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Graphs in maxima
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anyp(pred, seq) := lreduce(lambda([P, x], P or pred(x)), seq, false); | |
allp(pred, seq) := lreduce(lambda([P, x], P and pred(x)), seq, true); | |
walklength(seq) := (length(seq)-1)/2; | |
walkverts(seq) := makelist(seq[2*i-1], i, 1, walklength(seq)+1); | |
walkedges(seq) := makelist(seq[2*i], i, 1, walklength(seq)); | |
closedp(seq) := is(first(seq) = last(seq)); | |
vertexset(G) := first(G); | |
edgeset(G) := second(G); | |
incidentset(G) := third(G); | |
incidents(G, e) := assoc(e, incidentset(G), []); | |
vertexp(G, v) := member(v, vertexset(G)); | |
edgep(G, e) := member(e, edgeset(G)); | |
incidentp(G, e, v) := member(v, incidents(G, e)); | |
edgejoinsp(G, e, u, v) := | |
if is(u = v) then | |
(is(incidents(G, e) = [u, u]) or is(incidents(G, e) = {u})) | |
else | |
(incidentp(G, e, u) and incidentp(G, e, v)); | |
walkp(G, seq) := | |
if (is(length(seq) = 0) or not(vertexp(G, first(seq)))) then | |
false | |
else if is(length(seq) = 1) then | |
true | |
else | |
(length(seq) > 2 | |
and edgejoinsp(G, second(seq), first(seq), third(seq)) | |
and walkp(G, rest(seq, 2))); | |
pathp(G, seq) := | |
(walkp(G, seq)) and | |
block([vs], vs: walkverts(seq), | |
is(length(vs) = length(setify(vs)))); | |
cyclep(G, seq) := | |
closedp(seq) and | |
walkp(G, seq) and | |
(is(length(seq) = 1) or pathp(G, rest(seq, 2))) and | |
block([vs], es: walkedges(seq), | |
is(length(es) = length(setify(es)))); | |
forestp(G, edges) := | |
if is(length(edges) = 0) then | |
true | |
else if anyp(lambda([e], not(edgep(G, e))), edges) then | |
false | |
else block([verts, isforest], | |
verts: [], | |
isforest: true, | |
for e in edges do | |
if allp(lambda([v], member(v, verts)), listify(incidents(G, e))) then | |
(isforest: false) or return | |
else | |
verts: append(verts, listify(incidents(G, e))), | |
return(isforest) | |
); | |
spanningtreep(G, edges) := | |
is(length(edges) = length(vertexset(G)) - 1) and forestp(G, edges); | |
cyclelengthp(G, n, seq) := cyclep(G, seq) and is(walklength(seq) = n); | |
VV: {u,v,w,x}; | |
EE: [a,b,c,d,e,f,g]; | |
AA: [a={u,v}, b={v,w}, c={w,x}, d={w,x}, e={u,w}, f={u,x}, g={x,x}]; | |
GG: [VV, EE, AA]; | |
walkp(GG, [u, a, v, b, w, d, x, g, x, c, w]); | |
pathp(GG, [u, f, x, d, w]); | |
cyclep(GG, [u, f, x, d, w, e, u]); | |
walklength([u, f, x, d, w, e, u]); | |
walkp(GG, [u, a, x]); | |
spanningtreep(GG, [a, b, f]); | |
cyclelengthp(GG, 4, [u, f, x, d, w, e, u]); | |
cyclep(GG, [x,d,w,d,x]); |
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