Coverage for /usr/lib/python3/dist-packages/sympy/assumptions/ask_generated.py: 78%

1""" 

2Do NOT manually edit this file. 

3Instead, run ./bin/ask_update.py. 

4""" 

5 

6from sympy.assumptions.ask import Q 

7from sympy.assumptions.cnf import Literal 

8from sympy.core.cache import cacheit 

9 

10@cacheit 

11def get_all_known_facts(): 

12 """ 

13 Known facts between unary predicates as CNF clauses. 

14 """ 

15 return { 

16 frozenset((Literal(Q.algebraic, False), Literal(Q.imaginary, True), Literal(Q.transcendental, False))), 

17 frozenset((Literal(Q.algebraic, False), Literal(Q.negative, True), Literal(Q.transcendental, False))), 

18 frozenset((Literal(Q.algebraic, False), Literal(Q.positive, True), Literal(Q.transcendental, False))), 

19 frozenset((Literal(Q.algebraic, False), Literal(Q.rational, True))), 

20 frozenset((Literal(Q.algebraic, False), Literal(Q.transcendental, False), Literal(Q.zero, True))), 

21 frozenset((Literal(Q.algebraic, True), Literal(Q.finite, False))), 

22 frozenset((Literal(Q.algebraic, True), Literal(Q.transcendental, True))), 

23 frozenset((Literal(Q.antihermitian, False), Literal(Q.hermitian, False), Literal(Q.zero, True))), 

24 frozenset((Literal(Q.antihermitian, False), Literal(Q.imaginary, True))), 

25 frozenset((Literal(Q.commutative, False), Literal(Q.finite, True))), 

26 frozenset((Literal(Q.commutative, False), Literal(Q.infinite, True))), 

27 frozenset((Literal(Q.complex_elements, False), Literal(Q.real_elements, True))), 

28 frozenset((Literal(Q.composite, False), Literal(Q.even, True), Literal(Q.positive, True), Literal(Q.prime, False))), 

29 frozenset((Literal(Q.composite, True), Literal(Q.even, False), Literal(Q.odd, False))), 

30 frozenset((Literal(Q.composite, True), Literal(Q.positive, False))), 

31 frozenset((Literal(Q.composite, True), Literal(Q.prime, True))), 

32 frozenset((Literal(Q.diagonal, False), Literal(Q.lower_triangular, True), Literal(Q.upper_triangular, True))), 

33 frozenset((Literal(Q.diagonal, True), Literal(Q.lower_triangular, False))), 

34 frozenset((Literal(Q.diagonal, True), Literal(Q.normal, False))), 

35 frozenset((Literal(Q.diagonal, True), Literal(Q.symmetric, False))), 

36 frozenset((Literal(Q.diagonal, True), Literal(Q.upper_triangular, False))), 

37 frozenset((Literal(Q.even, False), Literal(Q.odd, False), Literal(Q.prime, True))), 

38 frozenset((Literal(Q.even, False), Literal(Q.zero, True))), 

39 frozenset((Literal(Q.even, True), Literal(Q.odd, True))), 

40 frozenset((Literal(Q.even, True), Literal(Q.rational, False))), 

41 frozenset((Literal(Q.finite, False), Literal(Q.transcendental, True))), 

42 frozenset((Literal(Q.finite, True), Literal(Q.infinite, True))), 

43 frozenset((Literal(Q.fullrank, False), Literal(Q.invertible, True))), 

44 frozenset((Literal(Q.fullrank, True), Literal(Q.invertible, False), Literal(Q.square, True))), 

45 frozenset((Literal(Q.hermitian, False), Literal(Q.negative, True))), 

46 frozenset((Literal(Q.hermitian, False), Literal(Q.positive, True))), 

47 frozenset((Literal(Q.hermitian, False), Literal(Q.zero, True))), 

48 frozenset((Literal(Q.imaginary, True), Literal(Q.negative, True))), 

49 frozenset((Literal(Q.imaginary, True), Literal(Q.positive, True))), 

50 frozenset((Literal(Q.imaginary, True), Literal(Q.zero, True))), 

51 frozenset((Literal(Q.infinite, False), Literal(Q.negative_infinite, True))), 

52 frozenset((Literal(Q.infinite, False), Literal(Q.positive_infinite, True))), 

53 frozenset((Literal(Q.integer_elements, True), Literal(Q.real_elements, False))), 

54 frozenset((Literal(Q.invertible, False), Literal(Q.positive_definite, True))), 

55 frozenset((Literal(Q.invertible, False), Literal(Q.singular, False))), 

56 frozenset((Literal(Q.invertible, False), Literal(Q.unitary, True))), 

57 frozenset((Literal(Q.invertible, True), Literal(Q.singular, True))), 

58 frozenset((Literal(Q.invertible, True), Literal(Q.square, False))), 

59 frozenset((Literal(Q.irrational, False), Literal(Q.negative, True), Literal(Q.rational, False))), 

60 frozenset((Literal(Q.irrational, False), Literal(Q.positive, True), Literal(Q.rational, False))), 

61 frozenset((Literal(Q.irrational, False), Literal(Q.rational, False), Literal(Q.zero, True))), 

62 frozenset((Literal(Q.irrational, True), Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.zero, False))), 

63 frozenset((Literal(Q.irrational, True), Literal(Q.rational, True))), 

64 frozenset((Literal(Q.lower_triangular, False), Literal(Q.triangular, True), Literal(Q.upper_triangular, False))), 

65 frozenset((Literal(Q.lower_triangular, True), Literal(Q.triangular, False))), 

66 frozenset((Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.rational, True), Literal(Q.zero, False))), 

67 frozenset((Literal(Q.negative, True), Literal(Q.negative_infinite, True))), 

68 frozenset((Literal(Q.negative, True), Literal(Q.positive, True))), 

69 frozenset((Literal(Q.negative, True), Literal(Q.positive_infinite, True))), 

70 frozenset((Literal(Q.negative, True), Literal(Q.zero, True))), 

71 frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive, True))), 

72 frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive_infinite, True))), 

73 frozenset((Literal(Q.negative_infinite, True), Literal(Q.zero, True))), 

74 frozenset((Literal(Q.normal, False), Literal(Q.unitary, True))), 

75 frozenset((Literal(Q.normal, True), Literal(Q.square, False))), 

76 frozenset((Literal(Q.odd, True), Literal(Q.rational, False))), 

77 frozenset((Literal(Q.orthogonal, False), Literal(Q.real_elements, True), Literal(Q.unitary, True))), 

78 frozenset((Literal(Q.orthogonal, True), Literal(Q.positive_definite, False))), 

79 frozenset((Literal(Q.orthogonal, True), Literal(Q.unitary, False))), 

80 frozenset((Literal(Q.positive, False), Literal(Q.prime, True))), 

81 frozenset((Literal(Q.positive, True), Literal(Q.positive_infinite, True))), 

82 frozenset((Literal(Q.positive, True), Literal(Q.zero, True))), 

83 frozenset((Literal(Q.positive_infinite, True), Literal(Q.zero, True))), 

84 frozenset((Literal(Q.square, False), Literal(Q.symmetric, True))), 

85 frozenset((Literal(Q.triangular, False), Literal(Q.unit_triangular, True))), 

86 frozenset((Literal(Q.triangular, False), Literal(Q.upper_triangular, True))) 

87 } 

88 

89@cacheit 

90def get_known_facts_dict(): 

91 """ 

92 Logical relations between unary predicates as dictionary. 

93 

94 Each key is a predicate, and item is two groups of predicates. 

95 First group contains the predicates which are implied by the key, and 

96 second group contains the predicates which are rejected by the key. 

97 

98 """ 

99 return { 

100 Q.algebraic: (set([Q.algebraic, Q.commutative, Q.complex, Q.finite]), 

101 set([Q.infinite, Q.negative_infinite, Q.positive_infinite, 

102 Q.transcendental])), 

103 Q.antihermitian: (set([Q.antihermitian]), set([])), 

104 Q.commutative: (set([Q.commutative]), set([])), 

105 Q.complex: (set([Q.commutative, Q.complex, Q.finite]), 

106 set([Q.infinite, Q.negative_infinite, Q.positive_infinite])), 

107 Q.complex_elements: (set([Q.complex_elements]), set([])), 

108 Q.composite: (set([Q.algebraic, Q.commutative, Q.complex, Q.composite, 

109 Q.extended_nonnegative, Q.extended_nonzero, 

110 Q.extended_positive, Q.extended_real, Q.finite, Q.hermitian, 

111 Q.integer, Q.nonnegative, Q.nonzero, Q.positive, Q.rational, 

112 Q.real]), set([Q.extended_negative, Q.extended_nonpositive, 

113 Q.imaginary, Q.infinite, Q.irrational, Q.negative, 

114 Q.negative_infinite, Q.nonpositive, Q.positive_infinite, 

115 Q.prime, Q.transcendental, Q.zero])), 

116 Q.diagonal: (set([Q.diagonal, Q.lower_triangular, Q.normal, Q.square, 

117 Q.symmetric, Q.triangular, Q.upper_triangular]), set([])), 

118 Q.even: (set([Q.algebraic, Q.commutative, Q.complex, Q.even, 

119 Q.extended_real, Q.finite, Q.hermitian, Q.integer, Q.rational, 

120 Q.real]), set([Q.imaginary, Q.infinite, Q.irrational, 

121 Q.negative_infinite, Q.odd, Q.positive_infinite, 

122 Q.transcendental])), 

123 Q.extended_negative: (set([Q.commutative, Q.extended_negative, 

124 Q.extended_nonpositive, Q.extended_nonzero, Q.extended_real]), 

125 set([Q.composite, Q.extended_nonnegative, Q.extended_positive, 

126 Q.imaginary, Q.nonnegative, Q.positive, Q.positive_infinite, 

127 Q.prime, Q.zero])), 

128 Q.extended_nonnegative: (set([Q.commutative, Q.extended_nonnegative, 

129 Q.extended_real]), set([Q.extended_negative, Q.imaginary, 

130 Q.negative, Q.negative_infinite])), 

131 Q.extended_nonpositive: (set([Q.commutative, Q.extended_nonpositive, 

132 Q.extended_real]), set([Q.composite, Q.extended_positive, 

133 Q.imaginary, Q.positive, Q.positive_infinite, Q.prime])), 

134 Q.extended_nonzero: (set([Q.commutative, Q.extended_nonzero, 

135 Q.extended_real]), set([Q.imaginary, Q.zero])), 

136 Q.extended_positive: (set([Q.commutative, Q.extended_nonnegative, 

137 Q.extended_nonzero, Q.extended_positive, Q.extended_real]), 

138 set([Q.extended_negative, Q.extended_nonpositive, Q.imaginary, 

139 Q.negative, Q.negative_infinite, Q.nonpositive, Q.zero])), 

140 Q.extended_real: (set([Q.commutative, Q.extended_real]), 

141 set([Q.imaginary])), 

142 Q.finite: (set([Q.commutative, Q.finite]), set([Q.infinite, 

143 Q.negative_infinite, Q.positive_infinite])), 

144 Q.fullrank: (set([Q.fullrank]), set([])), 

145 Q.hermitian: (set([Q.hermitian]), set([])), 

146 Q.imaginary: (set([Q.antihermitian, Q.commutative, Q.complex, 

147 Q.finite, Q.imaginary]), set([Q.composite, Q.even, 

148 Q.extended_negative, Q.extended_nonnegative, 

149 Q.extended_nonpositive, Q.extended_nonzero, 

150 Q.extended_positive, Q.extended_real, Q.infinite, Q.integer, 

151 Q.irrational, Q.negative, Q.negative_infinite, Q.nonnegative, 

152 Q.nonpositive, Q.nonzero, Q.odd, Q.positive, 

153 Q.positive_infinite, Q.prime, Q.rational, Q.real, Q.zero])), 

154 Q.infinite: (set([Q.commutative, Q.infinite]), set([Q.algebraic, 

155 Q.complex, Q.composite, Q.even, Q.finite, Q.imaginary, 

156 Q.integer, Q.irrational, Q.negative, Q.nonnegative, 

157 Q.nonpositive, Q.nonzero, Q.odd, Q.positive, Q.prime, 

158 Q.rational, Q.real, Q.transcendental, Q.zero])), 

159 Q.integer: (set([Q.algebraic, Q.commutative, Q.complex, 

160 Q.extended_real, Q.finite, Q.hermitian, Q.integer, Q.rational, 

161 Q.real]), set([Q.imaginary, Q.infinite, Q.irrational, 

162 Q.negative_infinite, Q.positive_infinite, Q.transcendental])), 

163 Q.integer_elements: (set([Q.complex_elements, Q.integer_elements, 

164 Q.real_elements]), set([])), 

165 Q.invertible: (set([Q.fullrank, Q.invertible, Q.square]), 

166 set([Q.singular])), 

167 Q.irrational: (set([Q.commutative, Q.complex, Q.extended_nonzero, 

168 Q.extended_real, Q.finite, Q.hermitian, Q.irrational, 

169 Q.nonzero, Q.real]), set([Q.composite, Q.even, Q.imaginary, 

170 Q.infinite, Q.integer, Q.negative_infinite, Q.odd, 

171 Q.positive_infinite, Q.prime, Q.rational, Q.zero])), 

172 Q.is_true: (set([Q.is_true]), set([])), 

173 Q.lower_triangular: (set([Q.lower_triangular, Q.triangular]), set([])), 

174 Q.negative: (set([Q.commutative, Q.complex, Q.extended_negative, 

175 Q.extended_nonpositive, Q.extended_nonzero, Q.extended_real, 

176 Q.finite, Q.hermitian, Q.negative, Q.nonpositive, Q.nonzero, 

177 Q.real]), set([Q.composite, Q.extended_nonnegative, 

178 Q.extended_positive, Q.imaginary, Q.infinite, 

179 Q.negative_infinite, Q.nonnegative, Q.positive, 

180 Q.positive_infinite, Q.prime, Q.zero])), 

181 Q.negative_infinite: (set([Q.commutative, Q.extended_negative, 

182 Q.extended_nonpositive, Q.extended_nonzero, Q.extended_real, 

183 Q.infinite, Q.negative_infinite]), set([Q.algebraic, 

184 Q.complex, Q.composite, Q.even, Q.extended_nonnegative, 

185 Q.extended_positive, Q.finite, Q.imaginary, Q.integer, 

186 Q.irrational, Q.negative, Q.nonnegative, Q.nonpositive, 

187 Q.nonzero, Q.odd, Q.positive, Q.positive_infinite, Q.prime, 

188 Q.rational, Q.real, Q.transcendental, Q.zero])), 

189 Q.nonnegative: (set([Q.commutative, Q.complex, Q.extended_nonnegative, 

190 Q.extended_real, Q.finite, Q.hermitian, Q.nonnegative, 

191 Q.real]), set([Q.extended_negative, Q.imaginary, Q.infinite, 

192 Q.negative, Q.negative_infinite, Q.positive_infinite])), 

193 Q.nonpositive: (set([Q.commutative, Q.complex, Q.extended_nonpositive, 

194 Q.extended_real, Q.finite, Q.hermitian, Q.nonpositive, 

195 Q.real]), set([Q.composite, Q.extended_positive, Q.imaginary, 

196 Q.infinite, Q.negative_infinite, Q.positive, 

197 Q.positive_infinite, Q.prime])), 

198 Q.nonzero: (set([Q.commutative, Q.complex, Q.extended_nonzero, 

199 Q.extended_real, Q.finite, Q.hermitian, Q.nonzero, Q.real]), 

200 set([Q.imaginary, Q.infinite, Q.negative_infinite, 

201 Q.positive_infinite, Q.zero])), 

202 Q.normal: (set([Q.normal, Q.square]), set([])), 

203 Q.odd: (set([Q.algebraic, Q.commutative, Q.complex, 

204 Q.extended_nonzero, Q.extended_real, Q.finite, Q.hermitian, 

205 Q.integer, Q.nonzero, Q.odd, Q.rational, Q.real]), 

206 set([Q.even, Q.imaginary, Q.infinite, Q.irrational, 

207 Q.negative_infinite, Q.positive_infinite, Q.transcendental, 

208 Q.zero])), 

209 Q.orthogonal: (set([Q.fullrank, Q.invertible, Q.normal, Q.orthogonal, 

210 Q.positive_definite, Q.square, Q.unitary]), set([Q.singular])), 

211 Q.positive: (set([Q.commutative, Q.complex, Q.extended_nonnegative, 

212 Q.extended_nonzero, Q.extended_positive, Q.extended_real, 

213 Q.finite, Q.hermitian, Q.nonnegative, Q.nonzero, Q.positive, 

214 Q.real]), set([Q.extended_negative, Q.extended_nonpositive, 

215 Q.imaginary, Q.infinite, Q.negative, Q.negative_infinite, 

216 Q.nonpositive, Q.positive_infinite, Q.zero])), 

217 Q.positive_definite: (set([Q.fullrank, Q.invertible, 

218 Q.positive_definite, Q.square]), set([Q.singular])), 

219 Q.positive_infinite: (set([Q.commutative, Q.extended_nonnegative, 

220 Q.extended_nonzero, Q.extended_positive, Q.extended_real, 

221 Q.infinite, Q.positive_infinite]), set([Q.algebraic, 

222 Q.complex, Q.composite, Q.even, Q.extended_negative, 

223 Q.extended_nonpositive, Q.finite, Q.imaginary, Q.integer, 

224 Q.irrational, Q.negative, Q.negative_infinite, Q.nonnegative, 

225 Q.nonpositive, Q.nonzero, Q.odd, Q.positive, Q.prime, 

226 Q.rational, Q.real, Q.transcendental, Q.zero])), 

227 Q.prime: (set([Q.algebraic, Q.commutative, Q.complex, 

228 Q.extended_nonnegative, Q.extended_nonzero, 

229 Q.extended_positive, Q.extended_real, Q.finite, Q.hermitian, 

230 Q.integer, Q.nonnegative, Q.nonzero, Q.positive, Q.prime, 

231 Q.rational, Q.real]), set([Q.composite, Q.extended_negative, 

232 Q.extended_nonpositive, Q.imaginary, Q.infinite, Q.irrational, 

233 Q.negative, Q.negative_infinite, Q.nonpositive, 

234 Q.positive_infinite, Q.transcendental, Q.zero])), 

235 Q.rational: (set([Q.algebraic, Q.commutative, Q.complex, 

236 Q.extended_real, Q.finite, Q.hermitian, Q.rational, Q.real]), 

237 set([Q.imaginary, Q.infinite, Q.irrational, 

238 Q.negative_infinite, Q.positive_infinite, Q.transcendental])), 

239 Q.real: (set([Q.commutative, Q.complex, Q.extended_real, Q.finite, 

240 Q.hermitian, Q.real]), set([Q.imaginary, Q.infinite, 

241 Q.negative_infinite, Q.positive_infinite])), 

242 Q.real_elements: (set([Q.complex_elements, Q.real_elements]), set([])), 

243 Q.singular: (set([Q.singular]), set([Q.invertible, Q.orthogonal, 

244 Q.positive_definite, Q.unitary])), 

245 Q.square: (set([Q.square]), set([])), 

246 Q.symmetric: (set([Q.square, Q.symmetric]), set([])), 

247 Q.transcendental: (set([Q.commutative, Q.complex, Q.finite, 

248 Q.transcendental]), set([Q.algebraic, Q.composite, Q.even, 

249 Q.infinite, Q.integer, Q.negative_infinite, Q.odd, 

250 Q.positive_infinite, Q.prime, Q.rational, Q.zero])), 

251 Q.triangular: (set([Q.triangular]), set([])), 

252 Q.unit_triangular: (set([Q.triangular, Q.unit_triangular]), set([])), 

253 Q.unitary: (set([Q.fullrank, Q.invertible, Q.normal, Q.square, 

254 Q.unitary]), set([Q.singular])), 

255 Q.upper_triangular: (set([Q.triangular, Q.upper_triangular]), set([])), 

256 Q.zero: (set([Q.algebraic, Q.commutative, Q.complex, Q.even, 

257 Q.extended_nonnegative, Q.extended_nonpositive, 

258 Q.extended_real, Q.finite, Q.hermitian, Q.integer, 

259 Q.nonnegative, Q.nonpositive, Q.rational, Q.real, Q.zero]), 

260 set([Q.composite, Q.extended_negative, Q.extended_nonzero, 

261 Q.extended_positive, Q.imaginary, Q.infinite, Q.irrational, 

262 Q.negative, Q.negative_infinite, Q.nonzero, Q.odd, Q.positive, 

263 Q.positive_infinite, Q.prime, Q.transcendental])), 

264 }