\BOOKMARK [0][-]{chapter.1}{Index}{}% 1
\BOOKMARK [0][-]{chapter.2}{Introduction}{}% 2
\BOOKMARK [1][-]{section.2.1}{Notations used in this manual}{chapter.2}% 3
\BOOKMARK [1][-]{section.2.2}{Interfaces for the giac library}{chapter.2}% 4
\BOOKMARK [2][-]{subsection.2.2.1}{The Xcas interface }{section.2.2}% 5
\BOOKMARK [2][-]{subsection.2.2.2}{The command-line interface: icas giac \040}{section.2.2}% 6
\BOOKMARK [2][-]{subsection.2.2.3}{The Firefox interface}{section.2.2}% 7
\BOOKMARK [2][-]{subsection.2.2.4}{The TeXmacs interface}{section.2.2}% 8
\BOOKMARK [2][-]{subsection.2.2.5}{Checking the version of giac that you are using: version giac \040}{section.2.2}% 9
\BOOKMARK [0][-]{chapter.3}{The Xcas interface}{}% 10
\BOOKMARK [1][-]{section.3.1}{The entry levels}{chapter.3}% 11
\BOOKMARK [1][-]{section.3.2}{The starting window}{chapter.3}% 12
\BOOKMARK [1][-]{section.3.3}{Getting help}{chapter.3}% 13
\BOOKMARK [1][-]{section.3.4}{The menus}{chapter.3}% 14
\BOOKMARK [2][-]{subsection.3.4.1}{The File menu}{section.3.4}% 15
\BOOKMARK [2][-]{subsection.3.4.2}{The Edit menu}{section.3.4}% 16
\BOOKMARK [2][-]{subsection.3.4.3}{The Cfg menu}{section.3.4}% 17
\BOOKMARK [2][-]{subsection.3.4.4}{The Help menu}{section.3.4}% 18
\BOOKMARK [2][-]{subsection.3.4.5}{The Toolbox menu}{section.3.4}% 19
\BOOKMARK [2][-]{subsection.3.4.6}{The Expression menu}{section.3.4}% 20
\BOOKMARK [2][-]{subsection.3.4.7}{The Cmds menu}{section.3.4}% 21
\BOOKMARK [2][-]{subsection.3.4.8}{The Prg menu}{section.3.4}% 22
\BOOKMARK [2][-]{subsection.3.4.9}{The Graphic menu}{section.3.4}% 23
\BOOKMARK [2][-]{subsection.3.4.10}{The Geo menu}{section.3.4}% 24
\BOOKMARK [2][-]{subsection.3.4.11}{The Spreadsheet menu}{section.3.4}% 25
\BOOKMARK [2][-]{subsection.3.4.12}{The Phys menu}{section.3.4}% 26
\BOOKMARK [2][-]{subsection.3.4.13}{The Highschool menu}{section.3.4}% 27
\BOOKMARK [2][-]{subsection.3.4.14}{The Turtle menu}{section.3.4}% 28
\BOOKMARK [1][-]{section.3.5}{Configuring Xcas}{chapter.3}% 29
\BOOKMARK [2][-]{subsection.3.5.1}{The number of significant digits: Digits DIGITS \040 }{section.3.5}% 30
\BOOKMARK [2][-]{subsection.3.5.2}{The language mode: xcas\137mode \040}{section.3.5}% 31
\BOOKMARK [2][-]{subsection.3.5.3}{The units for angles: angle\137radian \040}{section.3.5}% 32
\BOOKMARK [2][-]{subsection.3.5.4}{Exact or approximate values: approx\137mode \040}{section.3.5}% 33
\BOOKMARK [2][-]{subsection.3.5.5}{Complex numbers: cfactor complex\137mode \040 }{section.3.5}% 34
\BOOKMARK [2][-]{subsection.3.5.6}{Complex variables: complex\137variables \040}{section.3.5}% 35
\BOOKMARK [2][-]{subsection.3.5.7}{Configuring the computations}{section.3.5}% 36
\BOOKMARK [2][-]{subsection.3.5.8}{Configuring the graphics}{section.3.5}% 37
\BOOKMARK [2][-]{subsection.3.5.9}{More configuration}{section.3.5}% 38
\BOOKMARK [2][-]{subsection.3.5.10}{The configuration file: widget\137size cas\137setup xcas\137mode xyztrange \040 \040 }{section.3.5}% 39
\BOOKMARK [1][-]{section.3.6}{Printing and saving}{chapter.3}% 40
\BOOKMARK [2][-]{subsection.3.6.1}{Saving a session }{section.3.6}% 41
\BOOKMARK [2][-]{subsection.3.6.2}{Saving a spreadsheet}{section.3.6}% 42
\BOOKMARK [2][-]{subsection.3.6.3}{Saving a program }{section.3.6}% 43
\BOOKMARK [2][-]{subsection.3.6.4}{Printing a session}{section.3.6}% 44
\BOOKMARK [1][-]{section.3.7}{Translating to other computer languages}{chapter.3}% 45
\BOOKMARK [2][-]{subsection.3.7.1}{Translating an expression to LaTeX: latex \040}{section.3.7}% 46
\BOOKMARK [2][-]{subsection.3.7.2}{Translating the entire session to LaTeX}{section.3.7}% 47
\BOOKMARK [2][-]{subsection.3.7.3}{Translating graphical output to LaTeX: graph2tex graph3d2tex \040}{section.3.7}% 48
\BOOKMARK [2][-]{subsection.3.7.4}{Translating an expression to MathML: mathml \040}{section.3.7}% 49
\BOOKMARK [2][-]{subsection.3.7.5}{Translating a spreadsheet to MathML}{section.3.7}% 50
\BOOKMARK [2][-]{subsection.3.7.6}{Indent an XML string: xml\137print \040}{section.3.7}% 51
\BOOKMARK [2][-]{subsection.3.7.7}{Export to presentation or content MathML: export\137mathml }{section.3.7}% 52
\BOOKMARK [2][-]{subsection.3.7.8}{Translating a Maple file to Xcas: maple2xcas \040}{section.3.7}% 53
\BOOKMARK [0][-]{chapter.4}{Entry in Xcas}{}% 54
\BOOKMARK [1][-]{section.4.1}{Suppressing output: nodisp :; \040}{chapter.4}% 55
\BOOKMARK [1][-]{section.4.2}{Entering comments: comment \040 }{chapter.4}% 56
\BOOKMARK [1][-]{section.4.3}{Editing expressions}{chapter.4}% 57
\BOOKMARK [2][-]{subsection.4.3.1}{Entering expressions in the editor: an example}{section.4.3}% 58
\BOOKMARK [2][-]{subsection.4.3.2}{Subexpressions }{section.4.3}% 59
\BOOKMARK [2][-]{subsection.4.3.3}{Manipulating subexpressions}{section.4.3}% 60
\BOOKMARK [1][-]{section.4.4}{Previous results: ans }{chapter.4}% 61
\BOOKMARK [1][-]{section.4.5}{Spreadsheet}{chapter.4}% 62
\BOOKMARK [2][-]{subsection.4.5.1}{Opening a spreadsheet}{section.4.5}% 63
\BOOKMARK [2][-]{subsection.4.5.2}{The spreadsheet window}{section.4.5}% 64
\BOOKMARK [0][-]{chapter.5}{CAS building blocks}{}% 65
\BOOKMARK [1][-]{section.5.1}{Numbers}{chapter.5}% 66
\BOOKMARK [1][-]{section.5.2}{Symbolic constants: e pi infinity inf i euler\137gamma \040 \040 \040 \040 \040 \040}{chapter.5}% 67
\BOOKMARK [1][-]{section.5.3}{Sequences, sets and lists}{chapter.5}% 68
\BOOKMARK [2][-]{subsection.5.3.1}{Sequences: seq[] \(\)}{section.5.3}% 69
\BOOKMARK [2][-]{subsection.5.3.2}{Sets: set[] }{section.5.3}% 70
\BOOKMARK [2][-]{subsection.5.3.3}{Lists: [ ]}{section.5.3}% 71
\BOOKMARK [2][-]{subsection.5.3.4}{Accessing elements}{section.5.3}% 72
\BOOKMARK [1][-]{section.5.4}{Variables}{chapter.5}% 73
\BOOKMARK [2][-]{subsection.5.4.1}{Variable names}{section.5.4}% 74
\BOOKMARK [2][-]{subsection.5.4.2}{Assigning values: := => = assign sto Store \040 \040 \040 }{section.5.4}% 75
\BOOKMARK [2][-]{subsection.5.4.3}{Assignment by reference: =< \040}{section.5.4}% 76
\BOOKMARK [2][-]{subsection.5.4.4}{Copying values of list: copy \040}{section.5.4}% 77
\BOOKMARK [2][-]{subsection.5.4.5}{Incrementing variables: += -= *= /= \040 \040}{section.5.4}% 78
\BOOKMARK [2][-]{subsection.5.4.6}{Storing and recalling variables and their values: archive unarchive \040}{section.5.4}% 79
\BOOKMARK [2][-]{subsection.5.4.7}{Copying variables: CopyVar \040}{section.5.4}% 80
\BOOKMARK [2][-]{subsection.5.4.8}{Assumptions on variables: about additionally assume purge supposons and or \040 \040 \040 \040}{section.5.4}% 81
\BOOKMARK [2][-]{subsection.5.4.9}{Unassigning variables: VARS purge DelVar del restart rm\137a\137z rm\137all\137vars \040 \040 \040 \040}{section.5.4}% 82
\BOOKMARK [2][-]{subsection.5.4.10}{The CST variable \040}{section.5.4}% 83
\BOOKMARK [1][-]{section.5.5}{Functions}{chapter.5}% 84
\BOOKMARK [2][-]{subsection.5.5.1}{Defining functions}{section.5.5}% 85
\BOOKMARK [1][-]{section.5.6}{Directories}{chapter.5}% 86
\BOOKMARK [2][-]{subsection.5.6.1}{Working directories: pwd cd \040 }{section.5.6}% 87
\BOOKMARK [2][-]{subsection.5.6.2}{Reading files: read load \040 }{section.5.6}% 88
\BOOKMARK [2][-]{subsection.5.6.3}{Internal directories: NewFold SetFold GetFold DelFold VARS \040 \040 \040}{section.5.6}% 89
\BOOKMARK [0][-]{chapter.6}{The CAS functions}{}% 90
\BOOKMARK [1][-]{section.6.1}{Booleans}{chapter.6}% 91
\BOOKMARK [2][-]{subsection.6.1.1}{The values of a boolean: true false \040 \040 }{section.6.1}% 92
\BOOKMARK [2][-]{subsection.6.1.2}{Tests: == != > >= < =< \040 \040 \040 }{section.6.1}% 93
\BOOKMARK [2][-]{subsection.6.1.3}{Defining functions with boolean tests: ifte ?: when \040 \040 }{section.6.1}% 94
\BOOKMARK [2][-]{subsection.6.1.4}{Boolean operators: or xor and not}{section.6.1}% 95
\BOOKMARK [2][-]{subsection.6.1.5}{Transform a boolean expression to a list: exp2list }{section.6.1}% 96
\BOOKMARK [2][-]{subsection.6.1.6}{Transform a list into a boolean expression: list2exp }{section.6.1}% 97
\BOOKMARK [2][-]{subsection.6.1.7}{Evaluate booleans: evalb }{section.6.1}% 98
\BOOKMARK [1][-]{section.6.2}{Bitwise operators}{chapter.6}% 99
\BOOKMARK [2][-]{subsection.6.2.1}{Basic operators: bitor bitxor bitand}{section.6.2}% 100
\BOOKMARK [2][-]{subsection.6.2.2}{Bitwise Hamming distance: hamdist}{section.6.2}% 101
\BOOKMARK [1][-]{section.6.3}{Strings}{chapter.6}% 102
\BOOKMARK [2][-]{subsection.6.3.1}{Characters and strings: "}{section.6.3}% 103
\BOOKMARK [2][-]{subsection.6.3.2}{The newline character: 92n}{section.6.3}% 104
\BOOKMARK [2][-]{subsection.6.3.3}{The length of a string: size length \040}{section.6.3}% 105
\BOOKMARK [2][-]{subsection.6.3.4}{The left and right parts of a string: left right \040 }{section.6.3}% 106
\BOOKMARK [2][-]{subsection.6.3.5}{First character, middle and end of a string: head mid tail \040 }{section.6.3}% 107
\BOOKMARK [2][-]{subsection.6.3.6}{Concatenation of a sequence of words: cumSum }{section.6.3}% 108
\BOOKMARK [2][-]{subsection.6.3.7}{ASCII code of a character: ord}{section.6.3}% 109
\BOOKMARK [2][-]{subsection.6.3.8}{ASCII code of a string: asc }{section.6.3}% 110
\BOOKMARK [2][-]{subsection.6.3.9}{String defined by the ASCII codes of its characters: char }{section.6.3}% 111
\BOOKMARK [2][-]{subsection.6.3.10}{Find a character in a string: inString }{section.6.3}% 112
\BOOKMARK [2][-]{subsection.6.3.11}{Concat objects into a string: cat }{section.6.3}% 113
\BOOKMARK [2][-]{subsection.6.3.12}{Add an object to a string: + \040}{section.6.3}% 114
\BOOKMARK [2][-]{subsection.6.3.13}{Transform a real number into a string: cat + \040}{section.6.3}% 115
\BOOKMARK [2][-]{subsection.6.3.14}{Transform a string into a number: expr}{section.6.3}% 116
\BOOKMARK [1][-]{section.6.4}{Write an integer in a different base}{chapter.6}% 117
\BOOKMARK [2][-]{subsection.6.4.1}{Writing an integer in base 2, 8 or 16}{section.6.4}% 118
\BOOKMARK [2][-]{subsection.6.4.2}{Writing an integer in an arbitrary base b: convert \040 }{section.6.4}% 119
\BOOKMARK [1][-]{section.6.5}{Integers \(and Gaussian Integers\)}{chapter.6}% 120
\BOOKMARK [2][-]{subsection.6.5.1}{GCD: gcd igcd Gcd }{section.6.5}% 121
\BOOKMARK [2][-]{subsection.6.5.2}{GCD of a list of integers: lgcd }{section.6.5}% 122
\BOOKMARK [2][-]{subsection.6.5.3}{The least common multiple: lcm}{section.6.5}% 123
\BOOKMARK [2][-]{subsection.6.5.4}{Decomposition into prime factors: ifactor }{section.6.5}% 124
\BOOKMARK [2][-]{subsection.6.5.5}{List of prime factors: ifactors }{section.6.5}% 125
\BOOKMARK [2][-]{subsection.6.5.6}{Matrix of factors: maple\137ifactors }{section.6.5}% 126
\BOOKMARK [2][-]{subsection.6.5.7}{The divisors of a number: idivis divisors \040}{section.6.5}% 127
\BOOKMARK [2][-]{subsection.6.5.8}{The integer Euclidean quotient: iquo intDiv div \040 \040}{section.6.5}% 128
\BOOKMARK [2][-]{subsection.6.5.9}{The integer Euclidean remainder: irem remain smod mods mod \045 \040 \040 \040}{section.6.5}% 129
\BOOKMARK [2][-]{subsection.6.5.10}{Euclidean quotient and Euclidean remainder of two integers: iquorem \040}{section.6.5}% 130
\BOOKMARK [2][-]{subsection.6.5.11}{Test of evenness: even }{section.6.5}% 131
\BOOKMARK [2][-]{subsection.6.5.12}{Test of oddness: odd }{section.6.5}% 132
\BOOKMARK [2][-]{subsection.6.5.13}{Test of pseudo-primality: is\137pseudoprime }{section.6.5}% 133
\BOOKMARK [2][-]{subsection.6.5.14}{Test of primality: is\137prime isprime isPrime \040 \040}{section.6.5}% 134
\BOOKMARK [2][-]{subsection.6.5.15}{The smallest pseudo-prime greater than n: nextprime }{section.6.5}% 135
\BOOKMARK [2][-]{subsection.6.5.16}{The greatest pseudo-prime less than n: prevprime }{section.6.5}% 136
\BOOKMARK [2][-]{subsection.6.5.17}{The nth pseudo-prime number: ithprime}{section.6.5}% 137
\BOOKMARK [2][-]{subsection.6.5.18}{The number of pseudo-primes less than or equal to n: nprimes }{section.6.5}% 138
\BOOKMARK [2][-]{subsection.6.5.19}{B\351zout's Identity: iegcd igcdex \040}{section.6.5}% 139
\BOOKMARK [2][-]{subsection.6.5.20}{Solving au+bv=c in Z: iabcuv }{section.6.5}% 140
\BOOKMARK [2][-]{subsection.6.5.21}{Chinese remainders: ichinrem ichrem chrem \040 }{section.6.5}% 141
\BOOKMARK [2][-]{subsection.6.5.22}{Solving a2+b2=p in Z: pa2b2 }{section.6.5}% 142
\BOOKMARK [2][-]{subsection.6.5.23}{The Euler indicatrix: euler phi \040}{section.6.5}% 143
\BOOKMARK [2][-]{subsection.6.5.24}{Legendre symbol: legendre\137symbol }{section.6.5}% 144
\BOOKMARK [2][-]{subsection.6.5.25}{Jacobi symbol: jacobi\137symbol }{section.6.5}% 145
\BOOKMARK [2][-]{subsection.6.5.26}{Listing all compositions of an integer into k parts: icomp }{section.6.5}% 146
\BOOKMARK [1][-]{section.6.6}{Combinatorial analysis}{chapter.6}% 147
\BOOKMARK [2][-]{subsection.6.6.1}{Factorial: factorial ! \040}{section.6.6}% 148
\BOOKMARK [2][-]{subsection.6.6.2}{Binomial coefficients: binomial comb nCr \040 \040 }{section.6.6}% 149
\BOOKMARK [2][-]{subsection.6.6.3}{Permutations: perm nPr \040}{section.6.6}% 150
\BOOKMARK [2][-]{subsection.6.6.4}{Wilf-Zeilberger pairs: wz\137certificate }{section.6.6}% 151
\BOOKMARK [1][-]{section.6.7}{Rational numbers}{chapter.6}% 152
\BOOKMARK [2][-]{subsection.6.7.1}{Transform a floating point number into a rational: exact float2rational }{section.6.7}% 153
\BOOKMARK [2][-]{subsection.6.7.2}{Integer and fractional part: propfrac propFrac \040 }{section.6.7}% 154
\BOOKMARK [2][-]{subsection.6.7.3}{Numerator of a fraction after simplification: numer getNum \040}{section.6.7}% 155
\BOOKMARK [2][-]{subsection.6.7.4}{Denominator of a fraction after simplification: denom getDenom \040}{section.6.7}% 156
\BOOKMARK [2][-]{subsection.6.7.5}{Numerator and denominator of a fraction: f2nd fxnd \040 }{section.6.7}% 157
\BOOKMARK [2][-]{subsection.6.7.6}{Simplification of a pair of integers: simp2 }{section.6.7}% 158
\BOOKMARK [2][-]{subsection.6.7.7}{Continued fraction representation of a real: dfc \040 }{section.6.7}% 159
\BOOKMARK [2][-]{subsection.6.7.8}{Transform a continued fraction representation into a real: dfc2f }{section.6.7}% 160
\BOOKMARK [2][-]{subsection.6.7.9}{The n-th Bernoulli number: bernoulli }{section.6.7}% 161
\BOOKMARK [2][-]{subsection.6.7.10}{Access to PARI/GP commands: pari \040}{section.6.7}% 162
\BOOKMARK [1][-]{section.6.8}{Real numbers}{chapter.6}% 163
\BOOKMARK [2][-]{subsection.6.8.1}{Evaluate a real at a given precision: evalf Digits DIGITS \040 \040}{section.6.8}% 164
\BOOKMARK [2][-]{subsection.6.8.2}{The standard infixed operators on real numbers: + - * / \136 \040 \040 \040}{section.6.8}% 165
\BOOKMARK [2][-]{subsection.6.8.3}{Prefixed division on reals: rdiv }{section.6.8}% 166
\BOOKMARK [2][-]{subsection.6.8.4}{n-th root: root }{section.6.8}% 167
\BOOKMARK [2][-]{subsection.6.8.5}{The exponential integral function: Ei }{section.6.8}% 168
\BOOKMARK [2][-]{subsection.6.8.6}{The logarithmic integral function: Li }{section.6.8}% 169
\BOOKMARK [2][-]{subsection.6.8.7}{The cosine integral function: Ci }{section.6.8}% 170
\BOOKMARK [2][-]{subsection.6.8.8}{The sine integral function: Si }{section.6.8}% 171
\BOOKMARK [2][-]{subsection.6.8.9}{The Heaviside function: Heaviside }{section.6.8}% 172
\BOOKMARK [2][-]{subsection.6.8.10}{The Dirac distribution: Dirac }{section.6.8}% 173
\BOOKMARK [2][-]{subsection.6.8.11}{Error function: erf }{section.6.8}% 174
\BOOKMARK [2][-]{subsection.6.8.12}{Complementary error function: erfc }{section.6.8}% 175
\BOOKMARK [2][-]{subsection.6.8.13}{The \040function: Gamma \040}{section.6.8}% 176
\BOOKMARK [2][-]{subsection.6.8.14}{The upper incomplete \040function: ugamma }{section.6.8}% 177
\BOOKMARK [2][-]{subsection.6.8.15}{The lower incomplete \040function: igamma \040}{section.6.8}% 178
\BOOKMARK [2][-]{subsection.6.8.16}{The \040function: Beta \040}{section.6.8}% 179
\BOOKMARK [2][-]{subsection.6.8.17}{Derivatives of the DiGamma function: Psi }{section.6.8}% 180
\BOOKMARK [2][-]{subsection.6.8.18}{The \040function: Zeta }{section.6.8}% 181
\BOOKMARK [2][-]{subsection.6.8.19}{Airy functions: Airy\137Ai and Airy\137Bi \040}{section.6.8}% 182
\BOOKMARK [1][-]{section.6.9}{Permutations}{chapter.6}% 183
\BOOKMARK [2][-]{subsection.6.9.1}{Random permutation: randperm shuffle \040}{section.6.9}% 184
\BOOKMARK [2][-]{subsection.6.9.2}{Previous and next permutation: prevperm nextperm \040}{section.6.9}% 185
\BOOKMARK [2][-]{subsection.6.9.3}{Decomposition of a permuation as a product of disjoint cycles: permu2cycles }{section.6.9}% 186
\BOOKMARK [2][-]{subsection.6.9.4}{Product of cycles to permutation: cycles2permu }{section.6.9}% 187
\BOOKMARK [2][-]{subsection.6.9.5}{Transform a cycle into a permutation: cycle2perm }{section.6.9}% 188
\BOOKMARK [2][-]{subsection.6.9.6}{Transform a permutation into a matrix: permu2mat \040}{section.6.9}% 189
\BOOKMARK [2][-]{subsection.6.9.7}{Checking for a permutation: is\137permu }{section.6.9}% 190
\BOOKMARK [2][-]{subsection.6.9.8}{Checking for a cycle: is\137cycle }{section.6.9}% 191
\BOOKMARK [2][-]{subsection.6.9.9}{Product of two permutations: p1op2 c1op2 p1oc2 c1oc2 \040 \040}{section.6.9}% 192
\BOOKMARK [2][-]{subsection.6.9.10}{Signature of a permutation: signature }{section.6.9}% 193
\BOOKMARK [2][-]{subsection.6.9.11}{Inverse of a permutation: perminv }{section.6.9}% 194
\BOOKMARK [2][-]{subsection.6.9.12}{Inverse of a cycle: cycleinv }{section.6.9}% 195
\BOOKMARK [2][-]{subsection.6.9.13}{Order of a permutation: permuorder }{section.6.9}% 196
\BOOKMARK [2][-]{subsection.6.9.14}{The group generated by two permutations: groupermu }{section.6.9}% 197
\BOOKMARK [1][-]{section.6.10}{Complex numbers}{chapter.6}% 198
\BOOKMARK [2][-]{subsection.6.10.1}{The usual complex operators: + - * / \136 \040 \040 \040}{section.6.10}% 199
\BOOKMARK [2][-]{subsection.6.10.2}{The real and imaginary parts of a complex number: re real im imag \040 \040 }{section.6.10}% 200
\BOOKMARK [2][-]{subsection.6.10.3}{Write a complex number z in rectangular form: evalc }{section.6.10}% 201
\BOOKMARK [2][-]{subsection.6.10.4}{The modulus and argument of a complex number: abs arg \040 }{section.6.10}% 202
\BOOKMARK [2][-]{subsection.6.10.5}{The normalized complex number: normalize unitV \040}{section.6.10}% 203
\BOOKMARK [2][-]{subsection.6.10.6}{Conjugate of a complex number: conj}{section.6.10}% 204
\BOOKMARK [2][-]{subsection.6.10.7}{Multiplication by the complex conjugate: mult\137c\137conjugate }{section.6.10}% 205
\BOOKMARK [2][-]{subsection.6.10.8}{Barycenter of complex numbers: barycenter \040}{section.6.10}% 206
\BOOKMARK [1][-]{section.6.11}{Algebraic numbers}{chapter.6}% 207
\BOOKMARK [2][-]{subsection.6.11.1}{Definition}{section.6.11}% 208
\BOOKMARK [2][-]{subsection.6.11.2}{Minimum polynomial of an algebraic number: pmin }{section.6.11}% 209
\BOOKMARK [1][-]{section.6.12}{Algebraic expressions}{chapter.6}% 210
\BOOKMARK [2][-]{subsection.6.12.1}{Evaluate an expression: eval \040}{section.6.12}% 211
\BOOKMARK [2][-]{subsection.6.12.2}{Change the evaluation level: eval\137level }{section.6.12}% 212
\BOOKMARK [2][-]{subsection.6.12.3}{Evaluate algebraic expressions: evala }{section.6.12}% 213
\BOOKMARK [2][-]{subsection.6.12.4}{Prevent evaluation: quote hold ' \040 \040}{section.6.12}% 214
\BOOKMARK [2][-]{subsection.6.12.5}{Force evaluation: unquote }{section.6.12}% 215
\BOOKMARK [2][-]{subsection.6.12.6}{Distribution: expand fdistrib \040}{section.6.12}% 216
\BOOKMARK [2][-]{subsection.6.12.7}{Canonical form: canonical\137form }{section.6.12}% 217
\BOOKMARK [2][-]{subsection.6.12.8}{Multiplication by the conjugate quantity: mult\137conjugate }{section.6.12}% 218
\BOOKMARK [2][-]{subsection.6.12.9}{Separation of variables: split }{section.6.12}% 219
\BOOKMARK [2][-]{subsection.6.12.10}{Factorization: factor cfactor }{section.6.12}% 220
\BOOKMARK [2][-]{subsection.6.12.11}{Zeros of an expression: zeros }{section.6.12}% 221
\BOOKMARK [2][-]{subsection.6.12.12}{Regrouping expressions: regroup \040}{section.6.12}% 222
\BOOKMARK [2][-]{subsection.6.12.13}{Normal form: normal }{section.6.12}% 223
\BOOKMARK [2][-]{subsection.6.12.14}{Simplify: simplify}{section.6.12}% 224
\BOOKMARK [2][-]{subsection.6.12.15}{Automatic simplification: autosimplify }{section.6.12}% 225
\BOOKMARK [2][-]{subsection.6.12.16}{Normal form for rational functions: ratnormal \040}{section.6.12}% 226
\BOOKMARK [2][-]{subsection.6.12.17}{Substitute a variable by a value: | }{section.6.12}% 227
\BOOKMARK [2][-]{subsection.6.12.18}{Substitute a variable by a value: subst}{section.6.12}% 228
\BOOKMARK [2][-]{subsection.6.12.19}{Substitute a variable by a value: \(\) }{section.6.12}% 229
\BOOKMARK [2][-]{subsection.6.12.20}{Substitute a variable by a value \(Maple and Mupad compatibility\): subs }{section.6.12}% 230
\BOOKMARK [2][-]{subsection.6.12.21}{Substitute a subexpression by another expression: algsubs }{section.6.12}% 231
\BOOKMARK [2][-]{subsection.6.12.22}{Eliminate one or more variables from a list of equations: eliminate }{section.6.12}% 232
\BOOKMARK [2][-]{subsection.6.12.23}{Evaluate a primitive at boundaries: preval }{section.6.12}% 233
\BOOKMARK [2][-]{subsection.6.12.24}{Sub-expression of an expression: part }{section.6.12}% 234
\BOOKMARK [1][-]{section.6.13}{Values of a sequence un}{chapter.6}% 235
\BOOKMARK [2][-]{subsection.6.13.1}{Array of values of a sequence : tablefunc }{section.6.13}% 236
\BOOKMARK [2][-]{subsection.6.13.2}{Values of a recurrence relation or a system: seqsolve \040}{section.6.13}% 237
\BOOKMARK [2][-]{subsection.6.13.3}{Values of a recurrence relation or a system: rsolve \040}{section.6.13}% 238
\BOOKMARK [2][-]{subsection.6.13.4}{Table of values and graph of a recurrent sequence: tableseq}{section.6.13}% 239
\BOOKMARK [1][-]{section.6.14}{Operators or infixed functions}{chapter.6}% 240
\BOOKMARK [2][-]{subsection.6.14.1}{Xcas operators: \040 \044 \045 \040 \040 }{section.6.14}% 241
\BOOKMARK [2][-]{subsection.6.14.2}{Define an operator: user\137operator \040 \040 \040}{section.6.14}% 242
\BOOKMARK [1][-]{section.6.15}{Functions and expressions with symbolic variables}{chapter.6}% 243
\BOOKMARK [2][-]{subsection.6.15.1}{The difference between a function and an expression \040 }{section.6.15}% 244
\BOOKMARK [2][-]{subsection.6.15.2}{Transform an expression into a function: unapply \040}{section.6.15}% 245
\BOOKMARK [2][-]{subsection.6.15.3}{Top and leaves of an expression: sommet feuille op left right \040 \040 \040}{section.6.15}% 246
\BOOKMARK [1][-]{section.6.16}{Functions}{chapter.6}% 247
\BOOKMARK [2][-]{subsection.6.16.1}{Context-dependent functions.}{section.6.16}% 248
\BOOKMARK [2][-]{subsection.6.16.2}{Standard functions}{section.6.16}% 249
\BOOKMARK [2][-]{subsection.6.16.3}{Defining algebraic functions}{section.6.16}% 250
\BOOKMARK [2][-]{subsection.6.16.4}{Composition of two functions: @}{section.6.16}% 251
\BOOKMARK [2][-]{subsection.6.16.5}{Repeated function composition: @@ }{section.6.16}% 252
\BOOKMARK [2][-]{subsection.6.16.6}{Define a function with history: as\137function\137of }{section.6.16}% 253
\BOOKMARK [1][-]{section.6.17}{Getting information about functions from R to R}{chapter.6}% 254
\BOOKMARK [2][-]{subsection.6.17.1}{The domain of a function: domain }{section.6.17}% 255
\BOOKMARK [2][-]{subsection.6.17.2}{Table of variations of a function: tabvar }{section.6.17}% 256
\BOOKMARK [1][-]{section.6.18}{Limits: limit }{chapter.6}% 257
\BOOKMARK [1][-]{section.6.19}{Derivation and applications}{chapter.6}% 258
\BOOKMARK [2][-]{subsection.6.19.1}{Functional derivative: function\137diff }{section.6.19}% 259
\BOOKMARK [2][-]{subsection.6.19.2}{Length of an arc: arcLen \040}{section.6.19}% 260
\BOOKMARK [2][-]{subsection.6.19.3}{Maximum and minimum of an expression: fMax fMin \040}{section.6.19}% 261
\BOOKMARK [2][-]{subsection.6.19.4}{Derivatives and partial derivatives \040 \040}{section.6.19}% 262
\BOOKMARK [2][-]{subsection.6.19.5}{Implicit differentiation: implicitdiff }{section.6.19}% 263
\BOOKMARK [1][-]{section.6.20}{Integration}{chapter.6}% 264
\BOOKMARK [2][-]{subsection.6.20.1}{Antiderivative and definite integral: integrate int Int \040 \040}{section.6.20}% 265
\BOOKMARK [2][-]{subsection.6.20.2}{Primitive and definite integral: risch }{section.6.20}% 266
\BOOKMARK [2][-]{subsection.6.20.3}{Discrete summation: sum \040}{section.6.20}% 267
\BOOKMARK [2][-]{subsection.6.20.4}{Riemann sum: sum\137riemann }{section.6.20}% 268
\BOOKMARK [2][-]{subsection.6.20.5}{Integration by parts}{section.6.20}% 269
\BOOKMARK [2][-]{subsection.6.20.6}{Change of variables: subst}{section.6.20}% 270
\BOOKMARK [2][-]{subsection.6.20.7}{Integrals and limits}{section.6.20}% 271
\BOOKMARK [1][-]{section.6.21}{Multivariate calculus}{chapter.6}% 272
\BOOKMARK [2][-]{subsection.6.21.1}{Gradient: derive deriver diff grad \040 \040 \040}{section.6.21}% 273
\BOOKMARK [2][-]{subsection.6.21.2}{Laplacian: laplacian }{section.6.21}% 274
\BOOKMARK [2][-]{subsection.6.21.3}{Hessian matrix: hessian \040}{section.6.21}% 275
\BOOKMARK [2][-]{subsection.6.21.4}{Divergence: divergence }{section.6.21}% 276
\BOOKMARK [2][-]{subsection.6.21.5}{Rotational: curl }{section.6.21}% 277
\BOOKMARK [2][-]{subsection.6.21.6}{Potential: potential }{section.6.21}% 278
\BOOKMARK [2][-]{subsection.6.21.7}{Conservative flux field: vpotential }{section.6.21}% 279
\BOOKMARK [2][-]{subsection.6.21.8}{Determining where a function is convex: convex }{section.6.21}% 280
\BOOKMARK [1][-]{section.6.22}{Calculus of variations}{chapter.6}% 281
\BOOKMARK [2][-]{subsection.6.22.1}{The Brachistochrone Problem}{section.6.22}% 282
\BOOKMARK [2][-]{subsection.6.22.2}{Euler-Lagrange equation\(s\): euler\137lagrange }{section.6.22}% 283
\BOOKMARK [2][-]{subsection.6.22.3}{Solution of the Brachistochrone Problem}{section.6.22}% 284
\BOOKMARK [2][-]{subsection.6.22.4}{Jacobi equation: jacobi\137equation }{section.6.22}% 285
\BOOKMARK [2][-]{subsection.6.22.5}{Finding conjugate points: conjugate\137equation }{section.6.22}% 286
\BOOKMARK [2][-]{subsection.6.22.6}{An example: Finding the surface of revolution with minimal area}{section.6.22}% 287
\BOOKMARK [1][-]{section.6.23}{Trigonometry}{chapter.6}% 288
\BOOKMARK [2][-]{subsection.6.23.1}{Expand a trigonometric expression: trigexpand \040}{section.6.23}% 289
\BOOKMARK [2][-]{subsection.6.23.2}{Linearize a trigonometric expression: tlin \040}{section.6.23}% 290
\BOOKMARK [2][-]{subsection.6.23.3}{Increase the phase by /2 in a trigonometric expression: shift\137phase }{section.6.23}% 291
\BOOKMARK [2][-]{subsection.6.23.4}{Put together sine and cosine of the same angle: tcollect tCollect \040 }{section.6.23}% 292
\BOOKMARK [2][-]{subsection.6.23.5}{Simplify: simplify }{section.6.23}% 293
\BOOKMARK [2][-]{subsection.6.23.6}{Simplify trigonometric expressions: trigsimplify }{section.6.23}% 294
\BOOKMARK [2][-]{subsection.6.23.7}{Transform arccos into arcsin: acos2asin }{section.6.23}% 295
\BOOKMARK [2][-]{subsection.6.23.8}{Transform arccos into arctan: acos2atan }{section.6.23}% 296
\BOOKMARK [2][-]{subsection.6.23.9}{Transform arcsin into arccos: asin2acos }{section.6.23}% 297
\BOOKMARK [2][-]{subsection.6.23.10}{Transform arcsin into arctan: asin2atan }{section.6.23}% 298
\BOOKMARK [2][-]{subsection.6.23.11}{Transform arctan into arcsin: atan2asin }{section.6.23}% 299
\BOOKMARK [2][-]{subsection.6.23.12}{Transform arctan into arccos: atan2acos }{section.6.23}% 300
\BOOKMARK [2][-]{subsection.6.23.13}{Transform complex exponentials into sin and cos: sincos exp2trig }{section.6.23}% 301
\BOOKMARK [2][-]{subsection.6.23.14}{Transform tan\(x\) into sin\(x\)/cos\(x\): tan2sincos }{section.6.23}% 302
\BOOKMARK [2][-]{subsection.6.23.15}{Transform sin\(x\) into cos\(x\)*tan\(x\): sin2costan }{section.6.23}% 303
\BOOKMARK [2][-]{subsection.6.23.16}{Transform cos\(x\) into sin\(x\)/tan\(x\): cos2sintan }{section.6.23}% 304
\BOOKMARK [2][-]{subsection.6.23.17}{Rewrite tan\(x\) with sin\(2x\) and cos\(2x\): tan2sincos2 }{section.6.23}% 305
\BOOKMARK [2][-]{subsection.6.23.18}{Rewrite tan\(x\) with cos\(2x\) and sin\(2x\): tan2cossin2 }{section.6.23}% 306
\BOOKMARK [2][-]{subsection.6.23.19}{Rewrite sin, cos, tan in terms of tan\(x/2\): halftan }{section.6.23}% 307
\BOOKMARK [2][-]{subsection.6.23.20}{Rewrite trigonometric functions as function of tan\(x/2\) and hyperbolic functions as function of exp\(x\): halftan\137hyp2exp }{section.6.23}% 308
\BOOKMARK [2][-]{subsection.6.23.21}{Transform trigonometric functions into complex exponentials : trig2exp }{section.6.23}% 309
\BOOKMARK [2][-]{subsection.6.23.22}{Transform inverse trigonometric functions into logarithms: atrig2ln }{section.6.23}% 310
\BOOKMARK [2][-]{subsection.6.23.23}{Simplify and express preferentially with sines: trigsin \040}{section.6.23}% 311
\BOOKMARK [2][-]{subsection.6.23.24}{Simplify and express preferentially with cosines: trigcos \040}{section.6.23}% 312
\BOOKMARK [2][-]{subsection.6.23.25}{Simplify and express preferentially with tangents: trigtan \040}{section.6.23}% 313
\BOOKMARK [2][-]{subsection.6.23.26}{Rewrite an expression with different options: convert convertir => \040 \040 \040 \040 \040 \040 \040 \040 \040 \040}{section.6.23}% 314
\BOOKMARK [1][-]{section.6.24}{Exponentials and Logarithms}{chapter.6}% 315
\BOOKMARK [2][-]{subsection.6.24.1}{Rewrite hyperbolic functions as exponentials: hyp2exp }{section.6.24}% 316
\BOOKMARK [2][-]{subsection.6.24.2}{Expand exponentials: expexpand \040}{section.6.24}% 317
\BOOKMARK [2][-]{subsection.6.24.3}{Expand logarithms: lnexpand \040}{section.6.24}% 318
\BOOKMARK [2][-]{subsection.6.24.4}{Linearize exponentials: lin \040}{section.6.24}% 319
\BOOKMARK [2][-]{subsection.6.24.5}{Collect logarithms: lncollect \040}{section.6.24}% 320
\BOOKMARK [2][-]{subsection.6.24.6}{Expand powers: powexpand \040}{section.6.24}% 321
\BOOKMARK [2][-]{subsection.6.24.7}{Rewrite a power as an exponential: pow2exp \040}{section.6.24}% 322
\BOOKMARK [2][-]{subsection.6.24.8}{Rewrite exp\(n*ln\(x\)\) as a power: exp2pow }{section.6.24}% 323
\BOOKMARK [2][-]{subsection.6.24.9}{Simplify complex exponentials: tsimplify }{section.6.24}% 324
\BOOKMARK [1][-]{section.6.25}{Rewriting transcendental and trigonometric expressions}{chapter.6}% 325
\BOOKMARK [2][-]{subsection.6.25.1}{Expand a transcendental and trigonometric expression: texpand tExpand \040 }{section.6.25}% 326
\BOOKMARK [2][-]{subsection.6.25.2}{Combine terms of the same type: combine \040 }{section.6.25}% 327
\BOOKMARK [1][-]{section.6.26}{Fourier transformation}{chapter.6}% 328
\BOOKMARK [2][-]{subsection.6.26.1}{Fourier coefficients: fourier\137an and fourier\137bn or fourier\137cn }{section.6.26}% 329
\BOOKMARK [2][-]{subsection.6.26.2}{Continuous Fourier Transform: fourier ifourier addtable \040 \040}{section.6.26}% 330
\BOOKMARK [2][-]{subsection.6.26.3}{Discrete Fourier Transform and the Fast Fourier Transform}{section.6.26}% 331
\BOOKMARK [2][-]{subsection.6.26.4}{An exercise with fft}{section.6.26}% 332
\BOOKMARK [1][-]{section.6.27}{Polynomials}{chapter.6}% 333
\BOOKMARK [2][-]{subsection.6.27.1}{Polynomials of a single variable: poly1 \040}{section.6.27}% 334
\BOOKMARK [2][-]{subsection.6.27.2}{Polynomials of several variables: \045\045\045\173 \045\045\045\175}{section.6.27}% 335
\BOOKMARK [2][-]{subsection.6.27.3}{Apply a function to the internal sparse format of a polynomial: map }{section.6.27}% 336
\BOOKMARK [2][-]{subsection.6.27.4}{Convert to a symbolic polynomial: r2e poly2symb \040}{section.6.27}% 337
\BOOKMARK [2][-]{subsection.6.27.5}{Convert from a symbolic polynomial: e2r symb2poly \040}{section.6.27}% 338
\BOOKMARK [2][-]{subsection.6.27.6}{Transform a polynomial in internal format into a list, and conversely: convert \040}{section.6.27}% 339
\BOOKMARK [2][-]{subsection.6.27.7}{Coefficients of a polynomial: coeff coeffs \040}{section.6.27}% 340
\BOOKMARK [2][-]{subsection.6.27.8}{Polynomial degree: degree }{section.6.27}% 341
\BOOKMARK [2][-]{subsection.6.27.9}{Polynomial valuation: valuation ldegree \040}{section.6.27}% 342
\BOOKMARK [2][-]{subsection.6.27.10}{Leading coefficient of a polynomial: lcoeff }{section.6.27}% 343
\BOOKMARK [2][-]{subsection.6.27.11}{Trailing coefficient degree of a polynomial: tcoeff }{section.6.27}% 344
\BOOKMARK [2][-]{subsection.6.27.12}{Evaluation of a polynomial: peval polyEval \040}{section.6.27}% 345
\BOOKMARK [2][-]{subsection.6.27.13}{Factorize xn in a polynomial: factor\137xn }{section.6.27}% 346
\BOOKMARK [2][-]{subsection.6.27.14}{GCD of the coefficients of a polynomial: content }{section.6.27}% 347
\BOOKMARK [2][-]{subsection.6.27.15}{Primitive part of a polynomial: primpart }{section.6.27}% 348
\BOOKMARK [2][-]{subsection.6.27.16}{Factoring: collect \040}{section.6.27}% 349
\BOOKMARK [2][-]{subsection.6.27.17}{Square-free factorization: sqrfree }{section.6.27}% 350
\BOOKMARK [2][-]{subsection.6.27.18}{List of factors: factors }{section.6.27}% 351
\BOOKMARK [2][-]{subsection.6.27.19}{Evaluate a polynomial: horner }{section.6.27}% 352
\BOOKMARK [2][-]{subsection.6.27.20}{Rewrite in terms of the powers of \(x-a\): ptayl }{section.6.27}% 353
\BOOKMARK [2][-]{subsection.6.27.21}{Compute with the exact root of a polynomial: rootof \040}{section.6.27}% 354
\BOOKMARK [2][-]{subsection.6.27.22}{Exact roots of a polynomial: roots }{section.6.27}% 355
\BOOKMARK [2][-]{subsection.6.27.23}{Coefficients of a polynomial defined by its roots: pcoeff pcoef }{section.6.27}% 356
\BOOKMARK [2][-]{subsection.6.27.24}{Truncate of order n: truncate }{section.6.27}% 357
\BOOKMARK [2][-]{subsection.6.27.25}{Convert a series expansion into a polynomial: convert convertir \040 }{section.6.27}% 358
\BOOKMARK [2][-]{subsection.6.27.26}{Random polynomial: randpoly randPoly \040 }{section.6.27}% 359
\BOOKMARK [2][-]{subsection.6.27.27}{Change the order of variables: reorder }{section.6.27}% 360
\BOOKMARK [2][-]{subsection.6.27.28}{Random list: ranm }{section.6.27}% 361
\BOOKMARK [2][-]{subsection.6.27.29}{Lagrange polynomial: lagrange interp }{section.6.27}% 362
\BOOKMARK [2][-]{subsection.6.27.30}{Trigonometric interpolation: triginterp}{section.6.27}% 363
\BOOKMARK [2][-]{subsection.6.27.31}{Natural splines: spline }{section.6.27}% 364
\BOOKMARK [2][-]{subsection.6.27.32}{Natural interpolation: spline}{section.6.27}% 365
\BOOKMARK [2][-]{subsection.6.27.33}{Rational interpolation: thiele }{section.6.27}% 366
\BOOKMARK [1][-]{section.6.28}{Arithmetic and polynomials}{chapter.6}% 367
\BOOKMARK [2][-]{subsection.6.28.1}{The divisors of a polynomial: divis }{section.6.28}% 368
\BOOKMARK [2][-]{subsection.6.28.2}{Euclidean quotient: quo Quo \040}{section.6.28}% 369
\BOOKMARK [2][-]{subsection.6.28.3}{Euclidean remainder: rem Rem \040 }{section.6.28}% 370
\BOOKMARK [2][-]{subsection.6.28.4}{Quotient and remainder: quorem divide }{section.6.28}% 371
\BOOKMARK [2][-]{subsection.6.28.5}{GCD of two polynomials with the Euclidean algorithm: gcd Gcd \040 }{section.6.28}% 372
\BOOKMARK [2][-]{subsection.6.28.6}{GCD of two polynomials with the Euclidean algorithm: Gcd \040}{section.6.28}% 373
\BOOKMARK [2][-]{subsection.6.28.7}{Choosing the GCD algorithm of two polynomials: ezgcd heugcd modgcd psrgcd \040 \040}{section.6.28}% 374
\BOOKMARK [2][-]{subsection.6.28.8}{LCM of two polynomials: lcm }{section.6.28}% 375
\BOOKMARK [2][-]{subsection.6.28.9}{B\351zout's Identity: egcd gcdex \040}{section.6.28}% 376
\BOOKMARK [2][-]{subsection.6.28.10}{Solving au+bv=c over polynomials: abcuv }{section.6.28}% 377
\BOOKMARK [2][-]{subsection.6.28.11}{Chinese remainders: chinrem }{section.6.28}% 378
\BOOKMARK [2][-]{subsection.6.28.12}{Cyclotomic polynomial: cyclotomic }{section.6.28}% 379
\BOOKMARK [2][-]{subsection.6.28.13}{Sturm sequences and number of sign changes of P on \(a, b]: sturm sturmseq sturmab \040 }{section.6.28}% 380
\BOOKMARK [2][-]{subsection.6.28.14}{Sylvester matrix of two polynomials and resultant: sylvester resultant \040}{section.6.28}% 381
\BOOKMARK [1][-]{section.6.29}{Exact bounds for roots of a polynomial}{chapter.6}% 382
\BOOKMARK [2][-]{subsection.6.29.1}{Exact bounds for real roots of a polynomial: realroot }{section.6.29}% 383
\BOOKMARK [2][-]{subsection.6.29.2}{Exact bounds for complex roots of a polynomial: complexroot }{section.6.29}% 384
\BOOKMARK [2][-]{subsection.6.29.3}{Exact bounds for real roots of a polynomial: VAS }{section.6.29}% 385
\BOOKMARK [2][-]{subsection.6.29.4}{Exact bounds for positive real roots of a polynomial: VAS\137positive }{section.6.29}% 386
\BOOKMARK [2][-]{subsection.6.29.5}{An upper bound for the positive real roots of a polynomial: posubLMQ }{section.6.29}% 387
\BOOKMARK [2][-]{subsection.6.29.6}{A lower bound for the positive real roots of a polynomial: poslbdLMQ }{section.6.29}% 388
\BOOKMARK [2][-]{subsection.6.29.7}{Exact values of rational roots of a polynomial: rationalroot }{section.6.29}% 389
\BOOKMARK [2][-]{subsection.6.29.8}{Exact values of the complex rational roots of a polynomial: crationalroot }{section.6.29}% 390
\BOOKMARK [1][-]{section.6.30}{Orthogonal polynomials}{chapter.6}% 391
\BOOKMARK [2][-]{subsection.6.30.1}{Legendre polynomials: legendre }{section.6.30}% 392
\BOOKMARK [2][-]{subsection.6.30.2}{Hermite polynomial: hermite }{section.6.30}% 393
\BOOKMARK [2][-]{subsection.6.30.3}{Laguerre polynomials: laguerre }{section.6.30}% 394
\BOOKMARK [2][-]{subsection.6.30.4}{Tchebychev polynomials of the first kind: tchebyshev1 }{section.6.30}% 395
\BOOKMARK [2][-]{subsection.6.30.5}{Tchebychev polynomial of the second kind: tchebyshev2 }{section.6.30}% 396
\BOOKMARK [1][-]{section.6.31}{Gr\366bner basis and Gr\366bner reduction}{chapter.6}% 397
\BOOKMARK [2][-]{subsection.6.31.1}{Gr\366bner basis: gbasis }{section.6.31}% 398
\BOOKMARK [2][-]{subsection.6.31.2}{Gr\366bner reduction: greduce }{section.6.31}% 399
\BOOKMARK [2][-]{subsection.6.31.3}{Test if a polynomial or list of polynomials belongs to an ideal given by a Gr\366bner basis: in\137ideal }{section.6.31}% 400
\BOOKMARK [2][-]{subsection.6.31.4}{Build a polynomial from its evaluation: genpoly }{section.6.31}% 401
\BOOKMARK [1][-]{section.6.32}{Rational functions}{chapter.6}% 402
\BOOKMARK [2][-]{subsection.6.32.1}{Numerator: getNum }{section.6.32}% 403
\BOOKMARK [2][-]{subsection.6.32.2}{Numerator after simplification: numer }{section.6.32}% 404
\BOOKMARK [2][-]{subsection.6.32.3}{Denominator: getDenom}{section.6.32}% 405
\BOOKMARK [2][-]{subsection.6.32.4}{Denominator after simplification: denom }{section.6.32}% 406
\BOOKMARK [2][-]{subsection.6.32.5}{Numerator and denominator: f2nd fxnd \040}{section.6.32}% 407
\BOOKMARK [2][-]{subsection.6.32.6}{Simplify: simp2 }{section.6.32}% 408
\BOOKMARK [2][-]{subsection.6.32.7}{Common denominator: comDenom }{section.6.32}% 409
\BOOKMARK [2][-]{subsection.6.32.8}{Polynomial and fractional part: propfrac }{section.6.32}% 410
\BOOKMARK [2][-]{subsection.6.32.9}{Partial fraction expansion: partfrac cpartfrac \040 }{section.6.32}% 411
\BOOKMARK [1][-]{section.6.33}{Exact roots and poles}{chapter.6}% 412
\BOOKMARK [2][-]{subsection.6.33.1}{Roots and poles of a rational function: froot }{section.6.33}% 413
\BOOKMARK [2][-]{subsection.6.33.2}{Rational function given by roots and poles: fcoeff }{section.6.33}% 414
\BOOKMARK [1][-]{section.6.34}{Computing in Z/pZ or in Z/pZ[x] }{chapter.6}% 415
\BOOKMARK [2][-]{subsection.6.34.1}{Expand and reduce: normal }{section.6.34}% 416
\BOOKMARK [2][-]{subsection.6.34.2}{Addition in Z/pZ or in \040Z/pZ[x]: + \040}{section.6.34}% 417
\BOOKMARK [2][-]{subsection.6.34.3}{Subtraction in Z/pZ or in \040Z/pZ[x]: - }{section.6.34}% 418
\BOOKMARK [2][-]{subsection.6.34.4}{Multiplication in Z/pZ or in \040Z/pZ[x]: * }{section.6.34}% 419
\BOOKMARK [2][-]{subsection.6.34.5}{Euclidean quotient : quo }{section.6.34}% 420
\BOOKMARK [2][-]{subsection.6.34.6}{Euclidean remainder: rem }{section.6.34}% 421
\BOOKMARK [2][-]{subsection.6.34.7}{Euclidean quotient and euclidean remainder: quorem }{section.6.34}% 422
\BOOKMARK [2][-]{subsection.6.34.8}{Division in Z/pZ or in Z/pZ[x]: / }{section.6.34}% 423
\BOOKMARK [2][-]{subsection.6.34.9}{Power in Z/pZ and in Z/pZ[x]: \136}{section.6.34}% 424
\BOOKMARK [2][-]{subsection.6.34.10}{Compute an -5mumod5mu- p: powmod powermod }{section.6.34}% 425
\BOOKMARK [2][-]{subsection.6.34.11}{Inverse in Z/pZ: inv inverse / \040}{section.6.34}% 426
\BOOKMARK [2][-]{subsection.6.34.12}{Rebuild a fraction from its value modulo p: fracmod \040iratrecon \040}{section.6.34}% 427
\BOOKMARK [2][-]{subsection.6.34.13}{GCD in Z/pZ[x]: gcd }{section.6.34}% 428
\BOOKMARK [2][-]{subsection.6.34.14}{Factorization over Z/pZ[x]: factor factoriser \040}{section.6.34}% 429
\BOOKMARK [2][-]{subsection.6.34.15}{Determinant of a matrix in Z/pZ: det }{section.6.34}% 430
\BOOKMARK [2][-]{subsection.6.34.16}{Inverse of a matrix with coefficients in Z/pZ: inv inverse \040}{section.6.34}% 431
\BOOKMARK [2][-]{subsection.6.34.17}{Row reduction to echelon form in Z/pZ: rref \040}{section.6.34}% 432
\BOOKMARK [2][-]{subsection.6.34.18}{Construction of a Galois field: GF }{section.6.34}% 433
\BOOKMARK [2][-]{subsection.6.34.19}{Factorize a polynomial with coefficients in a Galois field: factor }{section.6.34}% 434
\BOOKMARK [1][-]{section.6.35}{Compute in Z/pZ[x] using Maple syntax \040 }{chapter.6}% 435
\BOOKMARK [2][-]{subsection.6.35.1}{Euclidean quotient: Quo }{section.6.35}% 436
\BOOKMARK [2][-]{subsection.6.35.2}{Euclidean remainder: Rem }{section.6.35}% 437
\BOOKMARK [2][-]{subsection.6.35.3}{GCD in Z/pZ[x]: Gcd }{section.6.35}% 438
\BOOKMARK [2][-]{subsection.6.35.4}{Factorization in Z/pZ[x]: Factor }{section.6.35}% 439
\BOOKMARK [2][-]{subsection.6.35.5}{Determinant of a matrix with coefficients in Z/pZ: Det }{section.6.35}% 440
\BOOKMARK [2][-]{subsection.6.35.6}{Inverse of a matrix in Z/pZ: Inverse }{section.6.35}% 441
\BOOKMARK [2][-]{subsection.6.35.7}{Row reduction to echelon form in Z/pZ: Rref }{section.6.35}% 442
\BOOKMARK [1][-]{section.6.36}{Taylor and asymptotic expansions}{chapter.6}% 443
\BOOKMARK [2][-]{subsection.6.36.1}{Division by increasing power order: divpc }{section.6.36}% 444
\BOOKMARK [2][-]{subsection.6.36.2}{Series expansion: taylor series \040 }{section.6.36}% 445
\BOOKMARK [2][-]{subsection.6.36.3}{The inverse of a series: revert }{section.6.36}% 446
\BOOKMARK [2][-]{subsection.6.36.4}{The residue of an expression at a point: residue }{section.6.36}% 447
\BOOKMARK [2][-]{subsection.6.36.5}{Pad\351 expansion: pade }{section.6.36}% 448
\BOOKMARK [1][-]{section.6.37}{Ranges of values}{chapter.6}% 449
\BOOKMARK [2][-]{subsection.6.37.1}{Definition of a range of values: .. \040}{section.6.37}% 450
\BOOKMARK [2][-]{subsection.6.37.2}{Center of a range of values: interval2center }{section.6.37}% 451
\BOOKMARK [2][-]{subsection.6.37.3}{Ranges of values defined by their center: center2interval }{section.6.37}% 452
\BOOKMARK [1][-]{section.6.38}{Intervals}{chapter.6}% 453
\BOOKMARK [2][-]{subsection.6.38.1}{Defining intervals: i[] }{section.6.38}% 454
\BOOKMARK [2][-]{subsection.6.38.2}{The endpoints of an interval: left right \040 }{section.6.38}% 455
\BOOKMARK [2][-]{subsection.6.38.3}{Interval arithmetic: + - * / \040 \040}{section.6.38}% 456
\BOOKMARK [2][-]{subsection.6.38.4}{The midpoint of an interval: midpoint }{section.6.38}% 457
\BOOKMARK [2][-]{subsection.6.38.5}{The union of intervals: union }{section.6.38}% 458
\BOOKMARK [2][-]{subsection.6.38.6}{The intersection of intervals: intersect }{section.6.38}% 459
\BOOKMARK [2][-]{subsection.6.38.7}{Test if an object is in an interval: contains }{section.6.38}% 460
\BOOKMARK [2][-]{subsection.6.38.8}{Convert a number to an interval: convert \040}{section.6.38}% 461
\BOOKMARK [1][-]{section.6.39}{Sequences and lists}{chapter.6}% 462
\BOOKMARK [2][-]{subsection.6.39.1}{Defining a sequence or a list: seq[ ] \(\) \040}{section.6.39}% 463
\BOOKMARK [2][-]{subsection.6.39.2}{Make a sequence or a list: seq \044 \040 }{section.6.39}% 464
\BOOKMARK [2][-]{subsection.6.39.3}{Length of a sequence or list: size nops length \040 \040}{section.6.39}% 465
\BOOKMARK [2][-]{subsection.6.39.4}{Get the first element of a sequence or list: head }{section.6.39}% 466
\BOOKMARK [2][-]{subsection.6.39.5}{Get a sequence or list without the first element: tail }{section.6.39}% 467
\BOOKMARK [2][-]{subsection.6.39.6}{Get an element of a sequence or a list: [] [[]] at \040 \040}{section.6.39}% 468
\BOOKMARK [2][-]{subsection.6.39.7}{Find a subsequence or a sublist \040}{section.6.39}% 469
\BOOKMARK [2][-]{subsection.6.39.8}{Concatenate two sequences: , }{section.6.39}% 470
\BOOKMARK [2][-]{subsection.6.39.9}{The + operator applied on sequences and lists \040}{section.6.39}% 471
\BOOKMARK [2][-]{subsection.6.39.10}{Transforming sequences into lists and lists into sequences: [] nop op makesuite \040 \040 }{section.6.39}% 472
\BOOKMARK [1][-]{section.6.40}{Operations on lists }{chapter.6}% 473
\BOOKMARK [2][-]{subsection.6.40.1}{Sizes of a list of lists: sizes }{section.6.40}% 474
\BOOKMARK [2][-]{subsection.6.40.2}{Make a list with a function: makelist \040}{section.6.40}% 475
\BOOKMARK [2][-]{subsection.6.40.3}{Make a list with zeros: newList }{section.6.40}% 476
\BOOKMARK [2][-]{subsection.6.40.4}{Make a list of integers: range \040}{section.6.40}% 477
\BOOKMARK [2][-]{subsection.6.40.5}{Select the elements of a list: select }{section.6.40}% 478
\BOOKMARK [2][-]{subsection.6.40.6}{The left and right portions of a list: left right \040 }{section.6.40}% 479
\BOOKMARK [2][-]{subsection.6.40.7}{Modifying the elements of a list: subsop \040}{section.6.40}% 480
\BOOKMARK [2][-]{subsection.6.40.8}{Remove an element in a list: suppress }{section.6.40}% 481
\BOOKMARK [2][-]{subsection.6.40.9}{Remove elements of a list: remove }{section.6.40}% 482
\BOOKMARK [2][-]{subsection.6.40.10}{Insert an element into a list or a string: insert }{section.6.40}% 483
\BOOKMARK [2][-]{subsection.6.40.11}{Append an element at the end of a list: append }{section.6.40}% 484
\BOOKMARK [2][-]{subsection.6.40.12}{Prepend an element at the beginning of a list: prepend }{section.6.40}% 485
\BOOKMARK [2][-]{subsection.6.40.13}{Concatenate two lists or a list and an element: concat augment \040 }{section.6.40}% 486
\BOOKMARK [2][-]{subsection.6.40.14}{Flatten a list: flatten \040}{section.6.40}% 487
\BOOKMARK [2][-]{subsection.6.40.15}{Reverse order in a list: revlist \040}{section.6.40}% 488
\BOOKMARK [2][-]{subsection.6.40.16}{Rotate a list: rotate }{section.6.40}% 489
\BOOKMARK [2][-]{subsection.6.40.17}{Shifting the elements of a list: shift }{section.6.40}% 490
\BOOKMARK [2][-]{subsection.6.40.18}{Sort: sort }{section.6.40}% 491
\BOOKMARK [2][-]{subsection.6.40.19}{Sort a list by increasing order: SortA }{section.6.40}% 492
\BOOKMARK [2][-]{subsection.6.40.20}{Sort a list by decreasing order: SortD }{section.6.40}% 493
\BOOKMARK [2][-]{subsection.6.40.21}{Number of elements equal to a given value: count\137eq }{section.6.40}% 494
\BOOKMARK [2][-]{subsection.6.40.22}{Number of elements smaller than a given value: count\137inf }{section.6.40}% 495
\BOOKMARK [2][-]{subsection.6.40.23}{Number of elements greater than a given value: count\137sup }{section.6.40}% 496
\BOOKMARK [2][-]{subsection.6.40.24}{Sum of elements of a list: sum add \040}{section.6.40}% 497
\BOOKMARK [2][-]{subsection.6.40.25}{Sum of list \(or matrix\) elements transformed by a function: count }{section.6.40}% 498
\BOOKMARK [2][-]{subsection.6.40.26}{Cumulated sum of the elements of a list: cumSum \040}{section.6.40}% 499
\BOOKMARK [2][-]{subsection.6.40.27}{Product: product mul \040 }{section.6.40}% 500
\BOOKMARK [2][-]{subsection.6.40.28}{Apply a function of one variable to the elements of a list: map apply \040 }{section.6.40}% 501
\BOOKMARK [2][-]{subsection.6.40.29}{Apply a bivariate function to the elements of two lists: zip }{section.6.40}% 502
\BOOKMARK [2][-]{subsection.6.40.30}{Fold operators: foldl foldr \040}{section.6.40}% 503
\BOOKMARK [2][-]{subsection.6.40.31}{List of differences of consecutive terms: deltalist }{section.6.40}% 504
\BOOKMARK [2][-]{subsection.6.40.32}{Make a matrix with a list: list2mat }{section.6.40}% 505
\BOOKMARK [2][-]{subsection.6.40.33}{Make a list with a matrix: mat2list }{section.6.40}% 506
\BOOKMARK [1][-]{section.6.41}{Operations on sets and lists}{chapter.6}% 507
\BOOKMARK [2][-]{subsection.6.41.1}{Defining a set or list: set[ ] \045\173 \045\175 \040 }{section.6.41}% 508
\BOOKMARK [2][-]{subsection.6.41.2}{Test if a value is in a list or a set: member contains \040}{section.6.41}% 509
\BOOKMARK [2][-]{subsection.6.41.3}{Union of two sets or of two lists: union }{section.6.41}% 510
\BOOKMARK [2][-]{subsection.6.41.4}{Intersection of two sets or of two lists: intersect }{section.6.41}% 511
\BOOKMARK [2][-]{subsection.6.41.5}{Difference of two sets or of two lists: minus }{section.6.41}% 512
\BOOKMARK [1][-]{section.6.42}{Functions for vectors}{chapter.6}% 513
\BOOKMARK [2][-]{subsection.6.42.1}{Norms of a vector: maxnorm l1norm l2norm norm }{section.6.42}% 514
\BOOKMARK [2][-]{subsection.6.42.2}{Normalize a vector: normalize unitV }{section.6.42}% 515
\BOOKMARK [2][-]{subsection.6.42.3}{Term by term sum of two lists: + .+ \040 }{section.6.42}% 516
\BOOKMARK [2][-]{subsection.6.42.4}{Term by term difference of two lists: - .- \040 }{section.6.42}% 517
\BOOKMARK [2][-]{subsection.6.42.5}{Term by term product of two lists: .* }{section.6.42}% 518
\BOOKMARK [2][-]{subsection.6.42.6}{Term by term quotient of two lists: ./ }{section.6.42}% 519
\BOOKMARK [2][-]{subsection.6.42.7}{Scalar product : scalar\137product * dotprod dot dotP scalar\137Product \040 \040 \040}{section.6.42}% 520
\BOOKMARK [2][-]{subsection.6.42.8}{Cross product: cross crossP crossproduct \040 }{section.6.42}% 521
\BOOKMARK [2][-]{subsection.6.42.9}{Statistics on lists: mean variance stddev stddevp median quantile quartiles boxwhisker \040 \040 \040 \040}{section.6.42}% 522
\BOOKMARK [1][-]{section.6.43}{Table with strings as indices: table \040}{chapter.6}% 523
\BOOKMARK [1][-]{section.6.44}{Matrices}{chapter.6}% 524
\BOOKMARK [2][-]{subsection.6.44.1}{Matrices}{section.6.44}% 525
\BOOKMARK [2][-]{subsection.6.44.2}{Special matrices}{section.6.44}% 526
\BOOKMARK [2][-]{subsection.6.44.3}{Combining matrices}{section.6.44}% 527
\BOOKMARK [2][-]{subsection.6.44.4}{Creating a matrix with a formula or function: makemat matrix \040 }{section.6.44}% 528
\BOOKMARK [2][-]{subsection.6.44.5}{Getting the parts of a matrix}{section.6.44}% 529
\BOOKMARK [2][-]{subsection.6.44.6}{Modifying matrices}{section.6.44}% 530
\BOOKMARK [1][-]{section.6.45}{Arithmetic and matrices}{chapter.6}% 531
\BOOKMARK [2][-]{subsection.6.45.1}{Evaluate a matrix: evalm }{section.6.45}% 532
\BOOKMARK [2][-]{subsection.6.45.2}{Addition and subtraction of two matrices: + - .+ .- \040 \040}{section.6.45}% 533
\BOOKMARK [2][-]{subsection.6.45.3}{Multiplication of two matrices: * \046* \040}{section.6.45}% 534
\BOOKMARK [2][-]{subsection.6.45.4}{Addition of elements of a column of a matrix: sum }{section.6.45}% 535
\BOOKMARK [2][-]{subsection.6.45.5}{Cumulated sum of elements of each column of a matrix: cumSum }{section.6.45}% 536
\BOOKMARK [2][-]{subsection.6.45.6}{Multiplication of elements of each column of a matrix: product \040}{section.6.45}% 537
\BOOKMARK [2][-]{subsection.6.45.7}{Power of a matrix: \136 \046\136 \040}{section.6.45}% 538
\BOOKMARK [2][-]{subsection.6.45.8}{Hadamard product: hadamard product .* \040 \040}{section.6.45}% 539
\BOOKMARK [2][-]{subsection.6.45.9}{Hadamard division: ./ }{section.6.45}% 540
\BOOKMARK [2][-]{subsection.6.45.10}{Hadamard power: .\136}{section.6.45}% 541
\BOOKMARK [2][-]{subsection.6.45.11}{The elementary row operations}{section.6.45}% 542
\BOOKMARK [2][-]{subsection.6.45.12}{Count the elements of a matrix satisfying a property: count }{section.6.45}% 543
\BOOKMARK [2][-]{subsection.6.45.13}{Count the elements equal to a given value: count\137eq }{section.6.45}% 544
\BOOKMARK [2][-]{subsection.6.45.14}{Count the elements smaller than a given value: count\137inf }{section.6.45}% 545
\BOOKMARK [2][-]{subsection.6.45.15}{Count the elements greater than a given value: count\137sup }{section.6.45}% 546
\BOOKMARK [2][-]{subsection.6.45.16}{Statistics functions acting on column matrices: mean stddev variance median quantile quartiles boxwhisker \040 \040 \040 \040}{section.6.45}% 547
\BOOKMARK [2][-]{subsection.6.45.17}{Dimension of a matrix: dim }{section.6.45}% 548
\BOOKMARK [2][-]{subsection.6.45.18}{Number of rows: rowdim rowDim nrows \040 }{section.6.45}% 549
\BOOKMARK [2][-]{subsection.6.45.19}{Number of columns: coldim colDim ncols \040 }{section.6.45}% 550
\BOOKMARK [1][-]{section.6.46}{Sparse matrices}{chapter.6}% 551
\BOOKMARK [2][-]{subsection.6.46.1}{Defining sparse matrices }{section.6.46}% 552
\BOOKMARK [2][-]{subsection.6.46.2}{Operations on sparse matrices}{section.6.46}% 553
\BOOKMARK [1][-]{section.6.47}{Linear algebra}{chapter.6}% 554
\BOOKMARK [2][-]{subsection.6.47.1}{Transpose of a matrix: tran transpose \040 }{section.6.47}% 555
\BOOKMARK [2][-]{subsection.6.47.2}{Inverse of a matrix: inv / }{section.6.47}% 556
\BOOKMARK [2][-]{subsection.6.47.3}{Trace of a matrix: trace }{section.6.47}% 557
\BOOKMARK [2][-]{subsection.6.47.4}{Determinant of a matrix: det \040 \040 \040 }{section.6.47}% 558
\BOOKMARK [2][-]{subsection.6.47.5}{Determinant of a sparse matrix: det\137minor }{section.6.47}% 559
\BOOKMARK [2][-]{subsection.6.47.6}{Rank of a matrix: rank }{section.6.47}% 560
\BOOKMARK [2][-]{subsection.6.47.7}{Transconjugate of a matrix: trn }{section.6.47}% 561
\BOOKMARK [2][-]{subsection.6.47.8}{Equivalent matrix: changebase }{section.6.47}% 562
\BOOKMARK [2][-]{subsection.6.47.9}{Basis of a linear subspace : basis }{section.6.47}% 563
\BOOKMARK [2][-]{subsection.6.47.10}{Basis of the intersection of two subspaces: ibasis }{section.6.47}% 564
\BOOKMARK [2][-]{subsection.6.47.11}{Image of a linear function: image }{section.6.47}% 565
\BOOKMARK [2][-]{subsection.6.47.12}{Kernel of a linear function: kernel nullspace ker \040 }{section.6.47}% 566
\BOOKMARK [2][-]{subsection.6.47.13}{Kernel of a linear function: Nullspace }{section.6.47}% 567
\BOOKMARK [2][-]{subsection.6.47.14}{Subspace generated by the columns of a matrix: colspace }{section.6.47}% 568
\BOOKMARK [2][-]{subsection.6.47.15}{Subspace generated by the rows of a matrix: rowspace }{section.6.47}% 569
\BOOKMARK [1][-]{section.6.48}{Matrix reduction}{chapter.6}% 570
\BOOKMARK [2][-]{subsection.6.48.1}{Eigenvalues: eigenvals }{section.6.48}% 571
\BOOKMARK [2][-]{subsection.6.48.2}{Eigenvalues: egvl eigenvalues eigVl \040 }{section.6.48}% 572
\BOOKMARK [2][-]{subsection.6.48.3}{Eigenvectors: egv eigenvectors eigenvects eigVc \040 \040}{section.6.48}% 573
\BOOKMARK [2][-]{subsection.6.48.4}{Rational Jordan matrix: rat\137jordan }{section.6.48}% 574
\BOOKMARK [2][-]{subsection.6.48.5}{Jordan normal form: jordan \040}{section.6.48}% 575
\BOOKMARK [2][-]{subsection.6.48.6}{Powers of a square matrix: matpow }{section.6.48}% 576
\BOOKMARK [2][-]{subsection.6.48.7}{Characteristic polynomial: charpoly }{section.6.48}% 577
\BOOKMARK [2][-]{subsection.6.48.8}{Characteristic polynomial using Hessenberg algorithm: pcar\137hessenberg }{section.6.48}% 578
\BOOKMARK [2][-]{subsection.6.48.9}{Minimal polynomial: pmin }{section.6.48}% 579
\BOOKMARK [2][-]{subsection.6.48.10}{Adjoint matrix: adjoint\137matrix }{section.6.48}% 580
\BOOKMARK [2][-]{subsection.6.48.11}{Companion matrix of a polynomial: companion }{section.6.48}% 581
\BOOKMARK [2][-]{subsection.6.48.12}{Hessenberg matrix reduction: hessenberg SCHUR \040}{section.6.48}% 582
\BOOKMARK [2][-]{subsection.6.48.13}{Hermite normal form: ihermite }{section.6.48}% 583
\BOOKMARK [2][-]{subsection.6.48.14}{Smith normal form in Z: ismith }{section.6.48}% 584
\BOOKMARK [2][-]{subsection.6.48.15}{Smith normal form: smith }{section.6.48}% 585
\BOOKMARK [1][-]{section.6.49}{Matrix factorizations}{chapter.6}% 586
\BOOKMARK [2][-]{subsection.6.49.1}{Cholesky decomposition: cholesky }{section.6.49}% 587
\BOOKMARK [2][-]{subsection.6.49.2}{QR decomposition: qr }{section.6.49}% 588
\BOOKMARK [2][-]{subsection.6.49.3}{QR decomposition \(for TI compatibility\): QR }{section.6.49}% 589
\BOOKMARK [2][-]{subsection.6.49.4}{LQ decomposition \(HP compatible\): LQ }{section.6.49}% 590
\BOOKMARK [2][-]{subsection.6.49.5}{LU decomposition: lu \040}{section.6.49}% 591
\BOOKMARK [2][-]{subsection.6.49.6}{LU decomposition \(for TI compatibility\): LU }{section.6.49}% 592
\BOOKMARK [2][-]{subsection.6.49.7}{Singular values \(HP compatible\): SVL svl \040 }{section.6.49}% 593
\BOOKMARK [2][-]{subsection.6.49.8}{Singular value decomposition: svd }{section.6.49}% 594
\BOOKMARK [2][-]{subsection.6.49.9}{Short basis of a lattice: lll }{section.6.49}% 595
\BOOKMARK [1][-]{section.6.50}{Different matrix norms}{chapter.6}% 596
\BOOKMARK [2][-]{subsection.6.50.1}{The Frobenius norm: frobenius\137norm }{section.6.50}% 597
\BOOKMARK [2][-]{subsection.6.50.2}{2 matrix norm: norm l2norm \040 }{section.6.50}% 598
\BOOKMARK [2][-]{subsection.6.50.3}{ matrix norm: maxnorm }{section.6.50}% 599
\BOOKMARK [2][-]{subsection.6.50.4}{Matrix row norm: rownorm rowNorm \040 \040}{section.6.50}% 600
\BOOKMARK [2][-]{subsection.6.50.5}{Matrix column norm: colnorm colNorm l1norm \040 \040}{section.6.50}% 601
\BOOKMARK [2][-]{subsection.6.50.6}{The operator norm of a matrix: matrix\137norm l1norm l2norm norm specnorm linfnorm \040 \040 \040}{section.6.50}% 602
\BOOKMARK [1][-]{section.6.51}{Isometries}{chapter.6}% 603
\BOOKMARK [2][-]{subsection.6.51.1}{Recognize an isometry: isom }{section.6.51}% 604
\BOOKMARK [2][-]{subsection.6.51.2}{Find the matrix of an isometry: mkisom }{section.6.51}% 605
\BOOKMARK [1][-]{section.6.52}{Linear Programming}{chapter.6}% 606
\BOOKMARK [2][-]{subsection.6.52.1}{Simplex algorithm: simplex\137reduce }{section.6.52}% 607
\BOOKMARK [2][-]{subsection.6.52.2}{Solving general linear programming problems: lpsolve }{section.6.52}% 608
\BOOKMARK [2][-]{subsection.6.52.3}{Solving the transportation problems: tpsolve }{section.6.52}% 609
\BOOKMARK [1][-]{section.6.53}{Nonlinear optimization}{chapter.6}% 610
\BOOKMARK [2][-]{subsection.6.53.1}{Global extrema: minimize maximize \040}{section.6.53}% 611
\BOOKMARK [2][-]{subsection.6.53.2}{Local extrema: extrema }{section.6.53}% 612
\BOOKMARK [2][-]{subsection.6.53.3}{Global extrema without using derivatives: nlpsolve }{section.6.53}% 613
\BOOKMARK [2][-]{subsection.6.53.4}{Minimax polynomial approximation: minimax }{section.6.53}% 614
\BOOKMARK [1][-]{section.6.54}{Quadratic forms}{chapter.6}% 615
\BOOKMARK [2][-]{subsection.6.54.1}{Matrix of a quadratic form: q2a }{section.6.54}% 616
\BOOKMARK [2][-]{subsection.6.54.2}{Transform a matrix into a quadratic form: a2q }{section.6.54}% 617
\BOOKMARK [2][-]{subsection.6.54.3}{Reduction of a quadratic form: gauss }{section.6.54}% 618
\BOOKMARK [2][-]{subsection.6.54.4}{The conjugate gradient algorithm: conjugate\137gradient }{section.6.54}% 619
\BOOKMARK [2][-]{subsection.6.54.5}{Gram-Schmidt orthonormalization: gramschmidt }{section.6.54}% 620
\BOOKMARK [2][-]{subsection.6.54.6}{Graph of a conic: conic }{section.6.54}% 621
\BOOKMARK [2][-]{subsection.6.54.7}{Conic reduction: reduced\137conic }{section.6.54}% 622
\BOOKMARK [2][-]{subsection.6.54.8}{Graph of a quadric: quadric }{section.6.54}% 623
\BOOKMARK [2][-]{subsection.6.54.9}{Quadric reduction: reduced\137quadric }{section.6.54}% 624
\BOOKMARK [1][-]{section.6.55}{Equations}{chapter.6}% 625
\BOOKMARK [2][-]{subsection.6.55.1}{Define an equation: equal }{section.6.55}% 626
\BOOKMARK [2][-]{subsection.6.55.2}{Transform an equation into a difference: equal2diff }{section.6.55}% 627
\BOOKMARK [2][-]{subsection.6.55.3}{Transform an equation into a list: equal2list }{section.6.55}% 628
\BOOKMARK [2][-]{subsection.6.55.4}{The left member of an equation: left gauche lhs \040 \040}{section.6.55}% 629
\BOOKMARK [2][-]{subsection.6.55.5}{The right member of an equation: right droit rhs \040 \040}{section.6.55}% 630
\BOOKMARK [2][-]{subsection.6.55.6}{Solving equation\(s\): solve cSolve \040 }{section.6.55}% 631
\BOOKMARK [1][-]{section.6.56}{Linear systems}{chapter.6}% 632
\BOOKMARK [2][-]{subsection.6.56.1}{Matrix of a system: syst2mat }{section.6.56}% 633
\BOOKMARK [2][-]{subsection.6.56.2}{Gauss reduction of a matrix: ref \040}{section.6.56}% 634
\BOOKMARK [2][-]{subsection.6.56.3}{Gauss-Jordan reduction: rref gaussjord \040 }{section.6.56}% 635
\BOOKMARK [2][-]{subsection.6.56.4}{Solving AX=b: simult }{section.6.56}% 636
\BOOKMARK [2][-]{subsection.6.56.5}{Step by step Gauss-Jordan reduction of a matrix: pivot }{section.6.56}% 637
\BOOKMARK [2][-]{subsection.6.56.6}{Linear system solving: linsolve }{section.6.56}% 638
\BOOKMARK [2][-]{subsection.6.56.7}{Solving a linear system using the Jacobi iteration method: jacobi\137linsolve }{section.6.56}% 639
\BOOKMARK [2][-]{subsection.6.56.8}{Solving a linear system using the Gauss-Seidel iteration method: gauss\137seidel\137linsolve }{section.6.56}% 640
\BOOKMARK [2][-]{subsection.6.56.9}{The least squares solution of a linear system: LSQ lsq \040}{section.6.56}% 641
\BOOKMARK [2][-]{subsection.6.56.10}{Finding linear recurrences: reverse\137rsolve }{section.6.56}% 642
\BOOKMARK [1][-]{section.6.57}{Differential equations}{chapter.6}% 643
\BOOKMARK [2][-]{subsection.6.57.1}{Solving differential equations: desolve deSolve dsolve \040 \040}{section.6.57}% 644
\BOOKMARK [2][-]{subsection.6.57.2}{Laplace transform and inverse Laplace transform: laplace ilaplace invlaplace \040 \040}{section.6.57}% 645
\BOOKMARK [2][-]{subsection.6.57.3}{Solving linear homogeneous second-order ODE with rational coefficients: kovacicsols \040}{section.6.57}% 646
\BOOKMARK [1][-]{section.6.58}{The Z-transform}{chapter.6}% 647
\BOOKMARK [2][-]{subsection.6.58.1}{The Z-transform of a sequence: ztrans }{section.6.58}% 648
\BOOKMARK [2][-]{subsection.6.58.2}{The inverse Z-transform of a rational function: invztrans }{section.6.58}% 649
\BOOKMARK [1][-]{section.6.59}{Other functions}{chapter.6}% 650
\BOOKMARK [2][-]{subsection.6.59.1}{Replace small values by 0: epsilon2zero }{section.6.59}% 651
\BOOKMARK [2][-]{subsection.6.59.2}{List of variables: lname indets \040}{section.6.59}% 652
\BOOKMARK [2][-]{subsection.6.59.3}{List of variables and of expressions: lvar }{section.6.59}% 653
\BOOKMARK [2][-]{subsection.6.59.4}{List of variables of an algebraic expressions: algvar }{section.6.59}% 654
\BOOKMARK [2][-]{subsection.6.59.5}{Test if a variable is in an expression: has }{section.6.59}% 655
\BOOKMARK [2][-]{subsection.6.59.6}{Numeric evaluation: evalf \040}{section.6.59}% 656
\BOOKMARK [2][-]{subsection.6.59.7}{Rational approximation: float2rational exact \040}{section.6.59}% 657
\BOOKMARK [1][-]{section.6.60}{The day of the week: dayofweek }{chapter.6}% 658
\BOOKMARK [0][-]{chapter.7}{Metric properties of curves}{}% 659
\BOOKMARK [1][-]{section.7.1}{The center of curvature}{chapter.7}% 660
\BOOKMARK [1][-]{section.7.2}{Computing the curvature and related values: curvature osculating\137circle evolute \040 }{chapter.7}% 661
\BOOKMARK [0][-]{chapter.8}{Graphs}{}% 662
\BOOKMARK [1][-]{section.8.1}{Generalities}{chapter.8}% 663
\BOOKMARK [1][-]{section.8.2}{The graphic screen }{chapter.8}% 664
\BOOKMARK [1][-]{section.8.3}{Graph and geometric objects attributes}{chapter.8}% 665
\BOOKMARK [2][-]{subsection.8.3.1}{Individual attributes \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 }{section.8.3}% 666
\BOOKMARK [2][-]{subsection.8.3.2}{Global attributes \040 \040 \040 \040 \040 \040 \040 \040 \040 \040}{section.8.3}% 667
\BOOKMARK [1][-]{section.8.4}{Graph of a function: plotfunc funcplot DrawFunc Graph \040 \040 \040 \040 }{chapter.8}% 668
\BOOKMARK [2][-]{subsection.8.4.1}{2-d graph}{section.8.4}% 669
\BOOKMARK [2][-]{subsection.8.4.2}{3-d graph}{section.8.4}% 670
\BOOKMARK [1][-]{section.8.5}{2d graph for Maple compatibility: plot \040}{chapter.8}% 671
\BOOKMARK [1][-]{section.8.6}{3d surfaces for Maple compatibility plot3d \040}{chapter.8}% 672
\BOOKMARK [1][-]{section.8.7}{Graph of a line and tangent to a graph}{chapter.8}% 673
\BOOKMARK [2][-]{subsection.8.7.1}{Draw a line: line }{section.8.7}% 674
\BOOKMARK [2][-]{subsection.8.7.2}{Draw a 2D horizontal line: LineHorz }{section.8.7}% 675
\BOOKMARK [2][-]{subsection.8.7.3}{Draw a 2D vertical line: LineVert }{section.8.7}% 676
\BOOKMARK [2][-]{subsection.8.7.4}{Tangent to a 2D graph: LineTan }{section.8.7}% 677
\BOOKMARK [2][-]{subsection.8.7.5}{Tangent to a 2D graph: tangent }{section.8.7}% 678
\BOOKMARK [2][-]{subsection.8.7.6}{Plot a line with a point and the slope: DrawSlp}{section.8.7}% 679
\BOOKMARK [2][-]{subsection.8.7.7}{Intersection of a 2D graph with the axis }{section.8.7}% 680
\BOOKMARK [1][-]{section.8.8}{Graph of inequalities with 2 variables: plotinequation inequationplot}{chapter.8}% 681
\BOOKMARK [1][-]{section.8.9}{The area under a curve: area }{chapter.8}% 682
\BOOKMARK [1][-]{section.8.10}{Graph of the area below a curve: plotarea areaplot}{chapter.8}% 683
\BOOKMARK [1][-]{section.8.11}{Contour lines: plotcontour contourplot DrwCtour \040 }{chapter.8}% 684
\BOOKMARK [1][-]{section.8.12}{2-d graph of a 2-d function with colors: plotdensity densityplot \040}{chapter.8}% 685
\BOOKMARK [1][-]{section.8.13}{Implicit graph: plotimplicit implicitplot}{chapter.8}% 686
\BOOKMARK [2][-]{subsection.8.13.1}{2D implicit curve}{section.8.13}% 687
\BOOKMARK [2][-]{subsection.8.13.2}{3D implicit surface}{section.8.13}% 688
\BOOKMARK [1][-]{section.8.14}{Parametric curves and surfaces: plotparam paramplot DrawParm \040 }{chapter.8}% 689
\BOOKMARK [2][-]{subsection.8.14.1}{2D parametric curve}{section.8.14}% 690
\BOOKMARK [2][-]{subsection.8.14.2}{3D parametric surface: plotparam paramplot DrawParm \040 }{section.8.14}% 691
\BOOKMARK [1][-]{section.8.15}{Bezier curves: bezier }{chapter.8}% 692
\BOOKMARK [1][-]{section.8.16}{Curve defined in polar coordinates: plotpolar polarplot DrawPol courbe\137polaire \040 \040}{chapter.8}% 693
\BOOKMARK [1][-]{section.8.17}{Graph of a recurrent sequence: plotseq seqplot graphe\137suite \040 }{chapter.8}% 694
\BOOKMARK [1][-]{section.8.18}{Tangent field: plotfield fieldplot \040 }{chapter.8}% 695
\BOOKMARK [1][-]{section.8.19}{Plotting a solution of a differential equation: plotode odeplot \040 }{chapter.8}% 696
\BOOKMARK [1][-]{section.8.20}{Interactive plotting of solutions of a differential equation: interactive\137plotode interactive\137odeplot \040 }{chapter.8}% 697
\BOOKMARK [1][-]{section.8.21}{Animated graphs \(2D, 3D or "4D"\)}{chapter.8}% 698
\BOOKMARK [2][-]{subsection.8.21.1}{Animation of a 2D graph: animate \040}{section.8.21}% 699
\BOOKMARK [2][-]{subsection.8.21.2}{Animation of a 3D graph: animate3d }{section.8.21}% 700
\BOOKMARK [2][-]{subsection.8.21.3}{Animation of a sequence of graphic objects: animation }{section.8.21}% 701
\BOOKMARK [0][-]{chapter.9}{Statistics}{}% 702
\BOOKMARK [1][-]{section.9.1}{One variable statistics}{chapter.9}% 703
\BOOKMARK [2][-]{subsection.9.1.1}{The mean: mean }{section.9.1}% 704
\BOOKMARK [2][-]{subsection.9.1.2}{Variance: variance }{section.9.1}% 705
\BOOKMARK [2][-]{subsection.9.1.3}{Standard deviation: stdev }{section.9.1}% 706
\BOOKMARK [2][-]{subsection.9.1.4}{The population standard deviation: stddevp stdDev \040}{section.9.1}% 707
\BOOKMARK [2][-]{subsection.9.1.5}{The median: median }{section.9.1}% 708
\BOOKMARK [2][-]{subsection.9.1.6}{Quartiles: quartiles quartile1 quartile3 \040 }{section.9.1}% 709
\BOOKMARK [2][-]{subsection.9.1.7}{Quantiles: quantile }{section.9.1}% 710
\BOOKMARK [2][-]{subsection.9.1.8}{The boxwhisker: boxwhisker mustache \040}{section.9.1}% 711
\BOOKMARK [2][-]{subsection.9.1.9}{Classes: classes \040}{section.9.1}% 712
\BOOKMARK [2][-]{subsection.9.1.10}{Histograms: histogram histogramme \040}{section.9.1}% 713
\BOOKMARK [2][-]{subsection.9.1.11}{Accumulating terms: accumulate\137head\137tail }{section.9.1}% 714
\BOOKMARK [2][-]{subsection.9.1.12}{Frequencies: frequencies frequences \040 }{section.9.1}% 715
\BOOKMARK [2][-]{subsection.9.1.13}{Cumulative frequencies: cumulated\137frequencies frequences\137cumulees \040}{section.9.1}% 716
\BOOKMARK [2][-]{subsection.9.1.14}{Bar graphs: bar\137plot }{section.9.1}% 717
\BOOKMARK [2][-]{subsection.9.1.15}{Pie charts: camembert }{section.9.1}% 718
\BOOKMARK [1][-]{section.9.2}{Two variable statistics}{chapter.9}% 719
\BOOKMARK [2][-]{subsection.9.2.1}{Covariance and correlation: covariance correlation covariance\137correlation \040 }{section.9.2}% 720
\BOOKMARK [2][-]{subsection.9.2.2}{Scatterplots: scatterplot nuaged\137points batons}{section.9.2}% 721
\BOOKMARK [2][-]{subsection.9.2.3}{Polygonal paths: polygonplot ligne\137polygonale linear\137interpolate listplot plotlist \040 \040 }{section.9.2}% 722
\BOOKMARK [2][-]{subsection.9.2.4}{Linear regression: linear\137regression linear\137regression\137plot \040}{section.9.2}% 723
\BOOKMARK [2][-]{subsection.9.2.5}{Exponential regression: exponential\137regression exponential\137regression\137plot \040}{section.9.2}% 724
\BOOKMARK [2][-]{subsection.9.2.6}{Logarithmic regression: logarithmic\137regression logarithmic\137regression\137plot \040}{section.9.2}% 725
\BOOKMARK [2][-]{subsection.9.2.7}{Power regression: power\137regression power\137regression\137plot \040}{section.9.2}% 726
\BOOKMARK [2][-]{subsection.9.2.8}{Polynomial regression: polynomial\137regression polynomial\137regression\137plot \040}{section.9.2}% 727
\BOOKMARK [2][-]{subsection.9.2.9}{Logistic regression: logistic\137regression logistic\137regression\137plot \040}{section.9.2}% 728
\BOOKMARK [1][-]{section.9.3}{Random numbers}{chapter.9}% 729
\BOOKMARK [2][-]{subsection.9.3.1}{Producing uniformly distributed random numbers: rand random alea hasard sample \040 \040 \040}{section.9.3}% 730
\BOOKMARK [2][-]{subsection.9.3.2}{Initializing the random number generator: srand randseed RandSeed \040 \040}{section.9.3}% 731
\BOOKMARK [2][-]{subsection.9.3.3}{Producing random numbers with the binomial distribution: randbinomial \040}{section.9.3}% 732
\BOOKMARK [2][-]{subsection.9.3.4}{Producing random numbers with a multinomial distribution: randmultinomial \040}{section.9.3}% 733
\BOOKMARK [2][-]{subsection.9.3.5}{Producing random numbers with a Poisson distribution: randpoisson \040}{section.9.3}% 734
\BOOKMARK [2][-]{subsection.9.3.6}{Producing random numbers with a normal distribution: randnorm randNorm \040 }{section.9.3}% 735
\BOOKMARK [2][-]{subsection.9.3.7}{Producing random numbers with Student's distribution: randstudent \040}{section.9.3}% 736
\BOOKMARK [2][-]{subsection.9.3.8}{Producing random numbers with the 2 distribution: randchisquare \040}{section.9.3}% 737
\BOOKMARK [2][-]{subsection.9.3.9}{Producing random numbers with the Fisher-Sn\351d\351cor distribution: randfisher \040}{section.9.3}% 738
\BOOKMARK [2][-]{subsection.9.3.10}{Producing random numbers with the gamma distribution: randgammad \040}{section.9.3}% 739
\BOOKMARK [2][-]{subsection.9.3.11}{Producing random numbers with the beta distribution: randbetad \040}{section.9.3}% 740
\BOOKMARK [2][-]{subsection.9.3.12}{Producing random numbers with the geometric distribution: randgeometric \040}{section.9.3}% 741
\BOOKMARK [2][-]{subsection.9.3.13}{Producing random numbers with the exponential distribution: randexp \040}{section.9.3}% 742
\BOOKMARK [2][-]{subsection.9.3.14}{Random variables: random\137variable randvar \040 }{section.9.3}% 743
\BOOKMARK [2][-]{subsection.9.3.15}{Make a random vector or list: randvector }{section.9.3}% 744
\BOOKMARK [2][-]{subsection.9.3.16}{Producing random matrices: randmatrix ranm randMat \040 \040}{section.9.3}% 745
\BOOKMARK [1][-]{section.9.4}{Density and distribution functions}{chapter.9}% 746
\BOOKMARK [2][-]{subsection.9.4.1}{Distributions and inverse distributions}{section.9.4}% 747
\BOOKMARK [2][-]{subsection.9.4.2}{The uniform distribution }{section.9.4}% 748
\BOOKMARK [2][-]{subsection.9.4.3}{The binomial distribution }{section.9.4}% 749
\BOOKMARK [2][-]{subsection.9.4.4}{The negative binomial distribution }{section.9.4}% 750
\BOOKMARK [2][-]{subsection.9.4.5}{The multinomial probability function: multinomial \040}{section.9.4}% 751
\BOOKMARK [2][-]{subsection.9.4.6}{The Poisson distribution }{section.9.4}% 752
\BOOKMARK [2][-]{subsection.9.4.7}{Normal distributions }{section.9.4}% 753
\BOOKMARK [2][-]{subsection.9.4.8}{Student's distribution }{section.9.4}% 754
\BOOKMARK [2][-]{subsection.9.4.9}{The 2 distribution }{section.9.4}% 755
\BOOKMARK [2][-]{subsection.9.4.10}{The Fisher-Sn\351d\351cor distribution }{section.9.4}% 756
\BOOKMARK [2][-]{subsection.9.4.11}{The gamma distribution }{section.9.4}% 757
\BOOKMARK [2][-]{subsection.9.4.12}{The beta distribution }{section.9.4}% 758
\BOOKMARK [2][-]{subsection.9.4.13}{The geometric distribution }{section.9.4}% 759
\BOOKMARK [2][-]{subsection.9.4.14}{The Cauchy distribution }{section.9.4}% 760
\BOOKMARK [2][-]{subsection.9.4.15}{The exponential distribution }{section.9.4}% 761
\BOOKMARK [2][-]{subsection.9.4.16}{The Weibull distribution }{section.9.4}% 762
\BOOKMARK [2][-]{subsection.9.4.17}{The Kolmogorov-Smirnov distribution: kolmogorovd \040}{section.9.4}% 763
\BOOKMARK [2][-]{subsection.9.4.18}{The Wilcoxon or Mann-Whitney distribution }{section.9.4}% 764
\BOOKMARK [2][-]{subsection.9.4.19}{Moment generating functions for probability distributions: mgf }{section.9.4}% 765
\BOOKMARK [2][-]{subsection.9.4.20}{Cumulative distribution functions: cdf }{section.9.4}% 766
\BOOKMARK [2][-]{subsection.9.4.21}{Inverse distribution functions: icdf}{section.9.4}% 767
\BOOKMARK [2][-]{subsection.9.4.22}{Kernel density estimation: kernel\137density kde \040}{section.9.4}% 768
\BOOKMARK [2][-]{subsection.9.4.23}{Distribution fitting by maximum likelihood: fitdistr }{section.9.4}% 769
\BOOKMARK [2][-]{subsection.9.4.24}{Markov chains: markov}{section.9.4}% 770
\BOOKMARK [2][-]{subsection.9.4.25}{Generating a random walks: randmarkov }{section.9.4}% 771
\BOOKMARK [1][-]{section.9.5}{Hypothesis testing}{chapter.9}% 772
\BOOKMARK [2][-]{subsection.9.5.1}{General}{section.9.5}% 773
\BOOKMARK [2][-]{subsection.9.5.2}{Testing the mean with the Z test: normalt }{section.9.5}% 774
\BOOKMARK [2][-]{subsection.9.5.3}{Testing the mean with the T test: studentt }{section.9.5}% 775
\BOOKMARK [2][-]{subsection.9.5.4}{Testing a distribution with the 2 distribution: chisquaret}{section.9.5}% 776
\BOOKMARK [2][-]{subsection.9.5.5}{Testing a distribution with the Kolmogorov-Smirnov distribution: kolmogorovt }{section.9.5}% 777
\BOOKMARK [0][-]{chapter.10}{Numerical computations}{}% 778
\BOOKMARK [1][-]{section.10.1}{Floating point representation.}{chapter.10}% 779
\BOOKMARK [2][-]{subsection.10.1.1}{Digits}{section.10.1}% 780
\BOOKMARK [2][-]{subsection.10.1.2}{Representation by hardware floats}{section.10.1}% 781
\BOOKMARK [2][-]{subsection.10.1.3}{Examples of representations of normalized floats}{section.10.1}% 782
\BOOKMARK [2][-]{subsection.10.1.4}{Difference between the representation of \(3.1-3\) and of 0.1}{section.10.1}% 783
\BOOKMARK [1][-]{section.10.2}{Approx. evaluation: evalf approx Digits \040 \040}{chapter.10}% 784
\BOOKMARK [1][-]{section.10.3}{Numerical algorithms}{chapter.10}% 785
\BOOKMARK [2][-]{subsection.10.3.1}{Approximate solution of an equation: newton }{section.10.3}% 786
\BOOKMARK [2][-]{subsection.10.3.2}{Approximate computation of the derivative number: nDeriv }{section.10.3}% 787
\BOOKMARK [2][-]{subsection.10.3.3}{Approximate computation of integrals: romberg nInt \040}{section.10.3}% 788
\BOOKMARK [2][-]{subsection.10.3.4}{Approximate integral with an adaptive Gaussian quadrature at 15 points: gaussquad }{section.10.3}% 789
\BOOKMARK [2][-]{subsection.10.3.5}{Approximate solution of y'=f\(t,y\): odesolve \040}{section.10.3}% 790
\BOOKMARK [2][-]{subsection.10.3.6}{Approximate solution of the system v'=f\(t,v\): odesolve }{section.10.3}% 791
\BOOKMARK [2][-]{subsection.10.3.7}{Approximate solution of a nonlinear second-order boundary value problem: bvpsolve }{section.10.3}% 792
\BOOKMARK [1][-]{section.10.4}{Solve equations with fsolve nSolve cfsolve \040 \040}{chapter.10}% 793
\BOOKMARK [2][-]{subsection.10.4.1}{fsolve with the option bisection\137solver }{section.10.4}% 794
\BOOKMARK [2][-]{subsection.10.4.2}{fsolve with the option brent\137solver }{section.10.4}% 795
\BOOKMARK [2][-]{subsection.10.4.3}{fsolve with the option falsepos\137solver }{section.10.4}% 796
\BOOKMARK [2][-]{subsection.10.4.4}{fsolve with the option newton\137solver }{section.10.4}% 797
\BOOKMARK [2][-]{subsection.10.4.5}{fsolve with the option secant\137solver }{section.10.4}% 798
\BOOKMARK [2][-]{subsection.10.4.6}{fsolve with the option steffenson\137solver }{section.10.4}% 799
\BOOKMARK [1][-]{section.10.5}{Solve systems with fsolve and cfsolve}{chapter.10}% 800
\BOOKMARK [2][-]{subsection.10.5.1}{fsolve with the option dnewton\137solver }{section.10.5}% 801
\BOOKMARK [2][-]{subsection.10.5.2}{fsolve with the option hybrid\137solver }{section.10.5}% 802
\BOOKMARK [2][-]{subsection.10.5.3}{fsolve with the option hybrids\137solver }{section.10.5}% 803
\BOOKMARK [2][-]{subsection.10.5.4}{fsolve with the option newtonj\137solver }{section.10.5}% 804
\BOOKMARK [2][-]{subsection.10.5.5}{fsolve with the option hybridj\137solver }{section.10.5}% 805
\BOOKMARK [2][-]{subsection.10.5.6}{fsolve with the option hybridsj\137solver }{section.10.5}% 806
\BOOKMARK [1][-]{section.10.6}{Numeric roots of a polynomial: proot \040}{chapter.10}% 807
\BOOKMARK [1][-]{section.10.7}{Numeric factorization of a matrix: cholesky qr lu svd}{chapter.10}% 808
\BOOKMARK [0][-]{chapter.11}{Unit objects and physical constants}{}% 809
\BOOKMARK [1][-]{section.11.1}{Unit objects}{chapter.11}% 810
\BOOKMARK [2][-]{subsection.11.1.1}{Notation of unit objects \040}{section.11.1}% 811
\BOOKMARK [2][-]{subsection.11.1.2}{Computing with units}{section.11.1}% 812
\BOOKMARK [2][-]{subsection.11.1.3}{Convert units into MKSA units: mksa }{section.11.1}% 813
\BOOKMARK [2][-]{subsection.11.1.4}{Convert units: convert => \040}{section.11.1}% 814
\BOOKMARK [2][-]{subsection.11.1.5}{Convert between Celsius and Fahrenheit: Celsius2Fahrenheit Fahrenheit2Celsius \040}{section.11.1}% 815
\BOOKMARK [2][-]{subsection.11.1.6}{Factorize a unit: ufactor }{section.11.1}% 816
\BOOKMARK [2][-]{subsection.11.1.7}{Simplify a unit: usimplify }{section.11.1}% 817
\BOOKMARK [1][-]{section.11.2}{Constants}{chapter.11}% 818
\BOOKMARK [2][-]{subsection.11.2.1}{Notation of physical constants }{section.11.2}% 819
\BOOKMARK [0][-]{chapter.12}{Programming }{}% 820
\BOOKMARK [1][-]{section.12.1}{Functions, programs and scripts}{chapter.12}% 821
\BOOKMARK [2][-]{subsection.12.1.1}{The program editor}{section.12.1}% 822
\BOOKMARK [2][-]{subsection.12.1.2}{Functions: function endfunction \173 \175 local return \040 \040 \040}{section.12.1}% 823
\BOOKMARK [2][-]{subsection.12.1.3}{Local variables}{section.12.1}% 824
\BOOKMARK [2][-]{subsection.12.1.4}{Default values of the parameters}{section.12.1}% 825
\BOOKMARK [2][-]{subsection.12.1.5}{Programs}{section.12.1}% 826
\BOOKMARK [2][-]{subsection.12.1.6}{Scripts}{section.12.1}% 827
\BOOKMARK [2][-]{subsection.12.1.7}{Code blocks }{section.12.1}% 828
\BOOKMARK [1][-]{section.12.2}{Basic instructions}{chapter.12}% 829
\BOOKMARK [2][-]{subsection.12.2.1}{Comments: // \040}{section.12.2}% 830
\BOOKMARK [2][-]{subsection.12.2.2}{Input: input Input InputStr textinput output Output \040 \040 \040}{section.12.2}% 831
\BOOKMARK [2][-]{subsection.12.2.3}{Reading a single keystroke: getKey }{section.12.2}% 832
\BOOKMARK [2][-]{subsection.12.2.4}{Checking conditions: assert }{section.12.2}% 833
\BOOKMARK [2][-]{subsection.12.2.5}{Checking the type of the argument: type subtype compare getType \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040 \040}{section.12.2}% 834
\BOOKMARK [2][-]{subsection.12.2.6}{Printing: print Disp ClrIO \040 }{section.12.2}% 835
\BOOKMARK [2][-]{subsection.12.2.7}{Displaying exponents: printpow }{section.12.2}% 836
\BOOKMARK [2][-]{subsection.12.2.8}{Infixed assignments: => := =< \040 }{section.12.2}% 837
\BOOKMARK [2][-]{subsection.12.2.9}{Assignment by copying: copy }{section.12.2}% 838
\BOOKMARK [2][-]{subsection.12.2.10}{The difference between := and =<}{section.12.2}% 839
\BOOKMARK [1][-]{section.12.3}{Control structures}{chapter.12}% 840
\BOOKMARK [2][-]{subsection.12.3.1}{if statements: if then else end elif \040 \040 }{section.12.3}% 841
\BOOKMARK [2][-]{subsection.12.3.2}{The switch statement: switch case default \040 }{section.12.3}% 842
\BOOKMARK [2][-]{subsection.12.3.3}{The for loop: for from to step do end\137for \040 \040 \040 }{section.12.3}% 843
\BOOKMARK [2][-]{subsection.12.3.4}{The repeat loop: repeat until \040}{section.12.3}% 844
\BOOKMARK [2][-]{subsection.12.3.5}{The while loop: while }{section.12.3}% 845
\BOOKMARK [2][-]{subsection.12.3.6}{Breaking out a loop: break }{section.12.3}% 846
\BOOKMARK [2][-]{subsection.12.3.7}{Going to the next iteration of a loop: continue}{section.12.3}% 847
\BOOKMARK [2][-]{subsection.12.3.8}{Changing the order of execution: goto label \040}{section.12.3}% 848
\BOOKMARK [1][-]{section.12.4}{Other useful instructions}{chapter.12}% 849
\BOOKMARK [2][-]{subsection.12.4.1}{Define a function with a variable number of arguments: args }{section.12.4}% 850
\BOOKMARK [2][-]{subsection.12.4.2}{Assignments in a program}{section.12.4}% 851
\BOOKMARK [2][-]{subsection.12.4.3}{Writing variable values to a file: write }{section.12.4}% 852
\BOOKMARK [2][-]{subsection.12.4.4}{Writing output to a file: fopen fclose fprint \040 }{section.12.4}% 853
\BOOKMARK [2][-]{subsection.12.4.5}{Using strings as names: \043 }{section.12.4}% 854
\BOOKMARK [2][-]{subsection.12.4.6}{Using strings as commands: expr }{section.12.4}% 855
\BOOKMARK [2][-]{subsection.12.4.7}{Converting an expression to a string: string }{section.12.4}% 856
\BOOKMARK [2][-]{subsection.12.4.8}{Converting a real number into a string: format }{section.12.4}% 857
\BOOKMARK [2][-]{subsection.12.4.9}{Working with the graphics screen: DispG DispHome ClrGraph ClrDraw \040 \040}{section.12.4}% 858
\BOOKMARK [2][-]{subsection.12.4.10}{Pausing a program: Pause WAIT \040}{section.12.4}% 859
\BOOKMARK [2][-]{subsection.12.4.11}{Dealing with errors: try catch throw error ERROR \040 \040 }{section.12.4}% 860
\BOOKMARK [1][-]{section.12.5}{Debugging}{chapter.12}% 861
\BOOKMARK [2][-]{subsection.12.5.1}{Starting the debugger: debug sst in sst\137in cont kill break breakpoint halt rmbrk rmbreakpoint watch rmwtch \040 \040 \040 \040 \040 \040 }{section.12.5}% 862
\BOOKMARK [0][-]{chapter.13}{Two-dimensional Graphics}{}% 863
\BOOKMARK [1][-]{section.13.1}{Introduction}{chapter.13}% 864
\BOOKMARK [2][-]{subsection.13.1.1}{Points, vectors and complex numbers}{section.13.1}% 865
\BOOKMARK [1][-]{section.13.2}{Basic commands}{chapter.13}% 866
\BOOKMARK [2][-]{subsection.13.2.1}{Clear the DispG screen: erase }{section.13.2}% 867
\BOOKMARK [2][-]{subsection.13.2.2}{Toggle the axes: switch\137axes }{section.13.2}% 868
\BOOKMARK [2][-]{subsection.13.2.3}{Draw unit vectors in the plane: Ox\1372d\137unit\137vector Oy\1372d\137unit\137vector frame\1372d \040 }{section.13.2}% 869
\BOOKMARK [2][-]{subsection.13.2.4}{Draw dotted paper: dot\137paper }{section.13.2}% 870
\BOOKMARK [2][-]{subsection.13.2.5}{Draw lined paper: line\137paper}{section.13.2}% 871
\BOOKMARK [2][-]{subsection.13.2.6}{Draw grid paper: grid\137paper }{section.13.2}% 872
\BOOKMARK [2][-]{subsection.13.2.7}{Draw triangular paper: triangle\137paper }{section.13.2}% 873
\BOOKMARK [1][-]{section.13.3}{Display features of graphics}{chapter.13}% 874
\BOOKMARK [2][-]{subsection.13.3.1}{Graphic features}{section.13.3}% 875
\BOOKMARK [2][-]{subsection.13.3.2}{Parameters for changing features}{section.13.3}% 876
\BOOKMARK [2][-]{subsection.13.3.3}{Commands for global display features}{section.13.3}% 877
\BOOKMARK [1][-]{section.13.4}{Define geometric objects without drawing them: nodisp}{chapter.13}% 878
\BOOKMARK [1][-]{section.13.5}{Geometric demonstrations: assume}{chapter.13}% 879
\BOOKMARK [1][-]{section.13.6}{Points in the plane}{chapter.13}% 880
\BOOKMARK [2][-]{subsection.13.6.1}{Points and complex numbers}{section.13.6}% 881
\BOOKMARK [2][-]{subsection.13.6.2}{The point in the plane: point }{section.13.6}% 882
\BOOKMARK [2][-]{subsection.13.6.3}{The difference and sum of two points in the plane:+ - \040}{section.13.6}% 883
\BOOKMARK [2][-]{subsection.13.6.4}{Define random points in the plane: point2d }{section.13.6}% 884
\BOOKMARK [2][-]{subsection.13.6.5}{Points in polar coordinates: polar\137point point\137polar \040}{section.13.6}% 885
\BOOKMARK [2][-]{subsection.13.6.6}{Find a point of intersection of two objects in the plane: single\137inter line\137inter \040}{section.13.6}% 886
\BOOKMARK [2][-]{subsection.13.6.7}{Find the points of intersection of two geometric objects in the plane: inter }{section.13.6}% 887
\BOOKMARK [2][-]{subsection.13.6.8}{Find the orthocenter of a triangle in the plane: orthocenter }{section.13.6}% 888
\BOOKMARK [2][-]{subsection.13.6.9}{Find the midpoint of a segment in the plane: midpoint }{section.13.6}% 889
\BOOKMARK [2][-]{subsection.13.6.10}{The barycenter in the plane: barycenter }{section.13.6}% 890
\BOOKMARK [2][-]{subsection.13.6.11}{The isobarycenter of n points in the plane: isobarycenter }{section.13.6}% 891
\BOOKMARK [2][-]{subsection.13.6.12}{The center of a circle in the plane: center }{section.13.6}% 892
\BOOKMARK [2][-]{subsection.13.6.13}{The vertices of a polygon in the plane: vertices vertices\137abc \040}{section.13.6}% 893
\BOOKMARK [2][-]{subsection.13.6.14}{The vertices of a polygon in the plane, closed: vertices\137abca }{section.13.6}% 894
\BOOKMARK [2][-]{subsection.13.6.15}{A point on a geometric object in the plane: element }{section.13.6}% 895
\BOOKMARK [1][-]{section.13.7}{Lines in plane geometry}{chapter.13}% 896
\BOOKMARK [2][-]{subsection.13.7.1}{Lines and directed lines in the plane: line }{section.13.7}% 897
\BOOKMARK [2][-]{subsection.13.7.2}{Half-lines in the plane: half\137line }{section.13.7}% 898
\BOOKMARK [2][-]{subsection.13.7.3}{Line segments in the plane: segment Line \040}{section.13.7}% 899
\BOOKMARK [2][-]{subsection.13.7.4}{Vectors in the plane: segment vector \040}{section.13.7}% 900
\BOOKMARK [2][-]{subsection.13.7.5}{Parallel lines in the plane: parallel }{section.13.7}% 901
\BOOKMARK [2][-]{subsection.13.7.6}{Perpendicular lines in the plane: perpendicular }{section.13.7}% 902
\BOOKMARK [2][-]{subsection.13.7.7}{Tangents to curves in the plane: tangent }{section.13.7}% 903
\BOOKMARK [2][-]{subsection.13.7.8}{The median of a triangle in the plane: median\137line }{section.13.7}% 904
\BOOKMARK [2][-]{subsection.13.7.9}{The altitude of a triangle: altitude }{section.13.7}% 905
\BOOKMARK [2][-]{subsection.13.7.10}{The perpendicular bisector of a segment in the plane: perpen\137bisector }{section.13.7}% 906
\BOOKMARK [2][-]{subsection.13.7.11}{The angle bisector: bisector }{section.13.7}% 907
\BOOKMARK [2][-]{subsection.13.7.12}{The exterior angle bisector: exbisector }{section.13.7}% 908
\BOOKMARK [1][-]{section.13.8}{Triangles in the plane}{chapter.13}% 909
\BOOKMARK [2][-]{subsection.13.8.1}{Arbitrary triangles in the plane: triangle }{section.13.8}% 910
\BOOKMARK [2][-]{subsection.13.8.2}{Isosceles triangles in the plane: isosceles\137triangle }{section.13.8}% 911
\BOOKMARK [2][-]{subsection.13.8.3}{Right triangles in the plane: right\137triangle }{section.13.8}% 912
\BOOKMARK [2][-]{subsection.13.8.4}{Equilateral triangles in the plane: equilateral\137triangle }{section.13.8}% 913
\BOOKMARK [1][-]{section.13.9}{Quadrilaterals in the plane}{chapter.13}% 914
\BOOKMARK [2][-]{subsection.13.9.1}{Squares in the plane: square }{section.13.9}% 915
\BOOKMARK [2][-]{subsection.13.9.2}{Rhombuses in the plane: rhombus }{section.13.9}% 916
\BOOKMARK [2][-]{subsection.13.9.3}{Rectangles in the plane: rectangle }{section.13.9}% 917
\BOOKMARK [2][-]{subsection.13.9.4}{Parallelograms in the plane: parallelogram }{section.13.9}% 918
\BOOKMARK [2][-]{subsection.13.9.5}{Arbitrary quadrilaterals in the plane: quadrilateral }{section.13.9}% 919
\BOOKMARK [1][-]{section.13.10}{Other polygons in the plane}{chapter.13}% 920
\BOOKMARK [2][-]{subsection.13.10.1}{Regular hexagons in the plane: hexagon }{section.13.10}% 921
\BOOKMARK [2][-]{subsection.13.10.2}{Regular polygons in the plane: isopolygon }{section.13.10}% 922
\BOOKMARK [2][-]{subsection.13.10.3}{General polygons in the plane: polygon }{section.13.10}% 923
\BOOKMARK [2][-]{subsection.13.10.4}{Polygonal lines in the plane: open\137polygon }{section.13.10}% 924
\BOOKMARK [2][-]{subsection.13.10.5}{Convex hulls: convexhull }{section.13.10}% 925
\BOOKMARK [1][-]{section.13.11}{Circles}{chapter.13}% 926
\BOOKMARK [2][-]{subsection.13.11.1}{Circles and arcs in the plane: circle }{section.13.11}% 927
\BOOKMARK [2][-]{subsection.13.11.2}{Circular arcs: arc }{section.13.11}% 928
\BOOKMARK [2][-]{subsection.13.11.3}{Circles \(TI compatibility\): Circle}{section.13.11}% 929
\BOOKMARK [2][-]{subsection.13.11.4}{Inscribed circles: incircle }{section.13.11}% 930
\BOOKMARK [2][-]{subsection.13.11.5}{Circumscribed circles: circumcircle }{section.13.11}% 931
\BOOKMARK [2][-]{subsection.13.11.6}{Excircles: excircle }{section.13.11}% 932
\BOOKMARK [2][-]{subsection.13.11.7}{The power of a point relative to a circle: powerpc }{section.13.11}% 933
\BOOKMARK [2][-]{subsection.13.11.8}{The radical axis of two circles: radical\137axis }{section.13.11}% 934
\BOOKMARK [1][-]{section.13.12}{Other conic sections}{chapter.13}% 935
\BOOKMARK [2][-]{subsection.13.12.1}{The ellipse in the plane: ellipse }{section.13.12}% 936
\BOOKMARK [2][-]{subsection.13.12.2}{The hyperbola in the plane: hyperbola }{section.13.12}% 937
\BOOKMARK [2][-]{subsection.13.12.3}{The parabola in the plane: parabola }{section.13.12}% 938
\BOOKMARK [1][-]{section.13.13}{Coordinates in the plane}{chapter.13}% 939
\BOOKMARK [2][-]{subsection.13.13.1}{The affix of a point or vector: affix \040}{section.13.13}% 940
\BOOKMARK [2][-]{subsection.13.13.2}{The abscissa of a point or vector in the plane: abscissa }{section.13.13}% 941
\BOOKMARK [2][-]{subsection.13.13.3}{The ordinate of a point or vector in the plane: ordinate }{section.13.13}% 942
\BOOKMARK [2][-]{subsection.13.13.4}{The coordinates of a point, vector or line in the plane: coordinates \040}{section.13.13}% 943
\BOOKMARK [2][-]{subsection.13.13.5}{The rectangular coordinates of a point: rectangular\137coordinates }{section.13.13}% 944
\BOOKMARK [2][-]{subsection.13.13.6}{The polar coordinates of a point: polar\137coordinates }{section.13.13}% 945
\BOOKMARK [2][-]{subsection.13.13.7}{The Cartesian equation of a geometric object in the plane: equation \040}{section.13.13}% 946
\BOOKMARK [2][-]{subsection.13.13.8}{The parametric equation of a geometric object in the plane: parameq \040}{section.13.13}% 947
\BOOKMARK [1][-]{section.13.14}{Measurements}{chapter.13}% 948
\BOOKMARK [2][-]{subsection.13.14.1}{Measurement and display: distanceat distanceatraw angleat angleatraw areaat areaatraw perimeterat perimeteratraw slopeat slopeatraw extract\137measure \040 \040 \040 \040 \040 }{section.13.14}% 949
\BOOKMARK [2][-]{subsection.13.14.2}{The distance between objects in the plane: distance }{section.13.14}% 950
\BOOKMARK [2][-]{subsection.13.14.3}{The length squared of a segment in the plane: distance2 }{section.13.14}% 951
\BOOKMARK [2][-]{subsection.13.14.4}{The measure of an angle in the plane: angle }{section.13.14}% 952
\BOOKMARK [2][-]{subsection.13.14.5}{The graphical representation of the area of a polygon: plotarea areaplot \040}{section.13.14}% 953
\BOOKMARK [2][-]{subsection.13.14.6}{The area of a polygon: area }{section.13.14}% 954
\BOOKMARK [2][-]{subsection.13.14.7}{The perimeter of a polygon: perimeter }{section.13.14}% 955
\BOOKMARK [2][-]{subsection.13.14.8}{The slope of a line: slope }{section.13.14}% 956
\BOOKMARK [2][-]{subsection.13.14.9}{The radius of a circle: radius }{section.13.14}% 957
\BOOKMARK [2][-]{subsection.13.14.10}{The length of a vector: abs }{section.13.14}% 958
\BOOKMARK [2][-]{subsection.13.14.11}{The angle of a vector: arg }{section.13.14}% 959
\BOOKMARK [2][-]{subsection.13.14.12}{Normalize a complex number: normalize }{section.13.14}% 960
\BOOKMARK [1][-]{section.13.15}{Transformations}{chapter.13}% 961
\BOOKMARK [2][-]{subsection.13.15.1}{General remarks}{section.13.15}% 962
\BOOKMARK [2][-]{subsection.13.15.2}{Translations in the plane: translation }{section.13.15}% 963
\BOOKMARK [2][-]{subsection.13.15.3}{Reflections in the plane: reflection }{section.13.15}% 964
\BOOKMARK [2][-]{subsection.13.15.4}{Rotation in the plane: rotation }{section.13.15}% 965
\BOOKMARK [2][-]{subsection.13.15.5}{Homothety in the plane: homothety }{section.13.15}% 966
\BOOKMARK [2][-]{subsection.13.15.6}{Similarity in the plane: similarity }{section.13.15}% 967
\BOOKMARK [2][-]{subsection.13.15.7}{Inversion in the plane: inversion }{section.13.15}% 968
\BOOKMARK [2][-]{subsection.13.15.8}{Orthogonal projection in the plane: projection \040}{section.13.15}% 969
\BOOKMARK [1][-]{section.13.16}{Properties}{chapter.13}% 970
\BOOKMARK [2][-]{subsection.13.16.1}{Check if a point is on an object in the plane: is\137element }{section.13.16}% 971
\BOOKMARK [2][-]{subsection.13.16.2}{Check if three points are collinear in the plane: is\137collinear }{section.13.16}% 972
\BOOKMARK [2][-]{subsection.13.16.3}{Check if four points are concyclic in the plane: is\137concyclic }{section.13.16}% 973
\BOOKMARK [2][-]{subsection.13.16.4}{Check if a point is in a polygon or circle: is\137inside }{section.13.16}% 974
\BOOKMARK [2][-]{subsection.13.16.5}{Check if an object is an equilateral triangle in the plane: is\137equilateral }{section.13.16}% 975
\BOOKMARK [2][-]{subsection.13.16.6}{Check if an object in the plane is an isosceles triangle: is\137isosceles }{section.13.16}% 976
\BOOKMARK [2][-]{subsection.13.16.7}{Check if an object in the plane is a right triangle or a rectangle: is\137rectangle }{section.13.16}% 977
\BOOKMARK [2][-]{subsection.13.16.8}{Check if an object in the plane is a square: is\137square }{section.13.16}% 978
\BOOKMARK [2][-]{subsection.13.16.9}{Check if an object in the plane is a rhombus: is\137rhombus }{section.13.16}% 979
\BOOKMARK [2][-]{subsection.13.16.10}{Check if an object in the plane is a parallelogram: is\137parallelogram }{section.13.16}% 980
\BOOKMARK [2][-]{subsection.13.16.11}{Check it two lines in the plane are parallel: is\137parallel }{section.13.16}% 981
\BOOKMARK [2][-]{subsection.13.16.12}{Check if two lines in the plane are perpendicular: is\137perpendicular }{section.13.16}% 982
\BOOKMARK [2][-]{subsection.13.16.13}{Check if two circles in the plane are orthogonal: is\137orthogonal }{section.13.16}% 983
\BOOKMARK [2][-]{subsection.13.16.14}{Check if elements are conjugates: is\137conjugate }{section.13.16}% 984
\BOOKMARK [2][-]{subsection.13.16.15}{Check if four points form a harmonic division: is\137harmonic }{section.13.16}% 985
\BOOKMARK [2][-]{subsection.13.16.16}{Check if lines are in a bundle: is\137harmonic\137line\137bundle }{section.13.16}% 986
\BOOKMARK [2][-]{subsection.13.16.17}{Check if circles are in a bundle: is\137harmonic\137circle\137bundle }{section.13.16}% 987
\BOOKMARK [1][-]{section.13.17}{Harmonic division}{chapter.13}% 988
\BOOKMARK [2][-]{subsection.13.17.1}{Find a point dividing a segment in the harminic ratio k: division\137point }{section.13.17}% 989
\BOOKMARK [2][-]{subsection.13.17.2}{The cross ratio of four collinear points: cross\137ratio }{section.13.17}% 990
\BOOKMARK [2][-]{subsection.13.17.3}{Harmonic division: harmonic\137division }{section.13.17}% 991
\BOOKMARK [2][-]{subsection.13.17.4}{The harmonic conjugate: harmonic\137conjugate }{section.13.17}% 992
\BOOKMARK [2][-]{subsection.13.17.5}{Pole and polar: pole polar \040}{section.13.17}% 993
\BOOKMARK [2][-]{subsection.13.17.6}{The polar reciprocal: reciprocation }{section.13.17}% 994
\BOOKMARK [1][-]{section.13.18}{Loci and envelopes}{chapter.13}% 995
\BOOKMARK [2][-]{subsection.13.18.1}{Loci: locus }{section.13.18}% 996
\BOOKMARK [2][-]{subsection.13.18.2}{Envelopes: envelope }{section.13.18}% 997
\BOOKMARK [2][-]{subsection.13.18.3}{The trace of a geometric object: trace}{section.13.18}% 998
\BOOKMARK [0][-]{chapter.14}{Three-dimensional Graphics}{}% 999
\BOOKMARK [1][-]{section.14.1}{Introduction}{chapter.14}% 1000
\BOOKMARK [1][-]{section.14.2}{Change the view}{chapter.14}% 1001
\BOOKMARK [1][-]{section.14.3}{The axes}{chapter.14}% 1002
\BOOKMARK [2][-]{subsection.14.3.1}{Draw unit vectors: Ox\1373d\137unit\137vector Oy\1373d\137unit\137vector Oz\1373d\137unit\137vector frame\1373d}{section.14.3}% 1003
\BOOKMARK [1][-]{section.14.4}{Points in space}{chapter.14}% 1004
\BOOKMARK [2][-]{subsection.14.4.1}{Define a point in three-dimensions: point}{section.14.4}% 1005
\BOOKMARK [2][-]{subsection.14.4.2}{Define a random point in three-dimensions: point3d}{section.14.4}% 1006
\BOOKMARK [2][-]{subsection.14.4.3}{Find an intersection point of two objects in space: single\137inter line\137inter}{section.14.4}% 1007
\BOOKMARK [2][-]{subsection.14.4.4}{Find the intersection points of two objects in space: inter}{section.14.4}% 1008
\BOOKMARK [2][-]{subsection.14.4.5}{Find the midpoint of a segment in space: midpoint}{section.14.4}% 1009
\BOOKMARK [2][-]{subsection.14.4.6}{Find the isobarycenter of a set of points in space: isobarycenter}{section.14.4}% 1010
\BOOKMARK [2][-]{subsection.14.4.7}{Find the barycenter of a set of points in space: barycenter}{section.14.4}% 1011
\BOOKMARK [1][-]{section.14.5}{Lines in space}{chapter.14}% 1012
\BOOKMARK [2][-]{subsection.14.5.1}{Lines and directed lines in space: line}{section.14.5}% 1013
\BOOKMARK [2][-]{subsection.14.5.2}{Half lines in space: half\137line}{section.14.5}% 1014
\BOOKMARK [2][-]{subsection.14.5.3}{Segments in space: segment}{section.14.5}% 1015
\BOOKMARK [2][-]{subsection.14.5.4}{Vectors in space: vector}{section.14.5}% 1016
\BOOKMARK [2][-]{subsection.14.5.5}{Parallel lines and planes in space: parallel}{section.14.5}% 1017
\BOOKMARK [2][-]{subsection.14.5.6}{Perpendicular lines and planes in space: perpendicular}{section.14.5}% 1018
\BOOKMARK [2][-]{subsection.14.5.7}{Planes orthogonal to lines and lines orthogonal to planes in space: orthogonal}{section.14.5}% 1019
\BOOKMARK [2][-]{subsection.14.5.8}{Common perpendiculars to lines in space: common\137perpendicular}{section.14.5}% 1020
\BOOKMARK [1][-]{section.14.6}{Planes in space}{chapter.14}% 1021
\BOOKMARK [2][-]{subsection.14.6.1}{Planes in space: plane}{section.14.6}% 1022
\BOOKMARK [2][-]{subsection.14.6.2}{The bisector plane in space: perpen\137bisector}{section.14.6}% 1023
\BOOKMARK [2][-]{subsection.14.6.3}{Tangent planes in space: tangent}{section.14.6}% 1024
\BOOKMARK [1][-]{section.14.7}{Triangles in space}{chapter.14}% 1025
\BOOKMARK [2][-]{subsection.14.7.1}{Draw a triangle in space: triangle}{section.14.7}% 1026
\BOOKMARK [2][-]{subsection.14.7.2}{Isosceles triangles in space: isosceles\137triangle}{section.14.7}% 1027
\BOOKMARK [2][-]{subsection.14.7.3}{Right triangles in space: right\137triangle}{section.14.7}% 1028
\BOOKMARK [2][-]{subsection.14.7.4}{Equilateral triangles in space: equilateral\137triangle}{section.14.7}% 1029
\BOOKMARK [1][-]{section.14.8}{Quadrilaterals in space}{chapter.14}% 1030
\BOOKMARK [2][-]{subsection.14.8.1}{Squares in space: square}{section.14.8}% 1031
\BOOKMARK [2][-]{subsection.14.8.2}{Rhombuses in space: rhombus}{section.14.8}% 1032
\BOOKMARK [2][-]{subsection.14.8.3}{Rectangles in space: rectangle}{section.14.8}% 1033
\BOOKMARK [2][-]{subsection.14.8.4}{Parallelograms in space: parallelogram}{section.14.8}% 1034
\BOOKMARK [2][-]{subsection.14.8.5}{Arbitrary quadrilaterals in space: quadrilateral}{section.14.8}% 1035
\BOOKMARK [1][-]{section.14.9}{Polygons in space}{chapter.14}% 1036
\BOOKMARK [2][-]{subsection.14.9.1}{Hexagons in space: hexagon}{section.14.9}% 1037
\BOOKMARK [2][-]{subsection.14.9.2}{Regular polygons in space: isopolygon}{section.14.9}% 1038
\BOOKMARK [2][-]{subsection.14.9.3}{General polygons in space: polygon}{section.14.9}% 1039
\BOOKMARK [2][-]{subsection.14.9.4}{Polygonal lines in space: open\137polygon}{section.14.9}% 1040
\BOOKMARK [1][-]{section.14.10}{Circles in space: circle}{chapter.14}% 1041
\BOOKMARK [1][-]{section.14.11}{Conics in space}{chapter.14}% 1042
\BOOKMARK [2][-]{subsection.14.11.1}{Ellipses in space: ellipse}{section.14.11}% 1043
\BOOKMARK [2][-]{subsection.14.11.2}{Hyperbolas in space: hyperbola}{section.14.11}% 1044
\BOOKMARK [2][-]{subsection.14.11.3}{Parabolas in space: parabola}{section.14.11}% 1045
\BOOKMARK [1][-]{section.14.12}{Three-dimensional coordinates}{chapter.14}% 1046
\BOOKMARK [2][-]{subsection.14.12.1}{The abscissa of a three-dimensional point: abscissa}{section.14.12}% 1047
\BOOKMARK [2][-]{subsection.14.12.2}{The ordinate of a three-dimensional point: ordinate}{section.14.12}% 1048
\BOOKMARK [2][-]{subsection.14.12.3}{The cote of a three-dimensional point: cote}{section.14.12}% 1049
\BOOKMARK [2][-]{subsection.14.12.4}{The coordinates of a point, vector or line in space: coordinates}{section.14.12}% 1050
\BOOKMARK [2][-]{subsection.14.12.5}{The Cartesian equation of an object in space: equation}{section.14.12}% 1051
\BOOKMARK [2][-]{subsection.14.12.6}{The parametric equation of an object in space: parameq}{section.14.12}% 1052
\BOOKMARK [2][-]{subsection.14.12.7}{The length of a segment in space: distance}{section.14.12}% 1053
\BOOKMARK [2][-]{subsection.14.12.8}{The length squared of a segment in space: distance2}{section.14.12}% 1054
\BOOKMARK [2][-]{subsection.14.12.9}{The measure of an angle in space: angle}{section.14.12}% 1055
\BOOKMARK [1][-]{section.14.13}{Properties}{chapter.14}% 1056
\BOOKMARK [2][-]{subsection.14.13.1}{Check if an object in space is on another object: is\137element}{section.14.13}% 1057
\BOOKMARK [2][-]{subsection.14.13.2}{Check if points and/or lines in space are coplanar: is\137coplanar}{section.14.13}% 1058
\BOOKMARK [2][-]{subsection.14.13.3}{Check if lines and/or planes in space are parallel: is\137parallel}{section.14.13}% 1059
\BOOKMARK [2][-]{subsection.14.13.4}{Check if lines and/or planes in space are perpendicular: is\137perpendicular}{section.14.13}% 1060
\BOOKMARK [2][-]{subsection.14.13.5}{Check if two lines or two spheres in space are orthogonal: is\137orthogonal}{section.14.13}% 1061
\BOOKMARK [2][-]{subsection.14.13.6}{Check if three points in space are collinear: is\137collinear}{section.14.13}% 1062
\BOOKMARK [2][-]{subsection.14.13.7}{Check if four points in space are cocyclic: is\137concyclic}{section.14.13}% 1063
\BOOKMARK [2][-]{subsection.14.13.8}{Check if five points in space are cospherical: is\137cospherical}{section.14.13}% 1064
\BOOKMARK [2][-]{subsection.14.13.9}{Check if an object in space is an equilateral triangle: is\137equilateral}{section.14.13}% 1065
\BOOKMARK [2][-]{subsection.14.13.10}{Check if an object in space is an isosceles triangle: is\137isosceles}{section.14.13}% 1066
\BOOKMARK [2][-]{subsection.14.13.11}{Check if an object in space is a right triangle or a rectangle: is\137rectangle}{section.14.13}% 1067
\BOOKMARK [2][-]{subsection.14.13.12}{Check if an object in space is a square: is\137square}{section.14.13}% 1068
\BOOKMARK [2][-]{subsection.14.13.13}{Check if an object in space is a rhombus: is\137rhombus}{section.14.13}% 1069
\BOOKMARK [2][-]{subsection.14.13.14}{Check if an object in space is a parallelogram: is\137parallelogram}{section.14.13}% 1070
\BOOKMARK [1][-]{section.14.14}{Transformations in space}{chapter.14}% 1071
\BOOKMARK [2][-]{subsection.14.14.1}{General remarks}{section.14.14}% 1072
\BOOKMARK [2][-]{subsection.14.14.2}{Translation in space: translation}{section.14.14}% 1073
\BOOKMARK [2][-]{subsection.14.14.3}{Reflection in space with respect to a plane, line or point: reflection symmetry}{section.14.14}% 1074
\BOOKMARK [2][-]{subsection.14.14.4}{Rotation in space: rotation}{section.14.14}% 1075
\BOOKMARK [2][-]{subsection.14.14.5}{Homothety in space: homothety}{section.14.14}% 1076
\BOOKMARK [2][-]{subsection.14.14.6}{Similarity in space: similarity}{section.14.14}% 1077
\BOOKMARK [2][-]{subsection.14.14.7}{Inversion in space: inversion}{section.14.14}% 1078
\BOOKMARK [2][-]{subsection.14.14.8}{Orthogonal projection in space: projection}{section.14.14}% 1079
\BOOKMARK [1][-]{section.14.15}{Surfaces}{chapter.14}% 1080
\BOOKMARK [2][-]{subsection.14.15.1}{Cones: cone}{section.14.15}% 1081
\BOOKMARK [2][-]{subsection.14.15.2}{Half-cones: half\137cone}{section.14.15}% 1082
\BOOKMARK [2][-]{subsection.14.15.3}{Cylinders: cylinder}{section.14.15}% 1083
\BOOKMARK [2][-]{subsection.14.15.4}{Spheres: sphere}{section.14.15}% 1084
\BOOKMARK [2][-]{subsection.14.15.5}{The graph of a function of two variables: funcplot}{section.14.15}% 1085
\BOOKMARK [2][-]{subsection.14.15.6}{The graph of parametric equations in space: paramplot}{section.14.15}% 1086
\BOOKMARK [1][-]{section.14.16}{Solids}{chapter.14}% 1087
\BOOKMARK [2][-]{subsection.14.16.1}{Cubes: cube}{section.14.16}% 1088
\BOOKMARK [2][-]{subsection.14.16.2}{Tetrahedrons: tetrahedron pyramid}{section.14.16}% 1089
\BOOKMARK [2][-]{subsection.14.16.3}{Parallelepipeds: parallelepiped}{section.14.16}% 1090
\BOOKMARK [2][-]{subsection.14.16.4}{Prisms: prism}{section.14.16}% 1091
\BOOKMARK [2][-]{subsection.14.16.5}{Polyhedra: polyhedron}{section.14.16}% 1092
\BOOKMARK [2][-]{subsection.14.16.6}{Vertices: vertices}{section.14.16}% 1093
\BOOKMARK [2][-]{subsection.14.16.7}{Faces: faces}{section.14.16}% 1094
\BOOKMARK [2][-]{subsection.14.16.8}{Edges: line\137segments}{section.14.16}% 1095
\BOOKMARK [1][-]{section.14.17}{Platonic solids}{chapter.14}% 1096
\BOOKMARK [2][-]{subsection.14.17.1}{Centered tetrahedra: centered\137tetrahedron}{section.14.17}% 1097
\BOOKMARK [2][-]{subsection.14.17.2}{Centered cubes: centered\137cube}{section.14.17}% 1098
\BOOKMARK [2][-]{subsection.14.17.3}{Octahedra: octahedron}{section.14.17}% 1099
\BOOKMARK [2][-]{subsection.14.17.4}{Dodecahedra: dodecahedron}{section.14.17}% 1100
\BOOKMARK [2][-]{subsection.14.17.5}{Icosahedra: icosahedron}{section.14.17}% 1101
\BOOKMARK [0][-]{chapter.15}{Multimedia}{}% 1102
\BOOKMARK [1][-]{section.15.1}{Audio Tools}{chapter.15}% 1103
\BOOKMARK [2][-]{subsection.15.1.1}{Creating audio clips: createwav \040}{section.15.1}% 1104
\BOOKMARK [2][-]{subsection.15.1.2}{Reading wav files from disk: readwav \040}{section.15.1}% 1105
\BOOKMARK [2][-]{subsection.15.1.3}{Writing wav files to disk: writewav \040}{section.15.1}% 1106
\BOOKMARK [2][-]{subsection.15.1.4}{Audio playback: playsnd}{section.15.1}% 1107
\BOOKMARK [2][-]{subsection.15.1.5}{Averaging channel data: stereo2mono \040}{section.15.1}% 1108
\BOOKMARK [2][-]{subsection.15.1.6}{Audio clip properties: channels bit\137depth samplerate duration \040 \040 }{section.15.1}% 1109
\BOOKMARK [2][-]{subsection.15.1.7}{Extracting samples from audio clips: channel\137data \040}{section.15.1}% 1110
\BOOKMARK [2][-]{subsection.15.1.8}{Changing the sampling rate: resample \040}{section.15.1}% 1111
\BOOKMARK [2][-]{subsection.15.1.9}{Visualizing waveforms: plotwav \040}{section.15.1}% 1112
\BOOKMARK [2][-]{subsection.15.1.10}{Visualizing power spectra: plotspectrum \040}{section.15.1}% 1113
\BOOKMARK [2][-]{subsection.15.1.11}{Reading a wav file: readwav}{section.15.1}% 1114
\BOOKMARK [2][-]{subsection.15.1.12}{Writing a wav file: writewav}{section.15.1}% 1115
\BOOKMARK [2][-]{subsection.15.1.13}{Listening to a digital sound: playsnd}{section.15.1}% 1116
\BOOKMARK [2][-]{subsection.15.1.14}{Preparing digital sound data: soundsec \040}{section.15.1}% 1117
\BOOKMARK [1][-]{section.15.2}{Signal Processing}{chapter.15}% 1118
\BOOKMARK [2][-]{subsection.15.2.1}{Boxcar function: boxcar}{section.15.2}% 1119
\BOOKMARK [2][-]{subsection.15.2.2}{Rectangle function: rect}{section.15.2}% 1120
\BOOKMARK [2][-]{subsection.15.2.3}{Triangle function: tri}{section.15.2}% 1121
\BOOKMARK [2][-]{subsection.15.2.4}{Cardinal sine function: sinc}{section.15.2}% 1122
\BOOKMARK [2][-]{subsection.15.2.5}{Cross-correlation of two signals: cross\137correlation}{section.15.2}% 1123
\BOOKMARK [2][-]{subsection.15.2.6}{Auto-correlation of a signal: auto\137correlation}{section.15.2}% 1124
\BOOKMARK [2][-]{subsection.15.2.7}{Convolution of two signals or functions: convolution }{section.15.2}% 1125
\BOOKMARK [2][-]{subsection.15.2.8}{Low-pass filtering: lowpass}{section.15.2}% 1126
\BOOKMARK [2][-]{subsection.15.2.9}{High-pass filtering: highpass}{section.15.2}% 1127
\BOOKMARK [2][-]{subsection.15.2.10}{Apply a moving average filter to a signal: moving\137average}{section.15.2}% 1128
\BOOKMARK [2][-]{subsection.15.2.11}{Perform thresholding operations on an array: threshold}{section.15.2}% 1129
\BOOKMARK [2][-]{subsection.15.2.12}{Bartlett-Hann window function: bartlett\137hann\137window}{section.15.2}% 1130
\BOOKMARK [2][-]{subsection.15.2.13}{Blackman-Harris window function: blackman\137harris\137window}{section.15.2}% 1131
\BOOKMARK [2][-]{subsection.15.2.14}{Blackman window function: blackman\137window}{section.15.2}% 1132
\BOOKMARK [2][-]{subsection.15.2.15}{Bohman window function: bohman\137window}{section.15.2}% 1133
\BOOKMARK [2][-]{subsection.15.2.16}{Cosine window function: cosine\137window}{section.15.2}% 1134
\BOOKMARK [2][-]{subsection.15.2.17}{Gaussian window function: gaussian\137window}{section.15.2}% 1135
\BOOKMARK [2][-]{subsection.15.2.18}{Hamming window function: hamming\137window}{section.15.2}% 1136
\BOOKMARK [2][-]{subsection.15.2.19}{Hann-Poisson window function: hann\137poisson\137window}{section.15.2}% 1137
\BOOKMARK [2][-]{subsection.15.2.20}{Hann window function: hann\137window}{section.15.2}% 1138
\BOOKMARK [2][-]{subsection.15.2.21}{Parzen window function: parzen\137window}{section.15.2}% 1139
\BOOKMARK [2][-]{subsection.15.2.22}{Poisson window function: poisson\137window}{section.15.2}% 1140
\BOOKMARK [2][-]{subsection.15.2.23}{Riemann window function: riemann\137window}{section.15.2}% 1141
\BOOKMARK [2][-]{subsection.15.2.24}{Triangular window function: triangle\137window}{section.15.2}% 1142
\BOOKMARK [2][-]{subsection.15.2.25}{Tukey window function: tukey\137window}{section.15.2}% 1143
\BOOKMARK [2][-]{subsection.15.2.26}{Welch window function: welch\137window}{section.15.2}% 1144
\BOOKMARK [2][-]{subsection.15.2.27}{An example: static noise removal by spectral subtraction}{section.15.2}% 1145
\BOOKMARK [1][-]{section.15.3}{Images}{chapter.15}% 1146
\BOOKMARK [2][-]{subsection.15.3.1}{Image structure in Xcas}{section.15.3}% 1147
\BOOKMARK [2][-]{subsection.15.3.2}{Reading images: readrgb}{section.15.3}% 1148
\BOOKMARK [2][-]{subsection.15.3.3}{Viewing images}{section.15.3}% 1149
\BOOKMARK [2][-]{subsection.15.3.4}{Creating or recreating images: writergb}{section.15.3}% 1150
\BOOKMARK [0][-]{chapter.16}{Using giac inside a program}{}% 1151
\BOOKMARK [1][-]{section.16.1}{Using giac inside a C++ program}{chapter.16}% 1152
\BOOKMARK [1][-]{section.16.2}{Defining new giac functions}{chapter.16}% 1153
