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‎test/test_combinatorica.py‎

Lines changed: 120 additions & 94 deletions
Original file line numberDiff line numberDiff line change
@@ -7,41 +7,32 @@
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from mathics.core.evaluation import Evaluation
88
import pytest
99

10-
11-
def test_combinatorica():
12-
session.evaluate(
13-
"""
14-
Needs["DiscreteMath`CombinatoricaV0.9`"]
10+
session.evaluate(
11+
"""
12+
Needs["DiscreteMath`CombinatoricaV0.9`"]
1513
"""
16-
)
14+
)
1715

18-
# A number of examples from Implementing Discrete Mathematics by
19-
# Steven Skiena and
20-
# A number of examples from Computation Discrete Mathematics by
21-
# Sriram Pemmaraju and Steven Skiena.
16+
# A number of examples from Implementing Discrete Mathematics by
17+
# Steven Skiena and
18+
# A number of examples from Computation Discrete Mathematics by
19+
# Sriram Pemmaraju and Steven Skiena.
2220

23-
# Page numbers below come from the first book
21+
# Page numbers below come from the first book
2422

2523

26-
# Permutation[3] doesn't work
27-
permutations3 = (
28-
r"{{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}"
29-
)
24+
def test_combinatorica_permutations_1_1():
25+
3026
for str_expr, str_expected, message in (
3127
(
3228
"Permute[{a, b, c, d}, Range[4]]",
3329
"{a, b, c, d}",
34-
"Permute list with simple list",
30+
"Permute list with simple list; 1.1 Page 3",
3531
),
3632
(
3733
"Permute[{a, b, c, d}, {1,2,2,4}]",
3834
"Permute[{a, b, c, d}, {1,2,2,4}]",
39-
"Incorrect permute: index 2 duplicated",
40-
),
41-
(
42-
"Permute[{A, B, C, D}, %s]" % permutations3,
43-
"{{A, B, C}, {A, C, B}, {B, A, C}, {B, C, A}, {C, A, B}, {C, B, A}}",
44-
"Permute",
35+
"Incorrect permute: index 2 duplicated; 1.1 Page 3",
4536
),
4637
(
4738
"LexicographicPermutations[{a,b,c,d}]",
@@ -53,74 +44,143 @@ def test_combinatorica():
5344
"{c, b, d, a}, {c, d, a, b}, {c, d, b, a}, "
5445
"{d, a, b, c}, {d, a, c, b}, {d, b, a, c}, "
5546
"{d, b, c, a}, {d, c, a, b}, {d, c, b, a}}",
56-
"LexicographicPermuations, Page 4"
47+
"LexicographicPermuations, 1.1.1 Page 4",
48+
),
49+
# NthPermutation does not work
50+
(
51+
"Map[RankPermutation, Permutations[Range[4]]]",
52+
"Range[0, 23]",
53+
"Permutations uses lexographic order; 1.1.2, Page 6",
5754
),
58-
59-
("Map[RankPermutation, Permutations[Range[4]]]",
60-
"Range[0, 23]",
61-
"Permutations uses lexographic order"
62-
),
63-
64-
("RandomPermutation1[20] === RandomPermutation2[20]",
65-
"False",
66-
"Not likey two of 20! permutations will be the same (different routines), Page 7"
67-
),
68-
("RandomPermutation1[20] === RandomPermutation1[20]",
69-
"False",
70-
"Not likley two of 20! permutations will be the same (same routine)"
71-
),
72-
("RankPermutation[{8, 9, 7, 1, 6, 4, 5, 3, 2}]", "321953", "RankPermutation"),
7355
(
74-
"Permute[{5,2,4,3,1}, InversePermutation[{5,2,4,3,1}]]",
75-
"{1, 2, 3, 4, 5}",
76-
"InversePermute",
56+
"RandomPermutation1[20] === RandomPermutation2[20]",
57+
"False",
58+
"Not likey two of the 20! permutations will be the same, 1.1.3, Page 7",
59+
),
60+
(
61+
"RandomPermutation1[20] === RandomPermutation1[20]",
62+
"False",
63+
"Not likley two of 20! permutations will be the same (same routine)",
7764
),
7865
(
7966
"MinimumChangePermutations[{a,b,c}]",
8067
"{{a, b, c}, {b, a, c}, {c, a, b}, {a, c, b}, {b, c, a}, {c, b, a}}",
81-
"MinimumChangePermuations, Page 11",
68+
"MinimumChangePermuations; 1.1.4, Page 11",
8269
),
8370
(
8471
"Union[Permutations[{a,a,a,a,a}]]",
8572
"{{a, a, a, a, a}}",
86-
"simple but wasteful Permutation duplication elimination, Page 12"
73+
"simple but wasteful Permutation duplication elimination, 1.1.5, Page 12",
8774
),
8875
(
8976
"DistinctPermutations[{1,1,2,2}]",
9077
"{{1, 1, 2, 2}, {1, 2, 1, 2}, {1, 2, 2, 1}, "
9178
"{2, 1, 1, 2}, {2, 1, 2, 1}, {2, 2, 1, 1}}",
92-
"DisctinctPermutations of multiset Binomial[6,3] permutations, Page 14"
79+
"DisctinctPermutations of multiset Binomial[6,3] permutations, 1.1.5, Page 14",
9380
),
81+
("Multinomial[3,3]", "20", "The built-in function Multinomial, Page 14"),
9482
(
95-
"Multinomial[3,3]",
83+
"DistinctPermutations[{A,B,C}]",
84+
"{{A, B, C}, {A, C, B}, {B, A, C}, {B, C, A}, {C, A, B}, {C, B, A}}",
85+
"DisctinctPermutations all n! permutations, Page 14",
86+
),
87+
(
88+
"BinarySearch[Table[2i,{i, 30}],40]",
9689
"20",
97-
"The built-in function Multinomial, Page 14"
90+
"BinarySearch: 40 is one of the first 30 even numbers; 1.1.6, Page 16",
9891
),
9992
(
100-
"DistinctPermutations[{A,B,C}]",
101-
"{{A, B, C}, {A, C, B}, {B, A, C}, {B, C, A}, {C, A, B}, {C, B, A}}",
102-
"DisctinctPermutations all n! permutations, Page 14"
93+
"BinarySearch[Table[2i,{i, 30}],41]",
94+
"41/2",
95+
"BinarySearch: BinarySearch: 41 is not even; 1.1.6, Page 16",
10396
),
10497
(
10598
"Sort[ Subsets [Range[4]],(Apply[Plus, #1]<=Apply[Plus,#2])& ]",
10699
"{{}, {1}, {2}, {3}, {1, 2}, {4}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, "
107100
"{1, 2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}",
108-
"Sort to total order subsets, Page 15"
101+
"Sort to total order subsets, Page 15",
109102
),
110103
(
111-
"Subsets[Range[3]]",
112-
"{{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}",
113-
"Subsets",
104+
"InversePermutation[{4,8,5,2,1,3,7,6}]",
105+
"{5, 4, 6, 1, 3, 8, 7, 2}",
106+
"InversePermutation: 7 is fixed point. Page 18",
114107
),
115108
(
116-
"BinarySearch[Table[2i,{i, 30}],40]",
117-
"20",
118-
"BinarySearch: 40 is one of the first 30 even numbers, Page 16"
109+
"star = Automorphisms[Star[5]]",
110+
"{{1, 2, 3, 4, 5}, {1, 2, 4, 3, 5}, {1, 3, 2, 4, 5}, {1, 3, 4, 2, 5}, "
111+
"{1, 4, 2, 3, 5}, {1, 4, 3, 2, 5}, {2, 1, 3, 4, 5}, {2, 1, 4, 3, 5}, "
112+
"{2, 3, 1, 4, 5}, {2, 3, 4, 1, 5}, {2, 4, 1, 3, 5}, {2, 4, 3, 1, 5}, "
113+
"{3, 1, 2, 4, 5}, {3, 1, 4, 2, 5}, {3, 2, 1, 4, 5}, {3, 2, 4, 1, 5}, "
114+
"{3, 4, 1, 2, 5}, {3, 4, 2, 1, 5}, {4, 1, 2, 3, 5}, {4, 1, 3, 2, 5}, "
115+
"{4, 2, 1, 3, 5}, {4, 2, 3, 1, 5}, {4, 3, 1, 2, 5}, {4, 3, 2, 1, 5}}",
116+
"Automorphisms, Page 19",
119117
),
118+
):
119+
check_evaluation(str_expr, str_expected, message)
120+
121+
122+
def test_combinatorica_permutations_1_2():
123+
124+
for str_expr, str_expected, message in (
120125
(
121-
"BinarySearch[Table[2i,{i, 30}],41]",
122-
"41/2",
123-
"BinarySearch: BinarySearch: 41 is not even"
126+
"MultiplicationTable[Permutations[Range[3]], Permute ]",
127+
"{{1, 2, 3, 4, 5, 6}, "
128+
"{2, 1, 5, 6, 3, 4}, "
129+
"{3, 4, 1, 2, 6, 5}, "
130+
"{4, 3, 6, 5, 1, 2}, "
131+
"{5, 6, 2, 1, 4, 3}, "
132+
"{6, 5, 4, 3, 2, 1}}",
133+
"Symmetric group S_n. S_n is not commutative. 1.2 Page 17"
134+
),
135+
(
136+
"InversePermutation[{4,8,5,2,1,3,7,6}]",
137+
"{5, 4, 6, 1, 3, 8, 7, 2}",
138+
"InversePermutation: 7 is fixed point. 1.2 Page 18",
139+
),
140+
(
141+
"star = Automorphisms[Star[5]]",
142+
"{{1, 2, 3, 4, 5}, {1, 2, 4, 3, 5}, {1, 3, 2, 4, 5}, {1, 3, 4, 2, 5}, "
143+
"{1, 4, 2, 3, 5}, {1, 4, 3, 2, 5}, {2, 1, 3, 4, 5}, {2, 1, 4, 3, 5}, "
144+
"{2, 3, 1, 4, 5}, {2, 3, 4, 1, 5}, {2, 4, 1, 3, 5}, {2, 4, 3, 1, 5}, "
145+
"{3, 1, 2, 4, 5}, {3, 1, 4, 2, 5}, {3, 2, 1, 4, 5}, {3, 2, 4, 1, 5}, "
146+
"{3, 4, 1, 2, 5}, {3, 4, 2, 1, 5}, {4, 1, 2, 3, 5}, {4, 1, 3, 2, 5}, "
147+
"{4, 2, 1, 3, 5}, {4, 2, 3, 1, 5}, {4, 3, 1, 2, 5}, {4, 3, 2, 1, 5}}",
148+
"Automorphisms, 1.2.3 Page 19",
149+
),
150+
(
151+
"relation = SamenessRelation[star]",
152+
"{{1, 1, 1, 1, 0}, "
153+
"{1, 1, 1, 1, 0}, "
154+
"{1, 1, 1, 1, 0}, "
155+
"{1, 1, 1, 1, 0}, "
156+
"{0, 0, 0, 0, 1}}",
157+
"Sameness, 1.2.3 Page 19",
158+
),
159+
# (
160+
# "PermutationGroupQ[Range[4], {4, 2, 3, 1}]",
161+
# "True",
162+
# "PermutationGroupQ, 1.2.3 Page 20",
163+
# ),
164+
):
165+
check_evaluation(str_expr, str_expected, message)
166+
167+
168+
def test_combinatorica_rest():
169+
170+
# Permutation[3] doesn't work
171+
permutations3 = (
172+
r"{{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}"
173+
)
174+
for str_expr, str_expected, message in (
175+
(
176+
"Permute[{A, B, C, D}, %s]" % permutations3,
177+
"{{A, B, C}, {A, C, B}, {B, A, C}, {B, C, A}, {C, A, B}, {C, B, A}}",
178+
"Permute",
179+
),
180+
(
181+
"Subsets[Range[3]]",
182+
"{{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}",
183+
"Subsets",
124184
),
125185
(
126186
"BinarySearch[{2, 3, 9}, 7] // N",
@@ -153,45 +213,11 @@ def test_combinatorica():
153213
"2",
154214
"BinarySearch - find where key is a list",
155215
),
156-
# (
157-
# "TableForm[ MultiplicationTable[Permutations[Range[3]], Permute ] ]",
158-
# "1 2 3 4 5 6\n"
159-
# "2 1 5 6 3 4\n"
160-
# "3 4 1 2 6 5\n"
161-
# "4 3 6 5 1 2\n"
162-
# "5 6 2 1 4 3\n"
163-
# "6 5 4 3 2 1\n",
164-
# "Symmetric group S_n. S_n is not commutative. Page 17"
165-
# ),
166216
(
167217
"InversePermutation[{4,8,5,2,1,3,7,6}]",
168218
"{5, 4, 6, 1, 3, 8, 7, 2}",
169219
"InversePermutation: 7 is fixed point. Page 18",
170220
),
171-
(
172-
"star = Automorphisms[Star[5]]",
173-
"{{1, 2, 3, 4, 5}, {1, 2, 4, 3, 5}, {1, 3, 2, 4, 5}, {1, 3, 4, 2, 5}, "
174-
"{1, 4, 2, 3, 5}, {1, 4, 3, 2, 5}, {2, 1, 3, 4, 5}, {2, 1, 4, 3, 5}, "
175-
"{2, 3, 1, 4, 5}, {2, 3, 4, 1, 5}, {2, 4, 1, 3, 5}, {2, 4, 3, 1, 5}, "
176-
"{3, 1, 2, 4, 5}, {3, 1, 4, 2, 5}, {3, 2, 1, 4, 5}, {3, 2, 4, 1, 5}, "
177-
"{3, 4, 1, 2, 5}, {3, 4, 2, 1, 5}, {4, 1, 2, 3, 5}, {4, 1, 3, 2, 5}, "
178-
"{4, 2, 1, 3, 5}, {4, 2, 3, 1, 5}, {4, 3, 1, 2, 5}, {4, 3, 2, 1, 5}}",
179-
"Automorphisms, Page 19"
180-
),
181-
(
182-
"KSubsets[Range[5], 3]",
183-
"{{1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}, {1, 4, 5}, "
184-
"{2, 3, 4}, {2, 3, 5}, {2, 4, 5}, {3, 4, 5}}",
185-
"Ksubsets",
186-
),
187-
(
188-
"Compositions[5,3]",
189-
"{{0, 0, 5}, {0, 1, 4}, {0, 2, 3}, {0, 3, 2}, {0, 4, 1}, {0, 5, 0}, "
190-
"{1, 0, 4}, {1, 1, 3}, {1, 2, 2}, {1, 3, 1}, {1, 4, 0}, {2, 0, 3}, "
191-
"{2, 1, 2}, {2, 2, 1}, {2, 3, 0}, {3, 0, 2}, {3, 1, 1}, {3, 2, 0}, "
192-
"{4, 0, 1}, {4, 1, 0}, {5, 0, 0}}",
193-
"Compositions",
194-
),
195221
# (
196222
# "SetPartitions[3]",
197223
# "{{{1, 2, 3}}, {{1}, {2, 3}}, {{1, 2}, {3}}, {{1, 3}, {2}}, {{1}, {2}, {3}}}",
@@ -200,7 +226,7 @@ def test_combinatorica():
200226
(
201227
"TransposePartition[{8, 6, 4, 4, 3, 1}]",
202228
"{6, 5, 5, 4, 2, 2, 1, 1}",
203-
"TransposePartition"
229+
"TransposePartition",
204230
),
205231
):
206232
check_evaluation(str_expr, str_expected, message)

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