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Bronstein M. — Symbolic integration 1. Transcendental functions |
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Предметный указатель |
Airy function 170
Bossel function 169 170
CanonicalRepresentation 101
Coefficient lifting 78 101 144
ConstantSystem 221
Content 25
CoupledDECancelExp 258
CoupledDECancelPrim 256
CoupledDECancelTan 261
Deflation 26 28 43 247
Derivation 73
Derivation induced 76
Differential 266
Differential extension 77
Differential field 73
Differential ring 73
Elementary extension 129 278 289
Elementary function 129
Elementary integral 129
Elementary monomial 129
Error function 241
Euclidean 10
Euclidean algorithm 10
Euclidean algorithm, extended 10
Euclidean division 8
Euclidean polynomial remainder sequence 22
Exponential extension 129
Exponential integral 241
Exponential monomial 129
ExtendedEuclidean 11-14
Extension, elementary, real 281
Factorization, irreducible 4
Factorization, prime 4
Factorization, split-squarefree 99 149
Factorization, splitting 97 98 100 101 144 178 180 214 242 247
Factorization, squarefree 28 39 41 42 45 51 55 71 99 134 148 178
FullPartialFraction 58
Gr bner basis 53
HalfExtendedEuclidean 11 13
Hermite reduction 40 41 43 71 134 171
HermiteReduce 40 41 44 135
Hilbert's Nullstellensatz 8 88
HorovitzCstrogradsky 46
Hyperexponential extension 125 288
Hypertangent extension 159
Indicia! equation 124
IntegrateHyperexponential 159
IntegrateHyperexponentialPolynomial 157
IntegrateHypertangent 167
IntegrateHypertangentPolynomial 162
IntegrateHypertangentReduced 165
IntegrateNonLinearNoSpecial 169
IntegratePrimitive 155
IntegratePrimitivePolynomial 154
IntegrateRationalFunction 52 59
IntegrateRealRationalFunction 70
IntRationalLogPart 48 51 54
LaurentSeries 57
LimitedlntegrateReduce 244
LinearConstraints 219
Liouville's theorem 138 140 141 150 174
Liouvillian extension 125
Liouvillian extension, log-explicit 289
Liouvillian monomial 127
Logarithmic derivative identity 74 102 265
Logarithmic derivative of a radical 95
Logarithmic extension 129
Logarithmic integral 148 150 154 241
Logarithmic monomial 129
LogToAtan 63
LogToReal 69
Monomial 89
Monomial, arctangent 281
Monomial, arctangent, elementary 129
Monomial, exponential 129 278 281
Monomial, hyperexponential 125 156 160 161 172 173 184 196 208 216 224 246 254 257
Monomial, hypertangent 159 172 173 187 210 217 240 254 260
Monomial, Liouvillian 127
Monomial, logarithmic 129 278 281
Monomial, nonlinear 89 93 122 136 137 151 168 197 209 225 238 258
| Monomial, primitive 125 153 171-173 184 190 207 216 223 241 255
Monomial, primitive, nonsimple 289
Monomial, real 281
Monomial, tangent 159 281
Newton - Leibniz - Bernoulli algorithm 36 58
Normal polynomial 90
ParametricLogarithmicDerivative 249
ParamPolyRischDENoCancel1 230
ParamPolyRischDENoCancel2 234
ParamRdeBoundDegreeBase 224
ParamRdeBoundDegreeExp 225
ParamRdeBoundDegreeNonLinear 225
ParamRdeBoundDegreePrim 223
ParamRdeNomalDenominator 215
ParamRdeSpecialDenomExp 217
ParamRdeSpecialDenomTan 218
ParSPDE 227
Partial fraction decomposition 15 16 36 39 47 54
PartialFraction 15 17
Polar multiplicity 134
PolyDivide 8
Polynomial remainder sequence 21
Polynomial, Euclidean 22
Polynomial, fundamental theorem 22
Polynomial, primitive 22
Polynomial, subresultant 23 49-51 148
PolynomialReduce 137
PolyPseudoDivide 9
PolyRischDECancelExp 209
PolyRischDECancelPrim 208
PolyRischDECancelTan 211
PolyRischDENoCancel1 204
PolyRischDENoCancel2 205
PolyRischDENoCancel3 206
Primitive extension 125 241
Primitive monomial 125 153 171-173 184 190 207 216 223 241 255
Primitive monomial, nonsimple 289
Primitive part 25
Primitive polynomial 25
Primitive polynomial remainder sequence 22
RdeBoundDegreeBase 195
RdeBoundDegreeExp 196
RdeBoundDegreeNonLinear 197
RdeBoundDegreePrim 194
RdeNormalDenominator 181
RdeSpecialDenomExp 186
RdeSpecialDenomTan 188
Real field 65
Real integration 59 159 172 173 187 210 217 240 260
Real structure theorem 284
Reduced function 101
Remainder 113
Residue 116 143
ResidueReduce 147 149
Risch differential equation 177
Risch differential equation, parametric 213
Risch structure theorem 279
Risch structure theorem, real 284
Rosenlicht's theorem 276
Rothstein - Trager resultant 47 67 71 122 144 172 173
Rothstem - Caviness theorem 289
Similarity 22 50
Simple function 101
SPDE 199
Special polynomial 90
Special polynomial of the first kind 96
SplitFactor 98
SplitSquarefreeFactor 100
Squarefree 29 32
Squarefree factorization 28 39 41 42 45 51 55 71 99 134 148 178
Squarefree polynomial 28
Subresultant 24
Sylvester matrix 18 19
Tangent extension 159
Tangent monomial 159
Value map at a point 110
Value map at infinity 114
ValueAtlnfinity 116
Weak normalization 177
WeakNormalizer 179
wronskian 71 86
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