A guide to Maple:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1999
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIII, 325 S. graph. Darst. |
| ISBN: | 0387941169 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | ERNIC KAMERICH A GUIDE TOMAPLE WITH 41 ILLUSTRATIONS SPRINGER CONTENTS
CHAPTER 1 BASIC ELEMENTS IN THE USE OF MAPLE 1 1.1 MEETING MAPLE:
SYMBOLIC CALCULATIONS 1 1.2 MEETING MAPLE: NUMERICAL CALCULATIONS 5 1.3
MEETING MAPLE: SYMBOLIC CALCULATIONS AGAIN 6 1.4 SPACES AND ASTERISKS 8
1.5 TERMINATING COMMANDS WITH SEMICOLONS OR COLONS 8 1.6 NAMES AND
ASSIGNMENTS 10 1.7 REFERRING TO PREVIOUS RESULTS WITH THE DITTO 11 1.8
REFERRING TO PREVIOUS RESULTS WITH OTHER FACILITIES 13 1.9 USING
PROCEDURES 14 1.10 PROCEDURES THAT SEEM TO DO NOTHING 14 1.11 THE SIGN %
FOR ABBREVIATIONS IN OUTPUT 16 1.12 ON-LINE HELP 17 CHAPTER 2 NUMBERS
AND ALGEBRAIC OPERATORS 19 2.1 ALGEBRAIC OPERATORS 19 2.2 PARENTHESES
AND PRECEDENCE RULES 20 2.3 RATIONAL NUMBERS 22 2.4 REAL CONSTANTS 22
2.5 COMPLEX NUMBERS 23 2.6 RADICALS 24 2.7 MANIPULATING RADICALS AND
COMPLEX NUMBERS*AN EXAMPLE .. 25 2.8 FLOATING-POINT NUMBERS,
APPROXIMATIONS 26 2.9 SOME EFFECTS OF AUTOMATIC SIMPLIFICATION OF
FLOATING-POINT NUMBERS 28 2.10 CALCULATIONS WITH INTEGERS 29 2.11
INTEGERS MODULO AN INTEGER 30 2.12 ALGEBRAIC EXTENSIONS AND GENERAL
RINGS 31 CHAPTER 3 NAMES AND EVALUATION 1: MATHEMATICAL VARIABLES 32 3.1
ASSIGNING NAMES TO OBJECTS AND EVALUATING NAMES TO OBJECTS 32 3.2
ASSIGNING NAMES AND EXPRESSIONS TO A NAME 33 3.3 UNASSIGNING 35 3.4
NAMES AND PROPERTIES 36 3.5 COMBINATIONS OF CHARACTERS THAT CAN BE
ACCEPTED AS NAMES 37 3.6 GREEK LETTER NAMES 38 3.7 NAMES WITH AN INDEX
39 3.8 SINGLE BACK QUOTES 40 3.9 THE CONCEPTS OF NAME, SYMBOL, AND
STRING IN MAPLE 41 3.10 RECURSIVE DEFINITIONS OF NAMES 41 CHAPTER 4
ELEMENTARY CALCULUS 43 4.1 DIFFERENTIATION 43 XV111 CONTENTS 4.2 THE
DERIVATIVE AT A POINT 45 4.3 SOME MORE TOOLS IN DIFFERENTIAL CALCULUS 46
4.4 ANTIDERIVATIVES 46 4.5 ~. SPECIAL ELEMENTS APPEARING IN THE RESULTS
OF THE PROCEDURE INT 47 4.6 DEFINITE INTEGRALS 50 4.7 HELPING MAPLE TO
FIND A DEFINITE INTEGRAL BY RESTRICTING THE DOMAIN OF A PARAMETER 50 4.8
HELPING MAPLE TO FIND AN ANTIDERIVATIVE BY CONVERSION TO ROOTOF 51 4.9
HELPING MAPLE TO FIND AN ANTIDERIVATIVE BY SUBSTITUTION 52 4.10 MORE
TOOLS FOR INTEGRATION 53 4.11 RELIABILITY OF THE CALCULATION OF
ANTIDERIVATIVES 53 4.12 DEFINITE INTEGRALS OF DISCONTINUOUS FUNCTIONS 55
4.13 DEFINITE INTEGRALS AND BRANCH CUTS OF FUNCTIONS 56 4.14 RELIABILITY
OF CALCULATIONS OF DEFINITE INTEGRALS 56 4.15 NUMERICAL INTEGRATION 57
4.16 NUMERICAL APPROXIMATIONS TO MULTIPLE INTEGRALS 58 4.17 DEFINITE AND
INDEFINITE SUMS AND PRODUCTS 60 4.18 OTHER TOOLS AND PEDAGOGICAL
FACILITIES 62 CHAPTER 5 NAMES AND EVALUATION 2: APPLYING PROCEDURES 64
5.1 EVALUATION OF NAMES IN ARGUMENTS OF PROCEDURES 64 5.2 OPTIONS OF
PROCEDURES 65 5.3 OUTPUT AND RESULTS OF PROCEDURES 66 5.4 ASSIGNING SIDE
RESULTS TO ARGUMENTS OF PROCEDURES 67 5.5 NAMES REFERRING TO PROCEDURES
67 5.6 THE MAPLE LIBRARY OF PROCEDURES 68 5.7 ASKING PROCEDURES FOR
ADDITIONAL INFORMATION WITH INFOLEVEL 70 5.8 PRINTING STANDARD
PROCEDURES FROM MAPLE S LIBRARY 71 CHAPTER 6 CREATING AND USING
MATHEMATICAL FUNCTIONS 72 6.1 STANDARD MATHEMATICAL FUNCTIONS 72 6.2
DEFINITIONS OF INVERSE FUNCTIONS, BRANCH CUTS .; 73 6.3 DENOTATION OF
THE FUNCTIONS EXP, GAMMA, AND ZETA 74 6.4 EXPRESSIONS VERSUS FUNCTIONS,
CREATING FUNCTIONS 75 6.5 CREATING FUNCTIONS IN SEVERAL ARGUMENTS 76 6.6
A PITFALL IN CREATING MATHEMATICAL FUNCTIONS 76 6.7 USING EXISTING
EXPRESSIONS FOR CREATING MATHEMATICAL FUNCTIONS 77 6.8 EVALUATION OF
NAMES OF PROCEDURES 79 6.9 DERIVATIVE FUNCTIONS 79 6.10 DERIVATIVES OF
FUNCTIONS OF MORE THAN ONE VARIABLE 81 6.11 CONVERSION BETWEEN DIF F AND
D 82 6.12 PIECEWISE-DEFINED FUNCTIONS AND EXPRESSIONS 82 CONTENTS XIX
6.13 CREATING FUNCTIONS BY ELEMENTARY OPERATIONS ON FUNCTIONS ... 85
CHAPTER 7 GRAPHICS 87 7.1 GRAPHS OF REAL FUNCTIONS IN ONE REAL PARAMETER
87 7.2 GRAPHS OF REAL FUNCTIONS IN TWO REAL PARAMETERS 88 7.3 ASSIGNING,
MANIPULATING, AND PRINTING GRAPHICAL OBJECTS 91 7.4 VERTICAL ASYMPTOTES
AND DISCONTINUITIES 92 7.5 GRAPHS WITH RANGES TO INFINITY 95 7.6
LOGARITHMIC SCALINGS 96 7.7 PARAMETERIZED CURVES AND SURFACES 97 7.8
DIFFERENT TYPES OF COORDINATES 99 7.9 EMPTY PLOTS CAUSED BY COMPLEX
VALUES 100 7.10 PLOTTING DATA 100 7.11 GRAPHS OF RELATIONS OR IMPLICITLY
DEFINED FUNCTIONS 103 7.12 COMBINING GRAPHS 103 7.13 MAPLE S MOVIES 105
7.14 MORE TOOLS IN GRAPHICS 105 CHAPTER 8 TAYLOR OR LAURENT EXPANSION
AND LIMITS 107 8.1 TAYLOR EXPANSION 107 8.2 THE ORDER OF A SERIES
EXPANSION 108 8.3 ESTIMATING THE ORDER TERM 108 8.4 THE SUBEXPRESSION
STRUCTURE OF RESULTS FROM SERIES 109 8.5 THE LEADING TERM 110 8.6
LAURENT, PUISSEUX, AND GENERALIZED TRUNCATED POWER SERIES ILL 8.7
APPLICATION OF SERIES TO INTEGRATION 112 8.8 NUMERICAL EVALUATION OF A
SERIES 113 8.9 MULTIVARIATE TAYLOR EXPANSION 113 8.10 CALCULATING LIMITS
114 8.11 MULTIPLE LIMITS 116 8.12 CONTINUITY, SINGULARITIES, AND
RESIDUES 116 8.13 OTHER FACILITIES FOR SERIES CALCULATIONS 116 CHAPTER 9
NUMERICAL CALCULATIONS WITH MAPLE 117 9.1 ACCURACY 117 9.2 SPEEDING UP
BY OPTIMIZING 118 9.3 SPEEDING UP WITH FLOATING-POINT FACILITIES OF THE
SYSTEM 121 9.4 SOME SPECIAL PROCEDURES 121 9.5 USING FORTRAN AND C IN
COMBINATION WITH MAPLE 122 9.6 DATA FILES 122 CHAPTER 10 MANIPULATING
SEVERAL OBJECTS AT ONCE 123 10.1 CREATION OF SEQUENCES, SETS, AND LISTS
123 10.2 SELECTING ELEMENTS OF SEQUENCES, SETS, AND LISTS 125 10.3
APPLYING A PROCEDURE TO SEVERAL OBJECTS AT ONCE 126 10.4 FINDING A
SPECIAL ELEMENT IN A SET OR A LIST 129 10.5 FINDING THE MINIMAL OR THE
MAXIMAL ELEMENT 129 XX CONTENTS 10.6 SELECTING THE ELEMENTS THAT SATISFY
A SPECIAL CONDITION 130 10.7 GENERATING SEQUENCES AS VALUES OF A
FUNCTION OR AN EXPRESSION 131 10.8 MANIPULATING SEQUENCES, SETS, AND
LISTS 132 10.9 CONVERSIONS BETWEEN SEQUENCES, SETS, AND LISTS 133 10.10
TABLES 134 CHAPTER 11 SUBSTITUTION AND SUBEXPRESSIONS 136 11.1 SOME
EXAMPLES OF SUBSTITUTION 136 11.2 A SUBSTITUTION THAT FAILS 137 11.3
SUBEXPRESSIONS OF POLYNOMIALS, SUBSTITUTION 138 11.4 SUBEXPRESSIONS OF
RATIONAL EXPRESSIONS, SUBSTITUTION 140 11.5 SUBEXPRESSIONS OF
UNEVALUATED FUNCTION CALLS 141 11.6 THE PROCEDURE EVAL 142 11.7 THE
PROCEDURES SUBS AND EVAL*A SURVEY 143 11.8 MORE THAN ONE SUBSTITUTION AT
ONCE 143 11.9 THE PROCEDURE PDETOOLS [DCHANGE] FOR CHANGING VARIABLES
144 11.10 SUBSTITUTION OF ALGEBRAIC SUBEXPRESSIONS 145 11.11 APPLYING
SIDE RELATIONS 146 11.12 FINDING THE STRUCTURE AND SUBEXPRESSIONS OF
LARGE EXPRESSIONS 147 11.13 SELECTING SUBOPERANDS 148 11.14 SUBSTITUTING
SOMETHING FOR ONE COMPONENT OF AN EXPRESSION 148 CHAPTER 12 MANIPULATING
AND CONVERTING NUMBERS 149 12.1 REAL AND IMAGINARY PARTS OF A COMPLEX
NUMBER 149 12.2 ARGUMENT AND ABSOLUTE VALUE OF A COMPLEX NUMBER 150 12.3
THE SIGN OF A REAL OR A COMPLEX NUMBER 150 12.4 MANIPULATING PRODUCTS
AND QUOTIENTS OF RADICALS 151 12.5 NESTED RADICALS AND ROOTS OF COMPLEX
NUMBERS 152 12.6 AN EXAMPLE: SUBSTITUTING EXPRESSIONS WITH RADICALS IN
POLYNOMIALS 153 12.7 CONVERTING FLOATING-POINT NUMBERS TO RATIONAL
NUMBERS 155 12.8 ROUNDING RATIONAL NUMBERS TO INTEGERS 155 CHAPTER 13
POLYNOMIALS AND RATIONAL EXPRESSIONS 157 13.1 POLYNOMIALS AND THE
STANDARD ARITHMETIC OPERATORS 157 13.2 DIVISION OF POLYNOMIALS WITH A
REMAINDER 158 13.3 THE GREATEST COMMON DIVISOR AND THE LEAST COMMON
MULTIPLE 159 13.4 THE RESULTANT OF TWO POLYNOMIALS 160 13.5 THE
COEFFICIENTS OF A POLYNOMIAL 161 13.6 TRUNCATING A POLYNOMIAL ABOVE SOME
DEGREE 163 13.7 SORTING A POLYNOMIAL 164 13.8 SIMPLIFYING RATIONAL
EXPRESSIONS 165 CONTENTS XXI 13.9 NUMERATOR AND DENOMINATOR 166 13.10
MORE TOOLS 167 13.11 RELIABILITY 167 CHAPTER 14 POLYNOMIAL EQUATIONS AND
FACTORING POLYNOMIALS 168 14.1 SOLVING POLYNOMIAL EQUATIONS SYMBOLICALLY
168 14.2 SOLVING MODEST SYSTEMS OF POLYNOMIAL EQUATIONS 170 14.3 FINDING
OR APPROXIMATING THE ELEMENTS REPRESENTED BY A ROOTOF EXPRESSION 173
14.4 CALCULATING WITH ROOTOF EXPRESSIONS 174 14.5 ROOTOF EXPRESSIONS
VERSUS RADICALS 175 14.6 FACTORING WITH THE PROCEDURE FACTOR 176 14.7
MORE TOOLS FOR FACTORING 177 14.8 SOLVING WITH NUMERICAL TOOLS 178 14.9
SOLVING COMPLICATED SYSTEMS OF POLYNOMIAL EQUATIONS WITH GROBNER BASIS
179 14.10 ALGEBRAIC EXTENSIONS OF THE RATIONAL NUMBER FIELD 182 14.11
POLYNOMIAL RINGS MODULO IDEALS 185 14.12 POLYNOMIALS OVER Z MOD P 185
CHAPTER 15 MANIPULATING ALGEBRAIC EXPRESSIONS 187 15.1 OPTIONS FOR
SIMPLIFY AND COMBINE 187 15.2 SIMPLIFICATIONS DEPENDING ON CONDITIONS
188 15.3 SUMS OF EXPONENTS, PRODUCTS OF POWERS WITH EQUAL BASIS ... 190
15.4 POWERS OF POWERS, PRODUCTS OF EXPONENTS 192 15.5 POWERS OF
PRODUCTS, PRODUCTS OF POWERS WITH EQUAL EXPONENTS 194 15.6 RADICALS 195
15.7 MANIPULATING LOGARITHMIC EXPRESSIONS 197 15.8 AN EXAMPLE OF THE USE
OF THE OPTION SYMBOLIC 200 15.9 MANIPULATING TRIGONOMETRIC EXPRESSIONS
202 15.10 MANIPULATING PARTS OF EXPRESSIONS 206 15.11 AN EXAMPLE:
CONVERTING A COMPLEX EXPRESSION INTO A REAL EXPRESSION 210 15.12
VERIFYING IDENTITIES 211 15.13 RELIABILITY 213 15.14 GENERAL ADVICE FOR
MANIPULATING 213 CHAPTER 16 SOLVING EQUATIONS AND INEQUALITIES IN
GENERAL 214 16.1 GENERAL PRINCIPLES IN USING MAPLE FOR SOLVING EQUATIONS
AND INEQUALITIES 214 16.2 AN EXAMPLE: A TRIGONOMETRIC EQUATION 215 16.3
ANOTHER EXAMPLE: AN EXPONENTIAL EQUATION 218 16.4 NO SOLUTIONS FOUND 219
16.5 INEQUALITIES AND SYSTEMS OF INEQUALITIES 220 16.6 MANIPULATING
EQUATIONS AND SETS OF EQUATIONS 221 16.7 SOLVING EQUATIONS NUMERICALLY
224 XX11 CONTENTS 16.8 SOLVING SYSTEMS OF EQUATIONS NUMERICALLY 225 16.9
SERIES OF AN IMPLICITLY DEFINED FUNCTION 226 16.10 RECURRENCE RELATIONS
229 16.11 SOLVING IDENTITIES, MATCHING PATTERNS 230 16.12 OTHER
PROCEDURES FOR SOLVING 231 CHAPTER 17 SOLVING DIFFERENTIAL EQUATIONS 232
17.1 ORDINARY DIFFERENTIAL EQUATIONS (ODES): DENOTING, SOLVING, CHECKING
SOLUTIONS 232 17.2 ORDINARY DIFFERENTIAL EQUATIONS WITH INITIAL
CONDITIONS 234 17.3 IMPLICIT SOLUTIONS AND CHECKING THEM 235 17.4 DESOL
EXPRESSIONS APPEARING IN SOLUTIONS 237 17.5 NUMERICAL APPROXIMATIONS TO
SOLUTIONS 237 17.6 SERIES DEVELOPMENT OF A SOLUTION 239 17.7 SYSTEMS OF
ODES 240 17.8 HELPING MAPLE IN SOLVING ODES 242 17.9 SYMBOLIC
REPRESENTATIONS OF SOLUTIONS: DESOL 243 17.10 GRAPHIC TOOLS FOR
DIFFERENTIAL EQUATIONS 245 17.11 MORE TOOLS 246 CHAPTER 18 VECTORS AND
MATRICES 247 18.1 THE LINEAR ALGEBRA PACKAGE 247 18.2 CREATING VECTORS
AND MATRICES 248 18.3 EVALUATION OF VECTORS AND MATRICES 249 18.4
ELEMENTS OF VECTORS AND MATRICES 250 18.5 MATRIX AND VECTOR ARITHMETIC
OPERATORS 250 18.6 MANIPULATING ALL THE ELEMENTS OF A MATRIX OR VECTOR
AT ONCE 252 18.7 PROCESSING A MATRIX THAT CONTAINS FLOATING-POINT
NUMBERS ... 253 18.8 NAMES CONTAINED IN ELEMENTS OF MATRICES AND VECTORS
254 18.9 DETERMINANT, BASIS, RANGE, KERNEL, GAUSSIAN ELIMINATION * 255
18.10 SYSTEMS OF LINEAR EQUATIONS 256 18.11 CHARACTERISTIC POLYNOMIALS
AND EIGENVALUES 258 18.12 DOT PRODUCT, CROSS PRODUCT, NORMS, AND
ORTHOGONAL SYSTEMS 261 18.13 VECTOR CALCULUS 262 18.14 CREATING NEW
VECTORS AND MATRICES FROM OLD ONES BY CHANGING ELEMENTS 263 18.15
CREATING NEW MATRICES FROM OLD ONES BY TRANSPOSING, CUTTING, AND PASTING
265 18.16 ALTERNATIVE WAYS OF CREATING VECTORS AND MATRICES 265 18.17
SPECIAL TYPES OF MATRICES: (ANTI)SYMMETRIC, SPARSE, IDENTITY 266 18.18
CREATING MORE SPECIAL TYPES OF MATRICES 270 18.19 FUNCTIONS YIELDING
VECTORS AND MATRICES 270 18.20 VECTORS AND MATRICES MODULO AN INTEGER
272 18.21 READING A MATRIX OF DATA FROM A FILE 273 CONTENTS XXM 18.22
PEDAGOGICAL FACILITIES 273 APPENDIX A TYPES, PROPERTIES, AND DOMAINS 274
A.1 BASIC TYPES 274 A.2 MORE TYPES 275 A.3 SELECTION ON TYPE 277 A.4
PROPERTIES, THE ASSUME FACILITY 277 A.5 DERIVED PROPERTIES 278 A.6
ASKING FOR THE ASSUMED PROPERTIES 278 A.7 ADDING PROPERTIES 279 A.8
COMBINING PROPERTIES 279 A.9 PROPERTIES AND ASSIGNING 280 A.10
PROPERTIES AND FORMAL PARAMETERS 281 A. 11 DOMAINS, THE DOMAINS PACKAGE
282 APPENDIX B NAMES AND EVALUATION 3: SOME SPECIAL FEATURES 284 B.I
CHANGING NAMES, ALIAS 284 B.2 FINDING NAMES USED 286 B.3 INDEXED NAMES
286 B.4 QUOTES WITH TABLE, ARRAYS, VECTORS, AND MATRICES 287 B.5
RECOVERING LOST PROCEDURES 288 B.6 EXCEPTIONS TO THE RULE OF AUTOMATIC
FULL EVALUATION 288 APPENDIX C THE USER INTERFACE FOR TEXT-ONLY VERSIONS
290 C. 1 STARTING, INTERRUPTING, AND QUITTING MAPLE 290 C.2 EDITING
COMMANDS 290 C.3 PICTURES 291 C.4 MAPLE SYSTEM MESSAGES 291 C.5 SAVING A
SESSION AND ITS RESULTS 291 APPENDIX D PROCEDURES REMEMBERING PREVIOUS
RESULTS 292 D.I REMEMBER TABLES OF PROCEDURES 292 D.2 CLEARING (PARTS
OF) THE REMEMBER TABLE 294 D.3 AN EXAMPLE OF SIDE EFFECTS OF THE
REMEMBER TABLE: INFOLEVEL 294 APPENDIX E CONTROL STRUCTURES 296 E.I
PROCEDURES 296 E.2 SEARCHING FOR CAUSES OF ODD BEHAVIOR WITH TRACE OR
PRINTLEVEL 298 E.3 USING IF ... FI FOR CHOICES 298 E.4 RECURSION 299 E.5
USING DO ... OD FOR REPEATING ACTIONS 301 E.6 AN EXAMPLE: CHECKING THE
RESULTS OF SOLVE BY SUBSTITUTING 304 ERROR MESSAGES AND WARNINGS 309
CATCHWORD INDEX 310
|
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| discipline | Informatik Mathematik |
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| indexdate | 2024-07-09T18:11:59Z |
| institution | BVB |
| isbn | 0387941169 |
| language | English |
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| physical | XXIII, 325 S. graph. Darst. |
| publishDate | 1999 |
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| publisher | Springer |
| record_format | marc |
| spelling | Kamerich, Ernic Verfasser aut A guide to Maple Ernic Kamerich New York [u.a.] Springer 1999 XXIII, 325 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics - Data processing Mathematik Maple Programm (DE-588)4209397-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Maple Programm (DE-588)4209397-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007789657&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kamerich, Ernic A guide to Maple Mathematics - Data processing Mathematik Maple Programm (DE-588)4209397-1 gnd |
| subject_GND | (DE-588)4209397-1 (DE-588)4151278-9 |
| title | A guide to Maple |
| title_auth | A guide to Maple |
| title_exact_search | A guide to Maple |
| title_full | A guide to Maple Ernic Kamerich |
| title_fullStr | A guide to Maple Ernic Kamerich |
| title_full_unstemmed | A guide to Maple Ernic Kamerich |
| title_short | A guide to Maple |
| title_sort | a guide to maple |
| topic | Mathematics - Data processing Mathematik Maple Programm (DE-588)4209397-1 gnd |
| topic_facet | Mathematics - Data processing Mathematik Maple Programm Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007789657&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kamerichernic aguidetomaple |