Daly T.0-201-13448-9
Table of contents :
Symbolic Computation……Page 18
Numeric Computation……Page 19
Graphics……Page 20
HyperDoc……Page 21
Interactive Programming……Page 22
Data Structures……Page 23
Mathematical Structures……Page 24
Pattern Matching……Page 25
Polymorphic Algorithms……Page 26
Extensibility……Page 27
Types are Defined by Abstract Datatype Programs……Page 28
The Type of Basic Objects is a Domain or Subdomain……Page 29
Operations Can Refer To Abstract Types……Page 30
Domains Belong to Categories by Assertion……Page 31
The Interpreter Builds Domains Dynamically……Page 32
Axiom is Extensible……Page 33
Basic Arithmetic……Page 34
Type Conversion……Page 36
Useful Functions……Page 38
Expressions Involving Symbols……Page 41
Complex Numbers……Page 43
Number Representations……Page 44
Modular Arithmetic……Page 48
Accessing Earlier Results……Page 49
Comments and Descriptions……Page 50
Control of Result Types……Page 51
Lists……Page 52
Segmented Lists……Page 60
Streams……Page 61
Arrays, Vectors, Strings, and Bits……Page 64
Flexible Arrays……Page 66
Blocks……Page 69
Functions……Page 73
Choices……Page 76
Loops……Page 77
Introduction……Page 1004
Clef……Page 90
)abbreviation……Page 1006
)cd……Page 1007
Arithmetic Expressions……Page 91
Previous Results……Page 92
Some Types……Page 93
Symbols, Variables, Assignments, and Declarations……Page 94
Calling Functions……Page 97
Some Predefined Macros……Page 98
Comments……Page 99
)close……Page 1008
)clear……Page 1009
)compile……Page 1010
)display……Page 1016
)edit……Page 1017
)frame……Page 1018
)history……Page 1020
)library……Page 1023
)load……Page 1024
Undo……Page 141
Categories……Page 1040
The Basic Idea……Page 146
Domain Constructors……Page 148
Writing Types and Modes……Page 154
Types with One Argument……Page 155
Abbreviations……Page 157
Declarations……Page 159
Records……Page 162
Unions Without Selectors……Page 166
Unions With Selectors……Page 169
The “Any” Domain……Page 171
Conversion……Page 172
Subdomains Again……Page 175
Package Calling and Target Types……Page 179
Resolving Types……Page 183
Exposing Domains and Packages……Page 185
Commands for Snooping……Page 187
Using HyperDoc……Page 192
Key Definitions……Page 193
Scroll Bars……Page 194
Radio Buttons and Toggles……Page 195
Logical Searches……Page 196
X Window Resources for HyperDoc……Page 197
Input Files……Page 200
The .axiom.input File……Page 201
Common Features of Using Output Formats……Page 202
Monospace Two-Dimensional Mathematical Format……Page 203
TeX Format……Page 204
FORTRAN Format……Page 205
Immediate and Delayed Assignments……Page 212
Blocks……Page 216
if-then-else……Page 220
Compiling vs. Interpreting Loops……Page 222
return in Loops……Page 223
break in Loops……Page 224
break vs. => in Loop Bodies……Page 225
More Examples of break……Page 226
while Loops……Page 229
for i in n..m repeat……Page 232
for i in n..m by s repeat……Page 234
for x in l repeat……Page 235
“Such that” Predicates……Page 237
Parallel Iteration……Page 238
Mixing Loop Modifiers……Page 240
Creating Lists and Streams with Iterators……Page 241
An Example: Streams of Primes……Page 244
Functions vs. Macros……Page 248
Macros……Page 249
Introduction to Functions……Page 252
Declaring the Type of Functions……Page 254
One-Line Functions……Page 255
Declared vs. Undeclared Functions……Page 257
Functions vs. Operations……Page 259
Delayed Assignments vs. Functions with No Arguments……Page 260
How Axiom Determines What Function to Use……Page 261
Compiling vs. Interpreting……Page 264
A Basic Example……Page 266
Picking Up the Pieces……Page 269
Predicates……Page 272
Caching Previously Computed Results……Page 274
Recurrence Relations……Page 275
Making Functions from Objects……Page 278
Functions Defined with Blocks……Page 282
Free and Local Variables……Page 286
Anonymous Functions……Page 292
Some Examples……Page 293
Declaring Anonymous Functions……Page 294
Example: A Database……Page 297
Example: A Famous Triangle……Page 300
Example: Testing for Palindromes……Page 302
Rules and Pattern Matching……Page 305
Graphics……Page 314
Plotting Two-Dimensional Functions of One Variable……Page 315
Plotting Two-Dimensional Parametric Plane Curves……Page 316
Plotting Plane Algebraic Curves……Page 317
Two-Dimensional Options……Page 318
Color……Page 320
Palette……Page 321
Two-Dimensional Control-Panel……Page 322
Operations for Two-Dimensional Graphics……Page 324
Addendum: Building Two-Dimensional Graphs……Page 327
Addendum: Appending a Graph to a Viewport Window Containing a Graph……Page 334
Plotting Three-Dimensional Functions of Two Variables……Page 335
Plotting Three-Dimensional Parametric Space Curves……Page 336
Plotting Three-Dimensional Parametric Surfaces……Page 337
Three-Dimensional Options……Page 339
The makeObject Command……Page 342
Building Three-Dimensional Objects From Primitives……Page 343
Coordinate System Transformations……Page 348
Three-Dimensional Control-Panel……Page 351
Operations for Three-Dimensional Graphics……Page 356
Customization using .Xdefaults……Page 360
Numeric Functions……Page 362
Integer and Rational Number Coefficients……Page 371
Finite Field Coefficients……Page 372
Simple Algebraic Extension Field Coefficients……Page 373
Factoring Rational Functions……Page 375
Using a Single Root of a Polynomial……Page 376
Using All Roots of a Polynomial……Page 378
Computation of Eigenvalues and Eigenvectors……Page 380
Solution of Systems of Linear Equations……Page 383
Solution of a Single Polynomial Equation……Page 386
Solution of Systems of Polynomial Equations……Page 388
Limits……Page 390
Laplace Transforms……Page 394
Integration……Page 396
Creation of Power Series……Page 400
Coefficients of Power Series……Page 402
Power Series Arithmetic……Page 404
Functions on Power Series……Page 405
Converting to Power Series……Page 408
Power Series from Formulas……Page 411
Example: Bernoulli Polynomials and Sums of Powers……Page 415
Solution of Differential Equations……Page 419
Closed-Form Solutions of Linear Differential Equations……Page 420
Closed-Form Solutions of Non-Linear Differential Equations……Page 423
Power Series Solutions of Differential Equations……Page 428
Modular Arithmetic and Prime Fields……Page 430
Extensions of Finite Fields……Page 434
Irreducible Modulus Polynomial Representations……Page 436
Cyclic Group Representations……Page 440
Normal Basis Representations……Page 442
Conversion Operations for Finite Fields……Page 445
Utility Operations for Finite Fields……Page 448
Primary Decomposition of Ideals……Page 456
Computation of Galois Groups……Page 459
Non-Associative Algebras and Modelling Genetic Laws……Page 468
AssociationList……Page 476
BalancedBinaryTree……Page 478
BasicOperator……Page 481
BinaryExpansion……Page 485
BinarySearchTree……Page 487
CardinalNumber……Page 489
CartesianTensor……Page 493
Character……Page 505
CharacterClass……Page 508
CliffordAlgebra……Page 510
The Complex Numbers as a Clifford Algebra……Page 511
The Quaternion Numbers as a Clifford Algebra……Page 512
The Exterior Algebra on a Three Space……Page 514
The Dirac Spin Algebra……Page 516
Complex……Page 518
ContinuedFraction……Page 521
CycleIndicators……Page 528
DeRhamComplex……Page 539
DecimalExpansion……Page 546
DistributedMultivariatePolynomial……Page 548
DoubleFloat……Page 550
EqTable……Page 553
Equation……Page 554
Exit……Page 556
Expression……Page 557
Decomposing Factored Objects……Page 563
Expanding Factored Objects……Page 565
Arithmetic with Factored Objects……Page 566
Creating New Factored Objects……Page 569
Factored Objects with Variables……Page 570
FactoredFunctions2……Page 571
File……Page 572
FileName……Page 575
FlexibleArray……Page 578
Introduction to Float……Page 582
Conversion Functions……Page 583
Output Functions……Page 586
An Example: Determinant of a Hilbert Matrix……Page 588
Fraction……Page 590
FullPartialFractionExpansion……Page 593
GeneralSparseTable……Page 597
GroebnerFactorizationPackage……Page 599
Heap……Page 602
HexadecimalExpansion……Page 603
Basic Functions……Page 605
Primes and Factorization……Page 611
Some Number Theoretic Functions……Page 612
IntegerLinearDependence……Page 614
IntegerNumberTheoryFunctions……Page 616
Kernel……Page 621
KeyedAccessFile……Page 625
LexTriangularPackage……Page 629
LazardSetSolvingPackage……Page 656
Library……Page 667
LieExponentials……Page 668
LiePolynomial……Page 671
Differential Operators with Series Coefficients……Page 675
Differential Operators with Rational Function Coefficients……Page 680
Differential Operators with Constant Coefficients……Page 685
Differential Operators with Matrix Coefficients Operating on Vectors……Page 688
Creating Lists……Page 692
Accessing List Elements……Page 693
Changing List Elements……Page 695
Other Functions……Page 697
Dot, Dot……Page 698
LyndonWord……Page 699
Magma……Page 703
MakeFunction……Page 706
MappingPackage1……Page 709
Creating Matrices……Page 714
Operations on Matrices……Page 719
MultiSet……Page 723
MultivariatePolynomial……Page 726
None……Page 728
Octonion……Page 729
OneDimensionalArray……Page 732
Operator……Page 734
OrderedVariableList……Page 739
OrderlyDifferentialPolynomial……Page 740
PartialFraction……Page 747
Permanent……Page 750
Polynomial……Page 751
Quaternion……Page 762
RadixExpansion……Page 764
RealClosure……Page 767
RegularTriangularSet……Page 781
RomanNumeral……Page 797
Segment……Page 800
SegmentBinding……Page 802
Set……Page 803
SingleInteger……Page 807
SparseTable……Page 809
SquareMatrix……Page 811
SquareFreeRegularTriangularSet……Page 812
Stream……Page 818
String……Page 821
Symbol……Page 828
Table……Page 833
TextFile……Page 837
TwoDimensionalArray……Page 839
UnivariatePolynomial……Page 844
UniversalSegment……Page 852
Vector……Page 854
Void……Page 856
WuWenTsunTriangularSet……Page 857
XPBWPolynomial……Page 861
XPolynomial……Page 869
XPolynomialRing……Page 872
ZeroDimensionalSolvePackage……Page 875
Drawing Ribbons Interactively……Page 898
A Ribbon Program……Page 900
Coloring and Positioning Ribbons……Page 902
Points, Lines, and Curves……Page 903
Drawing Complex Vector Fields……Page 905
Drawing Complex Functions……Page 907
Automatic Newton Iteration Formulas……Page 909
Names, Abbreviations, and File Structure……Page 914
Syntax……Page 915
Capsules……Page 916
Input Files vs. Packages……Page 917
Compiling Packages……Page 918
Parameters……Page 919
Conditionals……Page 921
Testing……Page 922
How Packages Work……Page 924
Categories……Page 928
Definitions……Page 929
Documentation……Page 930
Hierarchies……Page 931
Defaults……Page 932
Correctness……Page 934
Attributes……Page 935
Parameters……Page 936
Conditionals……Page 937
Anonymous Categories……Page 938
Domains vs. Packages……Page 940
Category Assertions……Page 941
A Demo……Page 943
Representation……Page 944
Multiple Representations……Page 945
Defaults……Page 946
Origins……Page 947
Example 1: Clifford Algebra……Page 948
Example 2: Building A Query Facility……Page 949
A Little Query Language……Page 950
The Database Constructor……Page 951
Query Equations……Page 953
DataLists……Page 954
Creating a Database……Page 955
Example Queries……Page 956
The Front Page: Searching the Library……Page 960
The Constructor Page……Page 964
Constructor Page Buttons……Page 967
Cross Reference……Page 970
Views Of Constructors……Page 974
The Description Page for Operations……Page 976
Views of Operations……Page 978
Capitalization Convention……Page 983
The New Axiom Library Compiler……Page 984
Interpreting NAG Documentation……Page 985
Using the Link……Page 987
Providing values for Argument Subprograms……Page 988
General Fortran-generation utilities in Axiom……Page 990
Some technical information……Page 998
Interactive Front-end and Language……Page 999
Library……Page 1000
HyperTex……Page 1001
Documentation……Page 1002
)pquit……Page 1025
)read……Page 1026
)set……Page 1027
)show……Page 1028
)synonym……Page 1029
)system……Page 1030
)trace……Page 1031
)undo……Page 1035
)what……Page 1036
constructorListing……Page 1042
Domains……Page 1050
Packages……Page 1082
Operations……Page 1092
images1.input……Page 1094
images5.input……Page 1095
images7.input……Page 1097
conformal.input……Page 1098
tknot.input……Page 1101
ntube.input……Page 1102
dhtri.input……Page 1103
tetra.input……Page 1104
antoine.input……Page 1106
scherk.input……Page 1107
Glossary……Page 1110
License……Page 1132
Reviews
There are no reviews yet.