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1 .Dd 2016-12-30
2 .Dt CLAV-MUTATION-FIND 1
3 .Os
4 .Sh NAME
5 .Nm clav-mutation-find
6 .Nd Find a sequence of mutations transforming one quiver to another.
7 .Sh SYNOPSIS
8 .Nm
9 .Fl s
10 .Ar start-file
11 .Fl e
12 .Ar end-file
13 .Oo
14 .Fl R
15 .Oc
16 .Oo
17 .Fl H
18 .Oc
19 .Oo
20 .Fl c
21 .Ar edge-cap
22 .Oc
23 .Oo
24 .Fl l
25 .Ar start-mutation-len
26 .Oc
27 .Oo
28 .Fl m
29 .Ar max-mutation-len
30 .Oc
31 .Oo
32 .Fl f
33 .Ar frozen-vertex
34 .Oo
35 .Fl f
36 .Ar frozen-vertex
37 .Oo ...
38 .Oc
39 .Oc
40 .Oc
41 .Sh DESCRIPTION
42 .Nm
43 loads two quivers from
44 .Ar start-file
45 and
46 .Ar end-file .
47 If they have the same number of vertices,
48 .Nm
49 will attempt to find all sequences of nontrivial mutations which will transform
50 .Ar start-file
51 into
52 .Ar end-file .
53 .Pp
54 Progress is printed
55 .Po although, due to optimizations used, it is not a good estimator of
56 completion time
57 .Pc regularly,
58 and immediate status is available by sending
59 .Ar SIGUSR1
60 to the process
61 .Pq see Sx BUGS .
62 .Pp
63 The search is exhaustive up to interchanging mutations which commute
64 .Po and up to edge-cap, see
65 .Sx BUGS
66 .Pc
67 and single-threaded, though some care has been taken to make it
68 efficient. Some known checks, such as trivial connectedness, are not
69 performed.
70 .Sh OPTIONS
71 .Bl -tag -width Ds
72 .It Fl s
73 The
74 .Ar start-file
75 as written by
76 .Xr clav-sdl 1
77 or
78 .Xr clav-cli 1 .
79 .It Fl e
80 The
81 .Ar end-file
82 as written by
83 .Xr clav-sdl 1
84 or
85 .Xr clav-cli 1 .
86 The vertices of
87 .Ar start-file
88 and
89 .Ar end-file
90 must match.
91 .It Fl c
92 Set the
93 .Ar edge-cap ,
94 as described in
95 .Sx BUGS .
96 If unspecified,
97 .Fa 1 + F
98 is used, where
99 .Fa F
100 is the maximum fatness of a vertex in
101 .Ar start-file .
102 .It Fl R
103 If set, require all non-frozen vertices to participate in the
104 mutation. This is useful for trying to find flips.
105 .It Fl H
106 If set, use a heuristic check (in not ε, not σ) rather than a
107 strict graph equality for checking whether a mutation sequence is
108 acceptable. This is useful for trying to find flips, in which the
109 general shape of the desired end graph is known, but it is not known
110 which labels in the start file correspond to which labels in the
111 end file.
112 .It Fl f
113 Mark a vertex
114 .Pq by name
115 as
116 .Sq frozen .
117 Frozen vertices are not considered for mutation. If you know which
118 vertices are frozen, this can greatly speed up the search.
119 .It Fl l
120 Start searching with mutations at length
121 .Ar start-mutation-length .
122 If unspecified,
123 .Ar 0
124 is used.
125 .It Fl m
126 Set the maximum mutation length. If unspecified, the program will perform
127 a search bounded by
128 .Fa (size_t) -1
129 , which
130 .Pq depending on hardware
131 may take multiple universe-lifespans to complete.
132 .El
133 .Sh EXAMPLES
134 .Dl % clav-mutation-find -s "data/C2_U02_C2.txt" -e "data/μ(C2_U02_C2).txt" -f 01 -f 10 -f 12 -f 21 -f 23 -f 32 -f 30 -f 03 -l 7 -m 9
135 .Dl Exhausted length 7
136 .Dl Exhausted length 8
137 .Dl SEQUENCE: \& \& \& \& 0, ∞, 1, 2, 1*, 1, 2*, 0, 1*
138 .Dl SEQUENCE: \& \& \& \& 0, ∞, 1, 2, 1*, 2*, 0, 1, 1*
139 .Dl Exhausted length 9
140 .Dl \&
141 .Dl % clav-mutation-find -s "data/C2_U02_C2.txt" -e "data/μ(C2_U02_C2).txt" -f 01 -f 10 -f 12 -f 21 -f 23 -f 32 -f 30 -f 03 -l 7 -m 9 -H -R
142 .Dl Exhausted length 7
143 .Dl Exhausted length 8
144 .Dl SEQUENCE: \& \& \& \& 0, ∞, 1, 2, 1*, 1, 2*, 0, 1*
145 .Dl SEQUENCE: \& \& \& \& 0, ∞, 1, 2, 1*, 2*, 0, 1, 1*
146 .Dl SEQUENCE: \& \& \& \& 0, ∞, 2, 0, ∞, 2, 1, 2*, 1*
147 .Dl SEQUENCE: \& \& \& \& 0, ∞, 2*, 0, ∞, 1*, 2*, 2, 1
148 .Dl SEQUENCE: \& \& \& \& 0, ∞, 2*, 0, ∞, 2*, 2, 1, 1*
149 .Dl SEQUENCE: \& \& \& \& ∞, 2, 0, ∞, 2*, 0, 1*, 2*, 1
150 .Dl SEQUENCE: \& \& \& \& ∞, 2, 0, ∞, 2*, 0, 2*, 1, 1*
151 .Dl SEQUENCE: \& \& \& \& ∞, 2, 0, 2*, 0, ∞, 1*, 2*, 1
152 .Dl SEQUENCE: \& \& \& \& ∞, 2, 0, 2*, 0, ∞, 2*, 1, 1*
153 .Dl SEQUENCE: \& \& \& \& ∞, 2*, 0, ∞, 2, 0, 2, 1, 1*
154 .Dl SEQUENCE: \& \& \& \& ∞, 2*, 0, 2, 0, ∞, 2, 1, 1*
155 .Dl SEQUENCE: \& \& \& \& 2, 0, ∞, 2*, 0, ∞, 1*, 2*, 1
156 .Dl SEQUENCE: \& \& \& \& 2, 0, ∞, 2*, 0, ∞, 2*, 1, 1*
157 .Dl SEQUENCE: \& \& \& \& 2, 1, ∞, 0, 2*, 0, 2*, ∞, 1*
158 .Dl SEQUENCE: \& \& \& \& 2, 1, 2*, 0, ∞, 1*, ∞, 1*, 0
159 .Dl SEQUENCE: \& \& \& \& 2*, 0, ∞, 2, 0, ∞, 2, 1, 1*
160 .Dl SEQUENCE: \& \& \& \& 2*, 0, 1*, ∞, 2, 0, ∞, 2, 1
161 .Dl Exhausted length 9
162 .Sh SEE ALSO
163 .Xr clav-sdl 1
164 .Xr clav-cli 1
165 .Sh BUGS
166 In general, mutations in quivers may cause edge weights εᵢⱼ to become
167 arbitrarily high. In general, mutations which cause edge weights to become
168 large are not interesting, therefore a rather naive implementation of
169 rational numbers is used for quiver edges. In order to protect this
170 implementation from overflow errors
171 .Po and to prevent the search from wasting time in uninteresting
172 implementations
173 .Pc
174 the finder will prune a sequence of mutations if it yields an edge with
175 any |εᵢⱼ| higher than
176 .Ar edge-cap .
177 .Pp
178 Sending
179 .Ar SIGUSR1
180 to
181 .Nm
182 will cause the current status to be printed. For portability concerns,
183 even if your system supports
184 .Ar SIGINFO ,
185 that signal will not cause the same effect. Patches welcome.
186 .Sh AUTHORS
187 .An S. Gilles Aq Mt sgilles@math.umd.edu