cdr atlaslist,
car atlaslist . passed,
edgelist))
atlas_sort (car atlaslist,edgelist)
else coeff_sort_f (passed,nil,edgelist)$
symbolic procedure coeff_sort_f (passed,farewell,edgelist)$
if null passed then
if null farewell then nil
else error(51,nil)
else
if s_atlas_coeff car passed then %NOT EMPTY COEFF
coeff_sort (append(
s_atlas_coeff car passed,
mk_atlas (s_atlas_map_ car passed,
nil,
s_atlas_den_om car passed) .
append(cdr passed,farewell)),
nil,
edgelist)
else coeff_sort_f (cdr passed,
car passed . farewell,
edgelist) $
%.......... 31.05.88 ::::::::::: $
symbolic procedure coeff_ordn (atlaslist,edgelist)$
for each satlas in
coeff_ordn1 (mk_spec_atlaslist (atlaslist,edgelist),nil)
collect cdr satlas$
symbolic procedure mk_spec_atlaslist (atlaslist,edgelist)$
for each atlas in atlaslist collect mk_spec_atlas (atlas,edgelist)$
symbolic procedure mk_spec_atlas (atlas,edgelist)$
%RETURN PAIR (PAIR1 . ATLAS)
%WHERE PAIR1 IS A PAIR - EDGES . PARENTS
%WHERE EDGES - ALL EDGES OF ATLAS
%WHERE PARENTS-THOSE PARENTS OF EDGES WICH NOT CONTAITED IN EDGELIST
(lambda edges$
(edges . diff_edges (edges_parents edges,edgelist)) . atlas)
atlas_edges atlas$
symbolic procedure edges_parents edgelist$
if null edgelist then nil
else
(lambda z$
append(z ,edges_parents cdr edgelist))
edge_new_parents car edgelist$
symbolic procedure edge_new_parents edge$
% SELECT EDGE PARENTS FROM NEW_EDGE_LIST$
if p_old_edge edge then nil else
(lambda names$
edge_new_parent list(car names,cdr names))
s_edge_prop_ edge$
symbolic procedure edge_new_parent namelist$
if null namelist then nil
else
(lambda z$
if z then z . edge_new_parent cdr namelist
else edge_new_parent cdr namelist)
assoc(car namelist,new_edge_list) $
symbolic procedure diff_edges (edgelist1,edgelist2)$
if null edgelist1 then nil
else
if p_member_edge (car edgelist1,edgelist2) then
diff_edges (cdr edgelist1,edgelist2)
else car edgelist1 .
diff_edges (cdr edgelist1,edgelist2)$
symbolic procedure coeff_ordn1 (satlaslist,passed)$
if null satlaslist then passed
else
%IF NULL CAAR SATLASLIST THEN %ATLAS HAS NO UNDEFINED
% COEFF_ORDN1 (CDR SATLASLIST,CAR SATLASLIST . PASSED)
%ELSE
(lambda z$ % Z - NIL OR SATLASLIST
if z then % SUBATLAS FINED AND ADDED$
coeff_ordn1 (z,passed)
else coeff_ordn1 (cdr satlaslist,car satlaslist . passed) )
p_subsatlaslist (car satlaslist,cdr satlaslist,nil)$
symbolic procedure p_subsatlaslist (satlas,satlaslist,passed)$
if null satlaslist then nil
else
if or_subsatlas(satlas,car satlaslist) then
embed_satlases (satlas,car satlaslist) .
nconc(passed,cdr satlaslist)
else p_subsatlaslist (satlas,
cdr satlaslist,
car satlaslist . passed)$
symbolic procedure or_subsatlas (satlas1,satlas2)$
p_subsatlas (satlas1,satlas2)
or
p_subsatlas (satlas2,satlas1) $
symbolic procedure p_subsatlas (satlas1,satlas2)$
p_subedgelist (caar satlas1,caar satlas2)
or
p_inbothlists (cdar satlas1,caar satlas2) $
symbolic procedure p_inbothlists (edgelist1,edgelist2)$
if null edgelist1 then nil
else p_member_edge (car edgelist1,edgelist2)
or
p_inbothlists (cdr edgelist1,edgelist2)$
symbolic procedure p_subedgelist (edgelist1,edgelist2)$
if null edgelist1 then t
else
p_member_edge (car edgelist1,edgelist2)
and
p_subedgelist (cdr edgelist1,edgelist2)$
symbolic procedure embed_satlases (satlas1,satlas2)$
if p_subsatlas (satlas1,satlas2) then embed_satlas (satlas1,satlas2)
else
if p_subsatlas (satlas2,satlas1) then embed_satlas (satlas2,satlas1)
else set_error_real ('embed_satlases,list(satlas1,satlas2)) $
symbolic procedure embed_satlas (satlas1,satlas2)$
car satlas2 . embed_atlas (cdr satlas1,cdr satlas2)$
symbolic procedure embed_atlas (atlas1,atlas2)$
%EMBED ATLAS1 INTO ATLAS2
mk_atlas (s_atlas_map_ atlas2,
atlas1 . s_atlas_coeff atlas2,
s_atlas_den_om atlas2)$
symbolic procedure coeff_sortl1 (atlaslist,passed,edgelist)$
if null atlaslist then
if null passed then nil
else list coeff_sort_f (passed,nil,edgelist)
else
(lambda z$
if z then %ATLAS SORTED
z . coeff_sortl1 (cdr atlaslist,passed,edgelist)
else coeff_sortl1 (cdr atlaslist,car atlaslist . passed,edgelist))
atlas_sort (car atlaslist,edgelist)$
% ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,$
%END$ %cvit82.red
%:*:*:*:*:*:*:*:*:*:*:*:* FACTORIZATION OF MAP_S :*:*:*:*:*:*:*:*:*:$
% 19.05.88 $
lisp$
symbolic procedure renamel_edges edges$
if not equal_edges (car edges,cadr edges) then
rename_edges (car edges ,cadr edges)$
symbolic procedure map__vertex_first map_$
mk_vertex1_map_
s_vertex_first map_$
symbolic procedure both_empty_map_s (map_1,map_2)$
p_empty_map_ map_1
and
p_empty_map_ map_2 $
symbolic procedure has_parents edge$
(lambda z$
car z neq '!? and
cdr z neq '!? )
s_edge_prop_ edge $
symbolic procedure less_edge (edge1,edge2,edgelist)$
% EDGE1 < EDGE2 IFF EDGE1 WAS CREATED EARLIER$
less_edge_name (s_edge_name edge1,
s_edge_name edge2,
edgelist)$
symbolic procedure less_edge_name (name1,name2,edgelist)$
if null edgelist then set_error_real ('less_edge_name ,
list(name1,name2,edgelist))
else
if name1 eq s_edge_name car edgelist then nil
else
if name2 eq s_edge_name car edgelist then t
else less_edge_name (name1,name2,cdr edgelist)$
symbolic procedure rename_edges (edge1,edge2)$
if p_old_edge edge1 then
%IF P_OLD_EDGE EDGE2 THEN OLD_EDGE_LIST
if p_old_edge edge2 then replace_old_edge (edge1,edge2)
else replace_edge (edge2,edge1,new_edge_list )
else
if p_old_edge edge2 then replace_edge (edge1,edge2,
new_edge_list )
else
if has_parents edge1 then
if has_parents edge2 then replace_new_edge (edge1,edge2)
else replace_edge (edge2,edge1,new_edge_list )
else
if has_parents edge2 then
replace_edge (edge1,edge2,new_edge_list )
else replace_new_edge (edge1,edge2)$
symbolic procedure replace_new_edge (edge1,edge2)$
replace_o_edge (edge1,edge2,new_edge_list )$
symbolic procedure replace_old_edge (edge1,edge2)$
% 31.08.90 RT
if is_indexp edge1 then
if is_indexp edge2 then
replace_o_edge (edge1,edge2,old_edge_list )
else replace_edge (edge1,edge2,old_edge_list)
else
if is_indexp edge2 then
replace_edge (edge2,edge1,old_edge_list)
else
replace_o_edge (edge1,edge2,old_edge_list )$
symbolic procedure replace_o_edge (edge1,edge2,edgelist)$
if less_edge (edge1,edge2,edgelist) then
replace_edge (edge2,edge1,edgelist)
else replace_edge (edge1,edge2,edgelist)$
symbolic procedure copy_edge edge$
car edge . cadr edge . caddr edge . nil $
symbolic procedure replace_edge2 (oldedge,newedge)$
<< rplaca(oldedge,car newedge)$
rplacd(oldedge,cdr newedge) >> $
symbolic procedure replace_edge (oldedge,newedge,edgelist)$
replace1_edge (copy_edge oldedge,newedge,edgelist)$
symbolic procedure replace1_edge (oldedge,newedge,edgelist)$
if null edgelist then nil
else
<< if equal_edges (oldedge,car edgelist) then
replace_edge2 (car edgelist,newedge)$
replace1_parents (oldedge,newedge,car edgelist)$
replace1_edge (oldedge,newedge,cdr edgelist) >> $
symbolic procedure replace1_parents (oldedge,newedge,edge)$
replace2_parents (s_edge_name oldedge,
s_edge_name newedge,
s_edge_prop_ edge)$
symbolic procedure replace2_parents (oldname,newname,edgeprop_)$
<< if oldname = car edgeprop_ then rplaca(edgeprop_,newname)$
if oldname = cdr edgeprop_ then rplacd(edgeprop_,newname) >> $
symbolic procedure mk_simple_map_ inmap_$
mk_simple_map_1 (inmap_,mk_empty_map_ (),nil,nil)$
symbolic procedure both_old edges$
p_old_edge car edges
and
p_old_edge cadr edges$
symbolic procedure both_vectors edges$ % 31.08.90 RT
not is_indexp car edges
and
not is_indexp cadr edges$
symbolic procedure old_renamel_edv (vertex,edges)$
% RENAMES EDGES IN VERTEX$
ren_edge (s_edge_name car edges .
s_edge_name cadr edges,vertex)$
symbolic procedure mk1_simple_map_ map_d$
%MAP_D IS A PAIR (MAP_.DEN_OM)$
mk_simple_map_1 (car map_d,mk_empty_map_ (),list cdr map_d,nil)$
symbolic procedure mk_simple_map_1 (inmap_,outmap_,den_om,coeff)$
if p_empty_map_ inmap_ then <<
% FIND_BUBLTR
outmap_ := mk_parents_map_ outmap_;
mk_atlas (outmap_ ,
if null coeff then nil
else for each map_ in coeff
collect mk1_simple_map_ map_,
den_om) >>
else
(lambda edges$
(lambda n$
if p_vertex_prim s_vertex_first inmap_ then
if n=2 then % VERTEX=(A,B)=DELTA(A,B) $
if both_old edges and both_vectors edges then % 31.08.90
mk_simple_map_1 (s_map__rest inmap_,
add_vertex (s_vertex_first inmap_,outmap_),
den_om,
coeff)
else
<< renamel_edges edges$
if both_empty_map_s (s_map__rest inmap_,outmap_) then
mk_simple_map_1 (s_map__rest inmap_,
add_vertex (s_vertex_first inmap_,outmap_),
den_om,
coeff)
else
mk_simple_map_1 (s_map__rest inmap_,
outmap_,
den_om,
coeff )
>>
else
mk_simple_map_1 ( s_map__rest inmap_,
add_vertex ( s_vertex_first inmap_,outmap_),
den_om,
coeff)
else
if n=2 then
if both_old edges and both_vectors edges then %11.09.90 RT
mk_simple_map_1 (add_vertex (mk_edges_vertex edges,
s_map__rest inmap_),
outmap_,
den_om,
(mk_vertex1_map_ (
old_renamel_edv(s_vertex_first inmap_,edges))
. old_renamel_edv(mk_edges_vertex edges,edges))
. coeff )
else
<< renamel_edges edges$
mk_simple_map_1 (s_map__rest inmap_,
outmap_,
den_om,
(map__vertex_first inmap_ . edges) . coeff)
>>
else
if n=3 and
((map__length (inmap_) + map__length (outmap_)) > 2 )
then
(lambda v$
mk_simple_map_1 (add_vertex (v,s_map__rest inmap_),
outmap_,
den_om,
(add_vertex (v,map__vertex_first inmap_) . v)
. coeff))
mk_edges_vertex edges
else
if
(lambda k$
k > 4 and
n < k ) %NOT ALL LINES EXTERNAL $
vertex_length s_vertex_first inmap_
then
(lambda firz$
mk_simple_map_1 (append_map_s (firz,s_map__rest inmap_),
outmap_,
den_om,
coeff) )
(mk_firz_op s_vertex_first inmap_) %26.04.88
else if t then
mk_simple_map_1 (s_map__rest inmap_,
add_vertex (s_vertex_first inmap_,outmap_),
den_om,
coeff)
else
mk_simple_map_1 (append_map_s (mk_simple_vertex
s_vertex_first inmap_,
s_map__rest inmap_),
outmap_,
den_om,
coeff) )
length edges)
(ext_edges s_vertex_first inmap_) $
% ?^?^?^?^?^?^?^?^?^?^?^?^? FIERZ OPTIMIZATION ?^?^?^?^?^?^?^?^?^?^?^?$
% 13.05.88$
global '(!*cvitop)$
flag('(cvitop),'switch)$
symbolic procedure mk_firz_op vertex$
if null !*cvitop then mk_firz vertex
else firz_op vertex$
symbolic procedure firz_op vertex$
mk_firz find_cycle (optimal_edge vertex,
vertex,
mk_empty_vertex ())$
symbolic procedure find_cycle (edge,vertex,passed)$
if equal_edges (edge,first_edge vertex) then
append_vertex (vertex,reversip_vertex passed)
else find_cycle (edge,
s_vertex_rest vertex,
add_edge (first_edge vertex,passed))$
symbolic procedure optimal_edge vertex$
optimal1_edge
internal_edges (vertex,mk_empty_vertex ())$
symbolic procedure internal_edges (vertex1,vertex2)$
if p_empty_vertex vertex1 then vertex2
else
if p_member_edge (first_edge vertex1,s_vertex_rest vertex1)
or
p_member_edge (first_edge vertex1,vertex2)
then internal_edges (s_vertex_rest vertex1,
add_edge (first_edge vertex1,vertex2))
else internal_edges (s_vertex_rest vertex1,vertex2)$
symbolic procedure optimal1_edge vertex$
% VERTEX CONTAINS ONLY PAIRED EDGES
(lambda (l,z)$
opt_edge (z,
edge_distance (z,vertex,l),
s_vertex_rest vertex,
add_edge (z,mk_empty_vertex ()),
l))
(vertex_length vertex,
first_edge vertex)$
symbolic procedure edge_distance (edge,vertex,l)$
% L - FULL VERTEX LENGTH
(lambda n$
min(n,l - n - 2))
edge_dist (edge,s_vertex_rest vertex)$
symbolic procedure edge_dist (edge,vertex)$
if equal_edges (edge,first_edge vertex) then 0
else add1 edge_dist (edge,s_vertex_rest vertex)$
symbolic procedure opt_edge (edge,distance,vertex,passed,n)$
% N - FULL VERTEX LENGTH
if distance = 0 or p_empty_vertex vertex then edge
else
(lambda firstedge$
if p_member_edge (firstedge,passed) then
opt_edge (edge,
distance,
s_vertex_rest vertex,
passed,
n)
else
(lambda dist$
if dist < distance then
opt_edge (firstedge,
dist,
s_vertex_rest vertex,
add_edge (firstedge,passed),
n)
else opt_edge (edge,
distance,
s_vertex_rest vertex,
add_edge (firstedge,passed),
n))
edge_distance (firstedge,vertex,n))
first_edge vertex $
%<?><?><?><?><?><?><?> END OF OPTIMIZATION PART <?><?><?><?><?><?> $
symbolic procedure mk_firz vertex$
% VERTEX=(A1,...,AM,Z,B1,...,BN,Z,C1,...,CK)
% RETURNS UNION MAP_ WHERE
% MAP_ =MAP_1 & MAP_2 WHERE
% MAP_1=((B1,...,BN,X)(Y,C1,...,CK,A1,...,AM)),
% MAP_2=((Z,X,Z,Y)) $
mk_firz1 (vertex,mk_empty_vertex ())$
symbolic procedure mk_firz1 (vertex1,vertex2)$
if p_empty_vertex vertex1 then reversip_vertex vertex2
else
(lambda z$
if z then %FIRST EDGE CONTAINS TWICE$
mk_firz2 (first_edge vertex1,
car z,
append_vertex (cdr z,reversip_vertex vertex2))
else
mk_firz1 (s_vertex_rest vertex1,
add_edge (first_edge vertex1,vertex2) ) )
mp_member_edge (first_edge vertex1,
s_vertex_rest vertex1)$
symbolic procedure mk_firz2 (edge,vertex1,vertex2)$
%RETURNS MAP_ =MAP_1 & MAP_2 ,
%VERTEX1=(B1,...,BN),
%VERTEX2=(C1,...,CK,A1,...,AM) $
(lambda (nedge,nedg1)$
append_map_s (
mk_coeff2 (edge,nedge,nedg1),
mk_vertex2_map_ (conc_vertex (vertex1,mk_edge1_vertex nedge),
add_edge (nedg1,vertex2))
))
(mk_nedge (),
mk_nedge ()) $
symbolic procedure mk_coeff2 (edge,nedge,nedg1)$
mk_vertex1_map_ mk_edge4_vertex (edge,nedge,edge,nedg1)$
symbolic procedure mk_nedge $
(lambda edge$
new_edge (edge,edge))
mk_edge ('!?,'!? . '!?,nil) $
symbolic procedure mp_member_edge (edge,vertex)$
% RETURNS NIL OR PAIR.
% IF VERTEX=(A1,...,AM,EDGE,...,B1,...,BN) THEN
% PAIR= (A1,...,AM) . (B1,...,BM) $
mp_member1_edge (edge,vertex,mk_empty_vertex ())$
symbolic procedure mp_member1_edge (edge,vertex,tail)$
if p_empty_vertex vertex then nil
else
if
equal_edges (edge,first_edge vertex) then
reversip_vertex tail .
s_vertex_rest vertex
else mp_member1_edge (edge,
s_vertex_rest vertex,
add_edge (first_edge vertex,tail) ) $
%END$ %cvit10.red
% ()()()()()()()()()()()()()() PRINTING ATLAS AND MAP_ ROUTINES ()()().
lisp$ %30.01.87$
fluid '(ntab!*)$
symbolic procedure print_atlas atlas$
begin
scalar ntab!*$
ntab!*:=0$
prin2_atlas atlas$
end$
symbolic procedure prin2_atlas atlas$
if null atlas then nil
else
<< print_map_ s_atlas_map_ atlas$
print_den_om s_atlas_den_om atlas$
print_coeff s_atlas_coeff atlas
>> $
symbolic procedure print_map_ map_$
<< pttab ntab!*$
prin2 "Map_ is: ("$
prin2_map_ map_$
prin2 " )"$
terpri() >> $
symbolic procedure prin2_map_ map_$
if p_empty_map_ map_ then nil
else
<< print_vertex s_vertex_first map_$
prin2_map_ s_map__rest map_ >> $
symbolic procedure print_vertex vertex$
<<
prin2 "( "$
prin2_vertex vertex$
prin2 ")" >> $
symbolic procedure prin2_vertex vertex$
if p_empty_vertex vertex then nil
else
<< print_edge first_edge vertex$
prin2_vertex s_vertex_rest vertex >> $
symbolic procedure print_edge edge$
<< prin2_edge edge$
prin2 " " >> $
symbolic procedure prin2_edge edge$
prin2 s_edge_name edge $
symbolic procedure pttab n$
<< spaces n $ % TTAB N$ % 07.06.90
prin2 n$
prin2 ":" >> $
symbolic procedure print_coeff coeff$
<< ntab!*:=ntab!*+1$
prin2_coeff coeff$
ntab!*:=ntab!*-1 >> $
symbolic procedure prin2_coeff atlases$
if null atlases then nil
else << prin2_atlas car atlases$
prin2_coeff cdr atlases >> $
symbolic procedure print_den_om den_list$
<< pttab ntab!*$
prin2 "DEN_OM is: "$
if null den_list then prin2 nil
else prin2_map_ den_list $
terpri() >> $
unfluid '(ntab!*)$
symbolic procedure print_old_edges ()$
print_edge_list old_edge_list $
symbolic procedure print_new_edges ()$
print_edge_list new_edge_list $
symbolic procedure print_edge_list edgelist$
if null edgelist then nil
else << print car edgelist$
print_edge_list cdr edgelist >> $
%END$ %cvit12.red
%---------------------- MAKES PARENTS AFTER FIERZING ----------------$
%24.05.88$
lisp$
symbolic procedure mk_simpl_map_ map_$
mk_simpl_map_1 (map_,mk_empty_map_ ())$
symbolic procedure mk_simpl_map_1 (inmap_,outmap_)$
if p_empty_map_ inmap_ then resto_map__order outmap_
else
if p_vertex_prim s_vertex_first inmap_ then
mk_simpl_map_1 ( s_map__rest inmap_,
add_vertex(mk_parents_prim s_vertex_first inmap_,
outmap_))
else
mk_simpl_map_1 (append_map_s(mk_simple_vertex s_vertex_first inmap_,
s_map__rest inmap_),
outmap_)$
symbolic procedure mk_simple_vertex vertex$
% VERTEX => MAP_ $
begin
scalar nedge,fedge,sedge$
fedge:=first_edge vertex$
sedge:=second_edge vertex$
if not has_parents fedge or not has_parents sedge then
return mk_simple_vertex cycl_vertex vertex$
nedge:=new_edge (fedge,sedge)$
vertex:=s_vertex_rest
s_vertex_rest vertex$
return
mk_vertex2_map_ ( mk_edge3_vertex (nedge,fedge,sedge),
add_edge (nedge,vertex))
end$
symbolic procedure mk_parents_map_ map_$
%MAKES PARENTS FOR ALL EDGES IN MAP_.
%THIS CAN BE DONE BECAUSE NEW EDGES NEVER CREATE CYCLES$
standard_map_
mk_simpl_map_
mk_parents1_map_ (map_,mk_empty_map_ (),mk_empty_map_ ())$
symbolic procedure standard_map_ map_$
if p_empty_map_ map_ then mk_empty_map_ ()
else
if vertex_length s_vertex_first map_ > 2 then
add_vertex (s_vertex_first map_,
standard_map_ s_map__rest map_)
else standard_map_ add_vertex (add_0_edge s_vertex_first map_,
s_map__rest map_)$
symbolic procedure add_0_edge vertex$
%ADDS SPECIAL VERTEX$
add_edge (!_0edge ,vertex)$
symbolic procedure mk_parents1_map_ (inmap_,outmap_,passed)$
if p_empty_map_ inmap_ then
if p_empty_map_ passed then outmap_ %ALL EDGES HAVE PARENTS$
else mk_parents1_map_ (passed,outmap_,mk_empty_map_ ())
else
(lambda edges$
if null edges then %IN FIRST VERTEX ALL EDGES HAVE PARENTS$
mk_parents1_map_ (s_map__rest inmap_,
add_vertex (s_vertex_first inmap_,outmap_),
passed)
else
if single_no_parents edges then %ONLY ONE EDGE IN THE VERTEX$
%HAS NO PARENTS$
mk_parents1_map_ (s_map__rest inmap_,
append_map_s (mk_parents_vertex
s_vertex_first inmap_,
outmap_),
passed)
else
mk_parents1_map_ (s_map__rest inmap_,
outmap_,
add_vertex (s_vertex_first inmap_,passed)))
s_noparents s_vertex_first inmap_ $
symbolic procedure s_noparents vertex$
%SELECTS EDGES WITHOUT PARENTS IN VERTEX$
if p_empty_vertex vertex then nil
else
if has_parents first_edge vertex then
s_noparents s_vertex_rest vertex
else
first_edge vertex .
s_noparents s_vertex_rest vertex$
symbolic procedure mk_parents_vertex vertex$
%MAKES PARENTS FOR THE SINGLE EDGE WITHOUT PARENTS IN VERTEX,
% (VERTEX HAS ONLY ONE EDGE WITHOUT PARENTS ^) $
mk_simpl_map_ mk_vertex1_map_ vertex$
symbolic procedure mk_parents_prim pvertex$
% CREATES PARENTS FOR THE ONLY EDGE WITHOUT PARENTS IN PRIMITIVE
% (THREE EDGES) VERTEX $
if vertex_length pvertex neq 3 then pvertex
else
(lambda edges$
if null edges then pvertex
else
<< mk_edge_parents (pvertex,car edges)$
pvertex >> )
s_noparents pvertex$
symbolic procedure mk_edge_parents (vertex,edge)$
mk_edge1_parents (delete_edge (edge,vertex),edge)$
symbolic procedure mk_edge1_parents (vertex2,edge)$
add_parents (edge,
mk_edge_prop_ (
s_edge_name first_edge vertex2,
s_edge_name second_edge vertex2))$
symbolic procedure add_parents (edge,names)$
add_parents0(edge,names,nil)$
symbolic procedure add_parents0 (edge,names,bool)$
addl_parents (new_edge_list,edge,names . list bool)$
symbolic procedure addl_parents (edgelist,edge,names)$
% NAMES IS A PAIR NAME1 . NAME2 $
if null edgelist then nil
else
(if equal_edges (car edgelist,edge) then
rep_parents (car edgelist,names)
else car edgelist) .
addl_parents (cdr edgelist,edge,names) $
symbolic procedure rep_parents (edge,names)$
<< rplacd(edge,names)$
edge >> $
%END$ %cvit14.red
%EEEEEEEEEEEEEEEEEEEEEEEEE SELECT ALL EDGES %%%%%%%%%%%%%%%%%%%%%%%%% $
% 07.06.88$
lisp$
symbolic procedure atlas_edges atlas$
union_edges (
union_edges (map__edges s_atlas_map_ atlas,
den__edges s_atlas_den_om atlas),
coeff_edges s_atlas_coeff atlas)$
symbolic procedure den__edges den_om$
map__edges den_om$
symbolic procedure coeff_edges atlaslist$
if null atlaslist then nil
else union_edges (atlas_edges car atlaslist,
coeff_edges cdr atlaslist) $
symbolic procedure map__edges map_$
if p_empty_map_ map_ then nil
else union_edges (vertex_edges s_vertex_first map_,
map__edges s_map__rest map_)$
symbolic procedure union_edges (newlist,oldlist)$
if null newlist then oldlist
else union_edges (cdr newlist,
union_edge (car newlist,oldlist))$
symbolic procedure union_edge (edge,edgelist)$
if memq_edgelist (edge,edgelist) then edgelist
else edge . edgelist$
symbolic procedure memq_edgelist (edge,edgelist)$
assoc(s_edge_name edge,
edgelist)$
symbolic procedure exclude_edges (edgelist,exclude)$
% EXCLUDE IS A LIST OF EDGES TO BE EXCLUDED FROM EDGELIST$
if null edgelist then nil
else
if memq_edgelist (car edgelist,exclude) then
exclude_edges (cdr edgelist,exclude)
else car edgelist .
exclude_edges (cdr edgelist,exclude) $
symbolic procedure constr_worlds (atlas,edgelist)$
(lambda edges$
actual_edges_world (
mk_world1 (actual_edges_map_ (edges,
edgelist,
s_atlas_map_ atlas),
constr_coeff (s_atlas_coeff atlas,
union_edges (edges,edgelist)),
s_atlas_den_om atlas
)
) )
union_edges(
den__edges s_atlas_den_om atlas,
map__edges s_atlas_map_ atlas)$
symbolic procedure constr_coeff (atlases,edgelist)$
if null atlases then nil
else
constr_worlds (car atlases,edgelist) .
constr_coeff (cdr atlases,edgelist)$
symbolic procedure actual_edges_map_ (edges,edgelist,map_)$
actedge_map_ (edges,edgelist,list_of_parents(edges,edgelist),nil)
%ACTEDGE_MAP_ (EDGES,EDGELIST,NIL,NIL)
. map_$
symbolic procedure list_of_parents (edges,edgelist)$
if null edges then nil
else append(list_of_parent (car edges,edgelist),
list_of_parents (cdr edges,edgelist))$
symbolic procedure list_of_parent (edge,edgelist)$
if p_old_edge edge or memq_edgelist (edge,edgelist) then nil
%IF EDGE IS DEF. THEN NO NEED IN ITS PARENTS
else
begin$
scalar pr1,pr2,p,s$
p:=s_edge_prop_ edge$
pr1:=assoc(car p,edgelist)$
if pr1 then s:=pr1 . s$
pr2:=assoc(cdr p,edgelist)$
if pr2 then s:=pr2 . s$
%IF NULL PR1 OR NULL PR2 THEN
% SET_ERROR (LIST_OF_PARENTS ,EDGE,EDGELIST)$
return s
end$
symbolic procedure actedge_map_ (edges,edgelist,old,new)$
if null edges then old . new
else
if memq_edgelist (car edges,edgelist) then
actedge_map_ (cdr edges,edgelist,car edges . old,new)
else actedge_map_ (cdr edges,edgelist,old,car edges . new) $
symbolic procedure actual_edges_world world1$
mk_world (actual_world (s_actual_world1 world1,
s_actual_coeff s_coeff_world1 world1),
world1)$
symbolic procedure mk_world1 (edges!-map_,coeff,den_om)$
mk_atlas (map_2_from_map_1 edges!-map_,coeff,den_om)$
symbolic procedure map_2_from_map_1 map_1$
list(map_1_to_strand1 map_1,
list nil,
mark_edges (cdar map_1,
% UNION_EDGES(OLD_EDGE_LIST,CAAR MAP_1),
caar map_1,
cdr map_1))$
symbolic procedure map_1_to_strand1 map_1$
car map_1 .
pre!-calc!-map_ (cdr map_1,
names_edgepair map__edges cdr map_1)$
symbolic procedure names_edgepair edgepair$
%NCONC(FOR EACH EDGE IN CAR EDGEPAIR COLLECT S_EDGE_NAME EDGE,
% FOR EACH EDGE IN CDR EDGEPAIR COLLECT S_EDGE_NAME EDGE)$
for each edge in edgepair collect s_edge_name edge $
symbolic procedure s_actual_world1 world1$
%RETURNS PAIR: OLDEDGES . NEWEDGES $
caar s_atlas_map_ world1$
symbolic procedure actual_world (map_edges,coeffedges)$
%MAP_EDGES IS A PAIR OLD . NEW,
%COEFFEDGES IS LIST OF ACTUAL EDGES OF COEEF.$
union_edges (car map_edges,
exclude_edges (coeffedges,cdr map_edges)) $
symbolic procedure s_actual_coeff worldlist$
if null worldlist then nil
else union_edges (s_edgelist_world car worldlist,
s_actual_coeff cdr worldlist) $
symbolic procedure world_from_atlas atlas$
%TOP LEVEL PROCEDURE$
constr_worlds (atlas,old_edge_list )$
%END$ %cvit16.red
%^^^^^^^^^^^^^^^^^^^^^^^^^^ CALCULATION OF WORLDS ^^^^^^^^^^^^^^^^^^^ $
%26.03.88$
lisp$
symbolic procedure s_world_names world$
for each edge in s_world_edges world
collect s_edge_name edge$
symbolic procedure calc_world (world,alst)$
% ALST LIST OF VALUES OF EXTERNAL EDGES: (... (EDGNAME . NUMBER) ...)$
begin
scalar s,v$
alst:=actual_alst (alst, %SELECT ONLY THOSE
s_world_names world)$ %EDGES WICH ARE IN WORLD
v:=s_world_var world $ %SELECT DATA BASE
s:=assoc(alst,cdr v)$ %CALC. PREVIOSLY?
if s then return cdr s$ %PREV. RESULT$
s:=reval
calc_atlas (s_world_atlas world,alst)$ %REAL CALCULATION
nconc (v,list(alst . s))$ %MODIFY DATA BASE
return s
end$
symbolic procedure actual_alst (alst,namelist)$
if null alst then nil
else
if memq(caar alst,namelist) then
car alst . actual_alst (cdr alst,namelist)
else actual_alst (cdr alst,namelist)$
symbolic procedure calc_atlas (atlas,alst)$
calc_map_2d (s_atlas_map_ atlas,
s_atlas_den_om atlas,
s_atlas_coeff atlas,
alst) $
symbolic procedure calc_coeff (worldlist,alst)$
if null worldlist then list 1
else
(lambda x$
if x=0 then list 0
else x . calc_coeff (cdr worldlist,alst))
calc_world (car worldlist,alst)$
symbolic procedure calc_map_2d (map_2,den_om,coeff,alst)$
coeff_calc (mk_names_map_2 caar map_2 .
cdar map_2 .
cadr map_2 .
den_om ,
coeff,
mk_binding (caddr map_2,alst)) $
symbolic procedure mk_names_map_2 edgespair$
% EDGESPAIR IS PAIR OF LISTS OF EDGES
% EDGELISTOLD . EDGELISTNEW $
for each edge in append(car edgespair,cdr edgespair)
collect s_edge_name edge$
symbolic procedure calc_coeffmap_ (s,coeff,alst)$
(lambda z$
if z = 0 then 0
else 'times . (z . calc_coeff (coeff,alst)))
calc_map_ (s,alst)$
symbolic procedure calc_map_ (mvd,alst)$
begin
scalar map_,v,names,s,den_om,al,d$
names:=car mvd$ %NAMES OF ALL EDGES
map_:=cadr mvd$ %SELECT MAP_
v:=caddr mvd$ %SELECT DATA BASE
den_om:=cdddr mvd$ %SELECT DEN_OMINATOR
al:=actual_alst (alst,names)$ %ACTUAL ALIST
if null al and names then return 0$ %NO VARIANTS OF
%COLOURING
s:=assoc(al,cdr v)$ %PREV.CALCULATED?
if s then s:=cdr s %YES, TAKE IT
else << %ELSE
s:=reval calc_map_tar (map_,al)$ %REAL CALCULATION
nconc(v,list(al . s)) %MODIFY DATA BASE
>> $
d:=calc_den_tar (den_om,alst)$ %CALC. DEN_OMINATOR
return
if d = 1 then s
else list('quotient,s,d) % 09.06.90 RT
end$
%SYMBOLIC PROCEDURE CALC_MAP_TAR (MAP_,BINDING)$
%1$
%SYMBOLIC PROCEDURE CALC_DEN_TAR (DEN_OMINATOR,BINDING)$
%1$
symbolic procedure coeff_calc (s,coeff,binding)$
%S IS EDGENAMES . MAP_ . DATABASE . DEN_OMINATOR $
reval
('plus . coeff1_calc (s,coeff,binding))$
symbolic procedure coeff1_calc (s,coeff,binding)$
if null binding then list 0
else calc_coeffmap_ (s,coeff,car binding) .
coeff1_calc (s,coeff,cdr binding) $
%TOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOPTOP$
symbolic procedure calc_spur0 u$
begin
scalar s$
if null u then return u$
s:=transform_map_ u$
old_edge_list := !_0edge . old_edge_list $
s:=find_bubltr s$
return
calc_world (world_from_atlas s,
for each edge in old_edge_list
collect s_edge_name edge .
car s_edge_prop_ edge )
end$
symbolic procedure calc_spur u$
simp!* calc_spur0 u$ %FOR KRYUKOV NEEDS$
endmodule;
end;