This is maxima.info, produced by makeinfo version 7.1.1 from
maxima.texi.

This is a Texinfo Maxima Manual

   Copyright 1994,2001 William F. Schelter

INFO-DIR-SECTION Math
START-INFO-DIR-ENTRY
* Maxima: (maxima).     A computer algebra system.
END-INFO-DIR-ENTRY


Indirect:
maxima.info-1: 266
maxima.info-2: 1006641
maxima.info-3: 2003564

Tag Table:
(Indirect)
Node: Top266
Node: Introduction to Maxima16582
Node: Bug Detection and Reporting23429
Node: Functions and Variables for Bug Detection and Reporting23671
Ref: run_testsuite23911
Ref: testsuite_files26181
Ref: bug_report27028
Ref: build_info27422
Node: Help29847
Node: Documentation30028
Node: Functions and Variables for Help31049
Ref: apropos31219
Ref: demo33002
Ref: describe34239
Ref: example37180
Ref: manual_demo38617
Node: Command Line38827
Node: Introduction to Command Line39085
Node: Functions and Variables for Command Line39299
Ref: __39560
Ref: _41369
Ref: %42888
Ref: %%43516
Ref: %th45168
Ref: ?46373
Ref: ??46953
Ref: $47286
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Ref: nolabels56475
Ref: optionset57301
Ref: outchar57930
Ref: playback58839
Ref: prompt60966
Ref: quit61179
Ref: read61584
Ref: readonly62154
Ref: reset62840
Ref: showtime63321
Ref: to_lisp63695
Ref: values64805
Node: Functions and Variables for Display65910
Ref: %edispflag66124
Ref: absboxchar66752
Ref: declare_index_properties67086
Ref: get_index_properties70694
Ref: remove_index_properties70871
Ref: display_index_separator71165
Ref: disp76417
Ref: display77109
Ref: display2d77993
Ref: display_format_internal79071
Ref: dispterms79781
Ref: expt80770
Ref: ncexpt80770
Ref: exptdispflag81097
Ref: grind81801
Ref: ibase86558
Ref: ldisp88608
Ref: ldisplay89725
Ref: leftjust91076
Ref: linel91596
Ref: lispdisp92045
Ref: negsumdispflag92578
Ref: obase92995
Ref: pfeformat94182
Ref: powerdisp95023
Ref: print95832
Ref: sqrtdispflag97211
Ref: stardisp97376
Ref: ttyoff97556
Node: Data Types and Structures97926
Node: Numbers98173
Node: Introduction to Numbers98395
Node: Functions and Variables for Numbers99159
Ref: bfloat99355
Ref: bfloatp101526
Ref: bftorat101638
Ref: bftrunc102780
Ref: evenp103091
Ref: float103316
Ref: float2bf103588
Ref: floatnump103814
Ref: fpprec103939
Ref: fpprintprec104222
Ref: integerp105207
Ref: m1pbranch106157
Ref: nonnegintegerp106766
Ref: numberp106879
Ref: numer108098
Ref: numer_pbranch108821
Ref: numerval109971
Ref: oddp110448
Ref: ratepsilon110669
Ref: rationalize110957
Ref: ratnump112434
Node: Strings112580
Node: Introduction to Strings112786
Node: Functions and Variables for Strings114871
Ref: concat115067
Ref: sconcat116552
Ref: string117208
Ref: stringdisp117515
Node: Constants118301
Node: Functions and Variables for Constants118483
Ref: %e118673
Ref: %i118889
Ref: false118964
Ref: %gamma119121
Ref: ind119204
Ref: inf119409
Ref: infinity119479
Ref: minf119553
Ref: %phi119639
Ref: %pi122127
Ref: true122337
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Ref: zerob123164
Node: Lists123404
Node: Introduction to Lists123640
Node: Functions and Variables for Lists124509
Ref: [124740
Ref: ]124740
Ref: append126284
Ref: assoc126665
Ref: cons128288
Ref: copylist129775
Ref: create_list129849
Ref: delete131093
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Ref: fifth135055
Ref: first135182
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Ref: join140233
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Ref: length144446
Ref: listarith145326
Ref: lreduce145778
Ref: makelist147169
Ref: member149087
Ref: ninth150483
Ref: pop150610
Ref: push150914
Ref: rest152212
Ref: reverse153380
Ref: rreduce153629
Ref: second155131
Ref: seventh155259
Ref: sixth155388
Ref: sort155515
Ref: sublist161590
Ref: sublist_indices161920
Ref: tenth163018
Ref: third163146
Ref: tree_reduce163273
Ref: unique164635
Ref: xreduce165022
Node: Performance considerations for Lists166771
Node: Arrays169038
Ref: hashed array169203
Ref: hashed arrays169203
Ref: undeclared array169203
Ref: undeclared arrays169203
Node: Functions and Variables for Arrays170415
Ref: array170590
Ref: arrayapply171434
Ref: arrayinfo171705
Ref: arraymake176227
Ref: arrays178032
Ref: arraysetapply179221
Ref: fillarray179447
Ref: listarray181626
Ref: make_array185423
Ref: rearray187605
Ref: remarray187987
Ref: subvar188570
Ref: subvarp189310
Ref: use_fast_arrays189433
Ref: translate_fast_arrays190139
Node: Structures190615
Node: Introduction to Structures190817
Node: Functions and Variables for Structures192488
Ref: structures192699
Ref: defstruct192827
Ref: new194408
Node: Expressions196832
Node: Introduction to Expressions197101
Node: Nouns and Verbs198696
Node: Identifiers201127
Node: Inequality203323
Node: Functions and Variables for Expressions203644
Ref: alias203839
Ref: aliases204068
Ref: allbut204342
Ref: args205382
Ref: atom206552
Ref: box206830
Ref: boxchar209007
Ref: collapse209350
Ref: copy209913
Ref: disolate210737
Ref: dispform211249
Ref: dpart213183
Ref: exptisolate213794
Ref: exptsubst214014
Ref: freeof214731
Ref: inflag218627
Ref: inpart219446
Ref: isolate220730
Ref: isolate_wrt_times221641
Ref: listconstvars222431
Ref: listdummyvars222964
Ref: listofvars223687
Ref: lfreeof224277
Ref: lpart224755
Ref: mainvar224977
Ref: noun225743
Ref: noundisp226367
Ref: nounify226583
Ref: nterms226993
Ref: op227361
Ref: operatorp229119
Ref: option_opsubst229486
Ref: optimize230368
Ref: optimprefix230749
Ref: ordergreat230912
Ref: orderless230912
Ref: ordergreatp231750
Ref: orderlessp231750
Ref: part235589
Ref: partition237114
Ref: partswitch237701
Ref: pickapart237931
Ref: piece240930
Ref: psubst241145
Ref: rembox242018
Ref: reveal244533
Ref: sqrtdenest247113
Ref: sublis247987
Ref: sublis_apply_lambda248464
Ref: subnumsimp248754
Ref: subst249367
Ref: substinpart252867
Ref: substpart255334
Ref: symbolp256527
Ref: unorder256661
Ref: verbify258106
Node: Operators258497
Node: Introduction to operators258802
Node: Arithmetic operators263073
Ref: +263253
Ref: -263253
Ref: *263253
Ref: /263253
Ref: ^263253
Ref: **270370
Ref: ^^271171
Ref: .271941
Node: Relational operators272417
Ref: <272589
Ref: <=272589
Ref: >=272589
Ref: >272589
Node: Logical operators275263
Ref: and275432
Ref: not276505
Ref: or277097
Node: Operators for Equations278159
Ref: #278340
Ref: =279117
Node: Assignment operators283371
Ref: :283551
Ref: ::286368
Ref: ::=287128
Ref: :=290173
Node: User defined operators296016
Ref: infix296168
Ref: matchfix300474
Ref: function_nary305191
Ref: nofix305806
Ref: postfix306375
Ref: prefix306866
Node: Evaluation307270
Node: Functions and Variables for Evaluation307441
Ref: quote307632
Ref: quote-quote312304
Ref: ev317809
Ref: eval326841
Ref: evflag327399
Ref: evfun329970
Ref: infeval332899
Ref: noeval333284
Ref: nouns333510
Ref: pred333824
Node: Simplification334199
Node: Introduction to Simplification334430
Node: Functions and Variables for Simplification344637
Ref: additive344864
Ref: antisymmetric345823
Ref: combine346880
Ref: commutative347466
Ref: demoivre348223
Ref: function_distrib348950
Ref: distribute_over349859
Ref: domain352135
Ref: evenfun352330
Ref: oddfun352330
Ref: expand353016
Ref: expandwrt357328
Ref: expandwert_denom357908
Ref: expandwrt_factored358330
Ref: expon358690
Ref: exponentialize358983
Ref: expop359585
Ref: lassociative360047
Ref: linear360268
Ref: maxnegex361996
Ref: maxposex362188
Ref: multiplicative362373
Ref: multthru364312
Ref: property_nary366653
Ref: negdistrib367386
Ref: opproperties368209
Ref: define_opproperty368674
Ref: outative370272
Ref: radcan371592
Ref: radexpand372836
Ref: rassociative373770
Ref: scsimp373983
Ref: simp374408
Ref: symmetric376115
Ref: xthru376369
Node: Mathematical Functions377603
Node: Functions for Numbers377959
Ref: abs378163
Ref: ceiling381625
Ref: entier385383
Ref: floor385599
Ref: fix387535
Ref: hstep387600
Ref: lmax387895
Ref: lmin388091
Ref: max388287
Ref: min388860
Ref: round389446
Ref: signum389785
Ref: truncate390574
Node: Functions for Complex Numbers390900
Ref: cabs391121
Ref: carg395079
Ref: conjugate397012
Ref: imagpart397534
Ref: polarform398138
Ref: realpart398812
Ref: rectform399396
Node: Combinatorial Functions399855
Ref: !!400085
Ref: binomial400832
Ref: factcomb401837
Ref: !402775
Ref: factorial402775
Ref: factlim406430
Ref: factorial_expand406622
Ref: genfact406874
Ref: minfactorial407117
Ref: sumsplitfact407664
Node: Root Exponential and Logarithmic Functions408678
Ref: %e_to_numlog408942
Ref: %emode409383
Ref: %enumer411043
Ref: exp412129
Ref: li413143
Ref: log415722
Ref: logabs417268
Ref: logarc418020
Ref: logconcoeffp418261
Ref: logcontract418698
Ref: logexpand419735
Ref: lognegint422983
Ref: logsimp423155
Ref: plog423320
Ref: sqrt423467
Node: Trigonometric Functions423629
Node: Introduction to Trigonometric423934
Node: Functions and Variables for Trigonometric425027
Ref: %piargs425265
Ref: %iargs427258
Ref: acos428302
Ref: acosh428348
Ref: acot428406
Ref: acoth428455
Ref: acsc428516
Ref: acsch428564
Ref: asec428624
Ref: asech428670
Ref: asin428728
Ref: asinh428772
Ref: atan428828
Ref: atan2428903
Ref: atanh429056
Ref: atrig1429115
Ref: cos429542
Ref: cosh429583
Ref: cot429636
Ref: coth429680
Ref: csc429736
Ref: csch429779
Ref: halfangles429834
Ref: sec432147
Ref: sech432188
Ref: sin432241
Ref: sinh432280
Ref: tan432331
Ref: tanh432373
Ref: trigexpand432427
Ref: trigexpandplus433891
Ref: trigexpandtimes434247
Ref: triginverses434613
Ref: trigreduce435140
Ref: trigsign435770
Ref: trigsimp436044
Ref: trigrat436461
Node: Random Numbers439355
Ref: make_random_state439501
Ref: set_random_state440276
Ref: random440425
Node: Maxima's Database442090
Node: Introduction to Maxima's Database442410
Node: Functions and Variables for Properties442649
Ref: alphabetic442914
Ref: bindtest443568
Ref: constant444148
Ref: constantp444724
Ref: declare446012
Ref: nary449434
Ref: decreasing451393
Ref: increasing451393
Ref: even452008
Ref: odd452008
Ref: feature452694
Ref: featurep453085
Ref: features453634
Ref: get455098
Ref: integer456145
Ref: noninteger456145
Ref: integervalued456628
Ref: nonarray457138
Ref: nonscalar457724
Ref: nonscalarp457868
Ref: posfun458100
Ref: printprops458273
Ref: properties458841
Ref: props458964
Ref: propvars459271
Ref: put459495
Ref: qput460408
Ref: rational461230
Ref: irrational461230
Ref: real461456
Ref: imaginary461456
Ref: complex461456
Ref: rem461734
Ref: remove462038
Ref: scalar463698
Ref: scalarp463836
Node: Functions and Variables for Facts464153
Ref: activate464413
Ref: activecontexts464825
Ref: askinteger465090
Ref: asksign465784
Ref: assume466198
Ref: assumescalar468703
Ref: assume_pos469692
Ref: assume_pos_pred470935
Ref: context473231
Ref: contexts473837
Ref: deactivate475252
Ref: facts475382
Ref: forget475861
Ref: is476220
Ref: killcontext478141
Ref: maybe478912
Ref: newcontext479725
Ref: sign480197
Ref: supcontext480628
Node: Functions and Variables for Predicates481146
Ref: charfun481369
Ref: compare481995
Ref: equal483185
Ref: notequal487577
Ref: unknown488516
Ref: zeroequiv488674
Node: Plotting489886
Node: Introduction to Plotting490192
Node: Plotting Formats492943
Node: Functions and Variables for Plotting496650
Ref: geomview_command496866
Ref: get_plot_option497332
Ref: gnuplot_command497755
Ref: gnuplot_file_args498237
Ref: gnuplot_view_args498855
Ref: julia500310
Ref: make_transform502087
Ref: mandelbrot502846
Ref: polar_to_xy504346
Ref: plot2d504665
Ref: plot3d513328
Ref: plot_options517760
Ref: remove_plot_option518064
Ref: set_plot_option518290
Ref: spherical_to_xyz519568
Node: Plotting Options520026
Ref: adapt_depth521244
Ref: axes521800
Ref: azimuth522452
Ref: option_box522984
Ref: color523314
Ref: color_bar524116
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Ref: elevation525442
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Ref: logx528592
Ref: logy528904
Ref: mesh_lines_color529214
Ref: nticks529897
Ref: palette530256
Ref: plotepsilon531967
Ref: plot_format532794
Ref: plot_real_part533150
Ref: point_type534069
Ref: pdf_file534654
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Ref: run_viewer537026
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Node: Gnuplot Options548376
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Ref: gnuplot_out_file551268
Ref: gnuplot_script_file552310
Ref: gnuplot_pm3d553659
Ref: gnuplot_preamble553831
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Ref: gnuplot_default_term_command554467
Ref: gnuplot_dumb_term_command554764
Ref: gnuplot_pdf_term_command555083
Ref: gnuplot_png_term_command555446
Ref: gnuplot_ps_term_command555771
Ref: gnuplot_strings556182
Ref: gnuplot_svg_term_command556771
Ref: gnuplot_curve_titles557091
Ref: gnuplot_curve_styles557224
Node: Gnuplot_pipes Format Functions557335
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Ref: gnuplot_replot557962
Ref: gnuplot_reset558231
Node: File Input and Output558431
Node: Comments558757
Node: Files560058
Node: Functions and Variables for File Input and Output561269
Ref: appendfile561548
Ref: batch561865
Ref: batchload564643
Ref: closefile565324
Ref: file_output_append565432
Ref: filename_merge566089
Ref: file_search566459
Ref: file_search_maxima568336
Ref: file_search_lisp568336
Ref: file_search_demo568336
Ref: file_search_usage568336
Ref: file_search_tests568336
Ref: file_type570010
Ref: file_type_lisp570933
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Ref: load571422
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Node: Functions and Variables for TeX Output584524
Ref: tex584965
Ref: tex1587314
Ref: texput587668
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Ref: get_tex_enviroment_default593986
Node: Functions and Variables for Fortran Output595210
Ref: fortindent595454
Ref: fortran595780
Ref: fortspaces598366
Node: Polynomials598548
Node: Introduction to Polynomials598772
Node: Functions and Variables for Polynomials601918
Ref: algebraic602114
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Ref: bezout602539
Ref: bothcoef603198
Ref: content607673
Ref: denom608148
Ref: divide608882
Ref: eliminate609516
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Ref: factor612354
Ref: factor_max_degree618776
Ref: factor_max_degree_print_warning620321
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Ref: factorsum621553
Ref: fasttimes622418
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Ref: fullratsubstflag626891
Ref: gcd627036
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Ref: lowpow634456
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Ref: modulus636742
Ref: num638653
Ref: polydecomp639429
Ref: polymod641391
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Ref: quotient643471
Ref: rat643827
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Ref: ratdenom647903
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Ref: ratexpand652719
Ref: ratfac655010
Ref: ratnumer656060
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Ref: radsubstflag659618
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Ref: ratvars661478
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Ref: option_resultant667718
Ref: savefactors668304
Ref: showratvars668622
Ref: sqfr668793
Ref: totaldisrep671849
Ref: untelltat672280
Node: Special Functions672388
Node: Introduction to Special Functions672835
Node: Bessel Functions674945
Ref: bessel_j675125
Ref: bessel_y675650
Ref: bessel_i676078
Ref: bessel_k676620
Ref: hankel_1677067
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Ref: scaled_bessel_i680453
Ref: scaled_bessel_i0680943
Ref: scaled_bessel_i1681028
Node: Airy Functions681232
Ref: airy_ai681800
Ref: airy_dai682005
Ref: airy_bi682122
Ref: airy_dbi682306
Node: Gamma and factorial Functions682441
Ref: bffac682810
Ref: bfpsi683030
Ref: cbffac683433
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Ref: gamma_incomplete687425
Ref: gamma_expand689361
Ref: gammalim691069
Ref: makegamma691485
Ref: beta691656
Ref: makefact714413
Node: Exponential Integrals715137
Node: Error Function717522
Ref: erf717812
Ref: erfc717916
Node: Struve Functions719372
Node: Hypergeometric Functions719871
Node: Parabolic Cylinder Functions722319
Node: Functions and Variables for Special Functions722921
Ref: specint723162
Ref: hgfred728870
Node: Elliptic Functions731855
Node: Introduction to Elliptic Functions and Integrals732164
Node: Functions and Variables for Elliptic Functions735960
Ref: jacobi_sn736263
Ref: jacobi_cn736344
Ref: jacobi_dn736425
Ref: jacobi_ns736506
Ref: jacobi_sc736599
Ref: jacobi_sd736698
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Ref: inverse_jacobi_dn737587
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Ref: inverse_jacobi_sd737899
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Ref: inverse_jacobi_ds738419
Ref: inverse_jacobi_dc738523
Node: Functions and Variables for Elliptic Integrals738627
Ref: elliptic_f738873
Ref: elliptic_e739090
Ref: elliptic_eu739327
Ref: elliptic_pi739677
Ref: elliptic_kc739856
Ref: elliptic_ec740147
Node: Limits740437
Node: Functions and Variables for Limits740604
Ref: lhospitallim740777
Ref: limit741023
Ref: limsubst743172
Ref: tlimit743459
Ref: tlimswitch743711
Node: Differentiation744208
Node: Functions and Variables for Differentiation744395
Ref: antid744613
Ref: antidiff747067
Ref: at749355
Ref: atomgrad752477
Ref: atvalue752621
Ref: cartan755268
Ref: init_cartan755869
Ref: del756665
Ref: delta757425
Ref: dependencies757788
Ref: depends759511
Ref: derivabbrev762239
Ref: derivdegree762512
Ref: derivlist763128
Ref: derivsubst763287
Ref: diff763511
Ref: symbol_diff766942
Ref: express767108
Ref: gradef769873
Ref: gradefs771945
Ref: laplace772244
Node: Integration777006
Node: Introduction to Integration777286
Node: Functions and Variables for Integration778302
Ref: changevar778549
Ref: dblint780886
Ref: defint783427
Ref: erfflag784006
Ref: ilt784244
Ref: intanalysis786577
Ref: integrate788078
Ref: integration_constant796829
Ref: integration_constant_counter797709
Ref: integrate_use_rootsof799071
Ref: ldefint801457
Ref: pwilt802206
Ref: potential803195
Ref: residue803755
Ref: risch804436
Ref: tldefint805514
Node: Introduction to QUADPACK805637
Ref: Introduction to QUADPACK-Footnote-1809413
Ref: Introduction to QUADPACK-Footnote-2809479
Ref: Introduction to QUADPACK-Footnote-3809545
Ref: Introduction to QUADPACK-Footnote-4809589
Ref: Introduction to QUADPACK-Footnote-5809651
Ref: Introduction to QUADPACK-Footnote-6809691
Ref: Introduction to QUADPACK-Footnote-7809733
Node: Functions and Variables for QUADPACK809918
Ref: quad_qag810120
Ref: quad_qags812923
Ref: quad_qagi815168
Ref: quad_qawc817706
Ref: quad_qawf820953
Ref: quad_qawo823665
Ref: quad_qaws826643
Ref: quad_qagp829596
Ref: quad_control832246
Node: Equations832860
Node: Functions and Variables for Equations833039
Ref: %rnum833227
Ref: %rnum_list833499
Ref: algepsilon834573
Ref: algexact834679
Ref: algsys835316
Ref: allroots840218
Ref: bfallroots842629
Ref: backsubst843048
Ref: breakup843778
Ref: dimension847088
Ref: dispflag847348
Ref: funcsolve847675
Ref: globalsolve848633
Ref: ieqn850693
Ref: ieqnprint854815
Ref: lhs855527
Ref: linsolve857179
Ref: linsolvewarn860383
Ref: linsolve_params860565
Ref: multiplicities860960
Ref: nroots861178
Ref: nthroot861596
Ref: polyfactor861953
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Ref: rootscontract866974
Ref: rootsepsilon869726
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Ref: solvedecomposes877091
Ref: solveexplicit877279
Ref: solvefactors877537
Ref: solvenullwarn877798
Ref: solveradcan878119
Ref: solvetrigwarn878386
Node: Differential Equations878650
Node: Introduction to Differential Equations878909
Node: Functions and Variables for Differential Equations879536
Ref: bc2879805
Ref: desolve880429
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Ref: ic2883149
Ref: ode2883828
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Node: Introduction to fast Fourier transform888348
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Ref: polartorect889164
Ref: recttopolar889800
Ref: inverse_fft890516
Ref: fft893164
Ref: real_fft897790
Ref: inverse_real_fft898571
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Ref: bf_inverse_real_fft899570
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Ref: fftpack5_inverse_fft902753
Ref: fftpack5_real_fft902923
Ref: fftpack5_inverse_real_fft903783
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Ref: horner904511
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Ref: bf_find_root905659
Ref: find_root_error905659
Ref: find_root_abs905659
Ref: find_root_rel905659
Ref: newton909843
Node: Introduction to numerical solution of differential equations911178
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Ref: rk923090
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Node: Introduction to Matrices and Linear Algebra926905
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Ref: cauchy_matrix933804
Ref: charpoly935215
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Ref: dot1simp943988
Ref: dotassoc944186
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Ref: eigenvectors948509
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Ref: invert_by_adjoint960871
Ref: invert961115
Ref: list_matrix_entries962281
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Ref: matrixexp969234
Ref: matrixmap969665
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Ref: matrix_element_add969954
Ref: matrix_element_mult971278
Ref: matrix_element_transpose973273
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Ref: scalefactors978894
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Ref: simtran980218
Ref: sparse981500
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Ref: triangularize982448
Ref: uniteigenvectors983514
Ref: ueivects983514
Ref: unitvector984853
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Ref: vectorpotential985099
Ref: vectorsimp985431
Ref: vect_cross986920
Ref: zeromatrix987150
Node: Affine987255
Node: Introduction to Affine987450
Node: Functions and Variables for Affine987693
Ref: fast_linsolve987882
Ref: grobner_basis988566
Ref: set_up_dot_simplifications989166
Ref: declare_weights990088
Ref: nc_degree990339
Ref: dotsimp990511
Ref: fast_central_elements990763
Ref: check_overlaps991184
Ref: mono991836
Ref: monomial_dimensions992082
Ref: extract_linear_equations992252
Ref: list_nc_monomials992648
Ref: all_dotsimp_denoms992946
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Node: Introduction to itensor993495
Node: Functions and Variables for itensor1006641
Ref: dispcon1006900
Ref: entertensor1007176
Ref: changename1007497
Ref: listoftens1007882
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Ref: indices1008761
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Ref: remcon1014949
Ref: contract_Itensor1015216
Ref: indexed_tensor1015729
Ref: components1015980
Ref: remcomps1020167
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Ref: idummyx1023058
Ref: icounter1023193
Ref: kdelta1023442
Ref: kdels1024268
Ref: levi_civita1025131
Ref: lc2kdt1025387
Ref: lc_l1028854
Ref: lc_u1029940
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Ref: flush1deriv1047226
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Ref: lorentz1051203
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Ref: ic_convert1076096
Node: ctensor1078912
Node: Introduction to ctensor1079092
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Ref: csetup1083800
Ref: cmetric1084019
Ref: ct1084998
Ref: init1091303
Ref: christof1092712
Ref: ricci1093659
Ref: uricci1093945
Ref: scurvature1094506
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Ref: uriemann1097524
Ref: rinvariant1097726
Ref: weyl1097977
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Ref: invariant21119397
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Ref: symmetricp1120065
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Node: Introduction to atensor1144638
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Ref: init_atensor1148888
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Ref: asymbol1152549
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Ref: product1157308
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Ref: sumexpand1165557
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Ref: niceindicespref1171738
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Ref: taylorinfo1190735
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Ref: taylor_logexpand1191751
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Ref: taylor_simplifier1192682
Ref: taylor_truncate_polynomials1192822
Ref: taytorat1193133
Ref: trunc1193337
Ref: unsum1193910
Ref: verbose1195134
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Ref: fourier1197623
Ref: foursimp1197773
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Ref: cosnpiflag1198045
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Ref: fourcos1198390
Ref: foursin1198526
Ref: totalfourier1198660
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Ref: fourintcos1198954
Ref: forintsin1199089
Node: Functions and Variables for Poisson series1199222
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Ref: poisdiff1199913
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Ref: poisint1200202
Ref: poislim1200387
Ref: poismap1200687
Ref: poisplus1201005
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Ref: poisson1201210
Ref: poissubst1201325
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Ref: printpois1202732
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Ref: bfhzeta1204396
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Ref: cfdisrep1209912
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Ref: isqrt1217721
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Ref: primep_number_of_tests1223367
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Ref: zeta%pi1226065
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Ref: zn_factor_generators1231790
Ref: zn_invert_by_lu1232022
Ref: zn_log1233048
Ref: zn_mult_table1236288
Ref: zn_nth_root1241733
Ref: zn_order1246578
Ref: zn_power_table1248831
Ref: zn_primroot1253716
Ref: zn_primroot_limit1256284
Ref: zn_primroot_p1256619
Ref: zn_primroot_pretest1258461
Ref: zn_primroot_verbose1258997
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Ref: ele2pui1261689
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Ref: elem1262131
Ref: mon2schur1263588
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Ref: pui2ele1268555
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Ref: polynome2ele1283631
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Ref: resolvante_klein31294959
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Ref: multinomial1297186
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Ref: todd_coxeter1297883
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Ref: maxima_tempdir1302469
Ref: maxima_userdir1302940
Ref: room1303669
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Ref: parse_timedate1308928
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Ref: decode_time1315178
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Ref: elapsed_real_time1317362
Ref: elapsed_run_time1317869
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Node: Introduction to Miscellaneous Options1318712
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Ref: remvalue1322445
Ref: rncombine1322899
Ref: setup_autoload1323618
Ref: tcl_output1325023
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Node: Introduction to Rules and Patterns1326507
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Ref: cartesian_product_list1379879
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Node: Introduction to Function Definition1423312
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Ref: memoizing function1426997
Ref: memoizing functions1426997
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Ref: Memoizing functions1426997
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Ref: tr_file_tty_messagesp1496792
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Ref: garbage_collect1507868
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Ref: timer_devalue1553515
Ref: timer_info1553955
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Ref: alt_display_output_type1561784
Ref: define_alt_display1563546
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Ref: asympa1571183
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Ref: augmented_lagrangian_method1572172
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Ref: bernstein_poly1576243
Ref: bernstein_explicit1578145
Ref: multibernstein_poly1578806
Ref: bernstein_approx1579253
Ref: bernstein_expand1580521
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Ref: bit_not1581667
Ref: bit_and1582212
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Ref: bit_xor1583928
Ref: bit_lsh1584793
Ref: bit_rsh1585565
Ref: bit_length1586345
Ref: bit_onep1586872
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Ref: bode_gain1588780
Ref: bode_phase1590192
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Node: Introduction to celine1592004
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Node: Functions and Variables for clebsch_gordan1596027
Ref: clebsch_gordan1596248
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Ref: racah_w1596542
Ref: wigner_3j1596685
Ref: wigner_6j1596846
Ref: wigner_9j1596942
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Ref: fmin_cobyla1599987
Ref: bf_fmin_cobyla1602807
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Ref: apply_cycles1607272
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Ref: perm_inverse1609500
Ref: perm_length1609948
Ref: perm_lex_next1610417
Ref: perm_lex_rank1610756
Ref: perm_lex_unrank1611176
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Ref: random_perm1618145
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Ref: contrib_ode1624861
Ref: odelin1625020
Ref: ode_check1625801
Ref: gauss_a1627328
Ref: gauss_b1627904
Ref: dgauss_a1627972
Ref: dgauss_b1628100
Ref: kummer_m1628228
Ref: kummer_u1628658
Ref: dkummer_m1628845
Ref: dkummer_u1628960
Ref: bessel_simplify1629075
Ref: expintegral_e_simplify1630253
Node: Possible improvements to contrib_ode1630500
Node: Test cases for contrib_ode1631644
Node: References for contrib_ode1632427
Node: descriptive-pkg1633972
Node: Introduction to descriptive1634297
Node: Functions and Variables for data manipulation1639459
Ref: build_sample1639754
Ref: continuous_freq1642107
Ref: discrete_freq1644864
Ref: standardize1646208
Ref: subsample1646589
Ref: transform_sample1652827
Node: Functions and Variables for descriptive statistics1654415
Ref: mean1654739
Ref: var1655612
Ref: var11656226
Ref: std1657081
Ref: std11657735
Ref: noncentral_moment1658396
Ref: central_moment1659337
Ref: cv1660300
Ref: smin1660962
Ref: smax1661604
Ref: range1662249
Ref: quantile1662725
Ref: median1663635
Ref: qrange1664375
Ref: mean_deviation1665127
Ref: median_deviation1666096
Ref: harmonic_mean1666995
Ref: geometric_mean1667934
Ref: kurtosis1668865
Ref: skewness1669754
Ref: pearson_skewness1670655
Ref: quartile_skewness1671496
Ref: km1672417
Ref: cdf_empirical1673887
Ref: cov1674907
Ref: cov11676177
Ref: global_variances1677447
Ref: cor1679321
Ref: list_correlations1681519
Ref: principal_components1684740
Node: Functions and Variables for statistical graphs1689029
Ref: barsplot1689291
Ref: barsplot_description1693957
Ref: boxplot1694861
Ref: boxplot_description1698682
Ref: histogram1698869
Ref: histogram_description1702729
Ref: piechart1703555
Ref: piechart_description1705251
Ref: scatterplot1705440
Ref: scatterplot_description1707403
Ref: starplot1707603
Ref: starplot_description1709992
Ref: stemplot1710181
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Node: Functions and Variables for diag1711343
Ref: diag_function1711514
Ref: JF1712781
Ref: jordan1713601
Ref: dispJordan1716067
Ref: minimalPoly1717247
Ref: ModeMatrix1718007
Ref: mat_function1719769
Node: distrib-pkg1723880
Node: Introduction to distrib1724138
Node: Functions and Variables for continuous distributions1730312
Ref: pdf_normal1730620
Ref: cdf_normal1730834
Ref: quantile_normal1731449
Ref: mean_normal1732056
Ref: var_normal1732242
Ref: std_normal1732438
Ref: skewness_normal1732642
Ref: kurtosis_normal1732869
Ref: random_normal1733096
Ref: pdf_student_t1733596
Ref: cdf_student_t1733829
Ref: quantile_student_t1734432
Ref: mean_student_t1734734
Ref: var_student_t1734941
Ref: std_student_t1735252
Ref: skewness_student_t1735444
Ref: kurtosis_student_t1735671
Ref: random_student_t1735870
Ref: pdf_noncentral_student_t1736699
Ref: cdf_noncentral_student_t1737806
Ref: quantile_noncentral_student_t1738245
Ref: mean_noncentral_student_t1738655
Ref: var_noncentral_student_t1739303
Ref: std_noncentral_student_t1739576
Ref: skewness_noncentral_student_t1739859
Ref: kurtosis_noncentral_student_t1740149
Ref: random_noncentral_student_t1740439
Ref: pdf_chi21741386
Ref: cdf_chi21741960
Ref: quantile_chi21742428
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Ref: var_chi21743142
Ref: std_chi21743434
Ref: skewness_chi21743742
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Ref: random_chi21744616
Ref: pdf_noncentral_chi21745029
Ref: cdf_noncentral_chi21745320
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Ref: mean_noncentral_chi21746001
Ref: var_noncentral_chi21746181
Ref: std_noncentral_chi21746364
Ref: skewness_noncentral_chi21746562
Ref: kurtosis_noncentral_chi21746767
Ref: random_noncentral_chi21746972
Ref: pdf_f1747384
Ref: cdf_f1747592
Ref: quantile_f1748056
Ref: mean_f1748404
Ref: var_f1748575
Ref: std_f1748748
Ref: skewness_f1748937
Ref: kurtosis_f1749133
Ref: random_f1749329
Ref: pdf_exp1749956
Ref: cdf_exp1750335
Ref: quantile_exp1750721
Ref: mean_exp1751355
Ref: var_exp1751734
Ref: std_exp1752162
Ref: skewness_exp1752558
Ref: kurtosis_exp1752878
Ref: random_exp1753198
Ref: pdf_lognormal1753572
Ref: cdf_lognormal1753792
Ref: quantile_lognormal1754388
Ref: mean_lognormal1754936
Ref: var_lognormal1755116
Ref: std_lognormal1755298
Ref: skewness_lognormal1755496
Ref: kurtosis_lognormal1755701
Ref: random_lognormal1755906
Ref: pdf_gamma1756352
Ref: cdf_gamma1756566
Ref: quantile_gamma1757035
Ref: mean_gamma1757333
Ref: var_gamma1757507
Ref: std_gamma1757683
Ref: skewness_gamma1757875
Ref: kurtosis_gamma1758074
Ref: random_gamma1758273
Ref: pdf_beta1759007
Ref: cdf_beta1759219
Ref: quantile_beta1759644
Ref: mean_beta1759940
Ref: var_beta1760112
Ref: std_beta1760286
Ref: skewness_beta1760476
Ref: kurtosis_beta1760673
Ref: random_beta1760870
Ref: pdf_continuous_uniform1761357
Ref: cdf_continuous_uniform1761595
Ref: quantile_continuous_uniform1761838
Ref: mean_continuous_uniform1762179
Ref: var_continuous_uniform1762377
Ref: std_continuous_uniform1762583
Ref: skewness_continuous_uniform1762799
Ref: kurtosis_continuous_uniform1763022
Ref: random_continuous_uniform1763245
Ref: pdf_logistic1763722
Ref: cdf_logistic1763941
Ref: quantile_logistic1764165
Ref: mean_logistic1764471
Ref: var_logistic1764650
Ref: std_logistic1764831
Ref: skewness_logistic1765028
Ref: kurtosis_logistic1765232
Ref: random_logistic1765436
Ref: pdf_pareto1765831
Ref: cdf_pareto1766047
Ref: quantile_pareto1766268
Ref: mean_pareto1766569
Ref: var_pareto1766746
Ref: std_pareto1766932
Ref: skewness_pareto1767128
Ref: kurtosis_pareto1767331
Ref: random_pareto1767534
Ref: pdf_weibull1767925
Ref: cdf_weibull1768143
Ref: quantile_weibull1768366
Ref: mean_weibull1768670
Ref: var_weibull1768848
Ref: std_weibull1769028
Ref: skewness_weibull1769224
Ref: kurtosis_weibull1769427
Ref: random_weibull1769630
Ref: pdf_rayleigh1770023
Ref: cdf_rayleigh1770459
Ref: quantile_rayleigh1770897
Ref: mean_rayleigh1771431
Ref: var_rayleigh1771822
Ref: std_rayleigh1772348
Ref: skewness_rayleigh1772856
Ref: kurtosis_rayleigh1773520
Ref: random_rayleigh1774164
Ref: pdf_laplace1774550
Ref: cdf_laplace1774766
Ref: quantile_laplace1774987
Ref: mean_laplace1775289
Ref: var_laplace1775465
Ref: std_laplace1775643
Ref: skewness_laplace1775837
Ref: kurtosis_laplace1776038
Ref: random_laplace1776239
Ref: pdf_cauchy1776630
Ref: cdf_cauchy1776844
Ref: quantile_cauchy1777063
Ref: random_cauchy1777363
Ref: pdf_gumbel1777750
Ref: cdf_gumbel1777964
Ref: quantile_gumbel1778183
Ref: mean_gumbel1778483
Ref: var_gumbel1778805
Ref: std_gumbel1778981
Ref: skewness_gumbel1779173
Ref: kurtosis_gumbel1779697
Ref: random_gumbel1779896
Node: Functions and Variables for discrete distributions1780283
Ref: pdf_general_finite_discrete1780555
Ref: cdf_general_finite_discrete1781408
Ref: quantile_general_finite_discrete1782280
Ref: mean_general_finite_discrete1782510
Ref: var_general_finite_discrete1782724
Ref: std_general_finite_discrete1782941
Ref: skewness_general_finite_discrete1783168
Ref: kurtosis_general_finite_discrete1783402
Ref: random_general_finite_discrete1783636
Ref: pdf_binomial1784274
Ref: cdf_binomial1784538
Ref: quantile_binomial1785009
Ref: mean_binomial1785357
Ref: var_binomial1785577
Ref: std_binomial1785800
Ref: skewness_binomial1786033
Ref: kurtosis_binomial1786273
Ref: random_binomial1786513
Ref: pdf_poisson1787078
Ref: cdf_poisson1787292
Ref: quantile_poisson1787636
Ref: mean_poisson1787933
Ref: var_poisson1788103
Ref: std_poisson1788276
Ref: skewness_poisson1788464
Ref: kurtosis_poisson1788659
Ref: random_poisson1788858
Ref: pdf_bernoulli1789402
Ref: cdf_bernoulli1789756
Ref: quantile_bernoulli1789987
Ref: mean_bernoulli1790302
Ref: var_bernoulli1790616
Ref: std_bernoulli1790936
Ref: skewness_bernoulli1791276
Ref: kurtosis_bernoulli1791740
Ref: random_bernoulli1792184
Ref: pdf_geometric1792628
Ref: cdf_geometric1792979
Ref: quantile_geometric1793370
Ref: mean_geometric1793831
Ref: var_geometric1794165
Ref: std_geometric1794506
Ref: skewness_geometric1794867
Ref: kurtosis_geometric1795225
Ref: random_geometric1795593
Ref: pdf_discrete_uniform1796153
Ref: cdf_discrete_uniform1796411
Ref: quantile_discrete_uniform1796670
Ref: mean_discrete_uniform1797025
Ref: var_discrete_uniform1797244
Ref: std_discrete_uniform1797466
Ref: skewness_discrete_uniform1797698
Ref: kurtosis_discrete_uniform1797937
Ref: random_discrete_uniform1798176
Ref: pdf_hypergeometric1798663
Ref: cdf_hypergeometric1799199
Ref: quantile_hypergeometric1799567
Ref: mean_hypergeometric1799955
Ref: var_hypergeometric1800221
Ref: std_hypergeometric1800488
Ref: skewness_hypergeometric1800761
Ref: kurtosis_hypergeometric1801041
Ref: random_hypergeometric1801321
Ref: pdf_negative_binomial1801945
Ref: cdf_negative_binomial1802223
Ref: quantile_negative_binomial1802645
Ref: mean_negative_binomial1803016
Ref: var_negative_binomial1803250
Ref: std_negative_binomial1803487
Ref: skewness_negative_binomial1803734
Ref: kurtosis_negative_binomial1803988
Ref: random_negative_binomial1804242
Node: draw-pkg1804755
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Ref: gr2d1807737
Ref: gr3d1809075
Ref: draw1809982
Ref: draw2d1812076
Ref: draw3d1812356
Ref: draw_file1812636
Ref: multiplot_mode1813089
Ref: set_draw_defaults1814467
Ref: adapt_depth_draw1815291
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Ref: axis_3d1816955
Ref: axis_bottom1817468
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Ref: axis_right1818375
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Ref: capping1820272
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Ref: cbtics1821844
Ref: color_draw1822556
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Ref: columns1827430
Ref: contour1828070
Ref: contour_levels1829222
Ref: data_file_name1831185
Ref: delay1831588
Ref: dimensions_draw1832436
Ref: draw_realpart1834028
Ref: enhanced3d1834727
Ref: error_type1840614
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Ref: fill_color1841583
Ref: fill_density1841806
Ref: filled_func1842031
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Ref: head_both1850003
Ref: head_length1850638
Ref: head_type1851349
Ref: interpolate_color1852203
Ref: ip_grid1855041
Ref: ip_grid_in1855244
Ref: key1855457
Ref: key_pos1856257
Ref: label_alignment1857338
Ref: label_orientation1858272
Ref: line_type1859223
Ref: line_width1860250
Ref: logcb1861016
Ref: logx_draw1861760
Ref: logx_secondary1862345
Ref: logy_draw1863240
Ref: logy_secondary1863694
Ref: logz1864555
Ref: palette_draw1865684
Ref: point_size1868968
Ref: point_type_draw1869576
Ref: points_joined1871366
Ref: proportional_axes1872575
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Ref: transform1878046
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Ref: xaxis_width1885953
Ref: xlabel_draw1886424
Ref: xlabel_secondary1886971
Ref: xrange1887724
Ref: xrange_secondary1888260
Ref: xtics_draw1888779
Ref: xtics_axis1890761
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Ref: xtics_rotate_secondary1891369
Ref: xtics_secondary1891669
Ref: xtics_secondary_axis1891884
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Ref: xyplane1893154
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Ref: yaxis1893944
Ref: yaxis_color1894390
Ref: yaxis_secondary1894894
Ref: yaxis_type1895609
Ref: yaxis_width1896113
Ref: ylabel_draw1896584
Ref: ylabel_secondary1897138
Ref: yrange1897987
Ref: yrange_secondary1898587
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Ref: ytics_axis1899620
Ref: ytics_rotate1899958
Ref: ytics_rotate_secondary1900228
Ref: ytics_secondary1900528
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Ref: zaxis1901879
Ref: zaxis_color1902438
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Ref: zaxis_width1903604
Ref: zlabel_draw1904171
Ref: zlabel_rotate1904758
Ref: zrange1905369
Ref: ztics_draw1905996
Ref: ztics_axis1906194
Ref: ztics_rotate1906532
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Ref: cylindrical1907759
Ref: elevation_grid1908518
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Ref: image1914297
Ref: implicit1918139
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Ref: rectangle1935078
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Ref: spherical1936858
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Ref: draw_renderer1940797
Node: Functions and Variables for pictures1940960
Ref: get_pixel1941212
Ref: make_level_picture1941380
Ref: make_rgb_picture1942556
Ref: negative_picture1943683
Ref: picture_equalp1943782
Ref: picturep1943900
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Ref: rgb2level1944118
Ref: take_channel1944255
Node: Functions and Variables for worldmap1945183
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Ref: numbered_boundaries1945816
Ref: make_poly_continent1946349
Ref: make_poly_country1946959
Ref: make_polygon1947319
Ref: region_boundaries1950454
Ref: region_boundaries_plus1951003
Ref: geomap1951639
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Ref: drawdf1960261
Node: dynamics-pkg1968805
Node: The dynamics package1969047
Node: Graphical analysis of discrete dynamical systems1969733
Ref: chaosgame1969999
Ref: evolution1970765
Ref: evolution2d1971511
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Ref: orbits1973973
Ref: staircase1975401
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Ref: scene_options1978997
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Ref: scene_background1979343
Ref: scene_elevation1979592
Ref: scene_height1979926
Ref: scene_restart1980104
Ref: scene_tstep1980357
Ref: scene_width1980561
Ref: scene_windowname1980736
Ref: scene_windowtitle1981041
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Ref: cube1982166
Ref: cylinder1982507
Ref: sphere1983164
Ref: object_options1983284
Ref: object_animation1983345
Ref: object_capping1983964
Ref: object_center1984222
Ref: object_color1984583
Ref: object_endphi1984800
Ref: object_endtheta1985266
Ref: object_height1985728
Ref: object_linewidth1985893
Ref: object_opacity1986080
Ref: object_orientation1986339
Ref: object_origin1986717
Ref: object_phiresolution1986993
Ref: object_points1987291
Ref: object_pointsize1987506
Ref: object_position1987690
Ref: object_radius1987911
Ref: object_resolution1988139
Ref: object_scale1988342
Ref: object_startphi1988797
Ref: object_starttheta1989264
Ref: object_surface1989727
Ref: object_thetaresolution1990030
Ref: object_track1990342
Ref: object_xlength1991333
Ref: object_ylength1991541
Ref: object_zlength1991749
Ref: object_wireframe1991957
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Node: Functions and Variables for engineering-format1992540
Ref: engineering_format_floats1992781
Ref: engineering_format_min1993355
Ref: engineering_format_max1994138
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Ref: physical_constants1998598
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Ref: declare_constvalue2015557
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Ref: small_rhombicuboctahedron_graph2066196
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Ref: snub_dodecahedron_graph2066364
Ref: truncated_cube_graph2066448
Ref: truncated_dodecahedron_graph2066526
Ref: truncated_icosahedron_graph2066620
Ref: truncated_tetrahedron_graph2066712
Ref: tutte_graph2066804
Ref: underlying_graph2066864
Ref: wheel_graph2066963
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Ref: clear_vertex_label2069909
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Ref: dimacs_export2097204
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Ref: graph6_decode2097559
Ref: graph6_encode2097670
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Ref: draw_graph2098546
Ref: draw_graph_program2101778
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Ref: vertices_to_cycle2106463
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Ref: poly_subtract2111740
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Ref: poly_normalize2112663
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Ref: poly_expt2114450
Ref: poly_content2114747
Ref: poly_pseudo_divide2114955
Ref: poly_exact_divide2115579
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Ref: poly_buchberger2116311
Ref: poly_reduction2117010
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Ref: Introduction to ODEPACK-Footnote-12269697
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Ref: hermite2301456
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