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README.md
In rim: Interface to 'Maxima', Enabling Symbolic Computation
rim - R’s interface to Maxima
Development version of CRAN package. rim provides an interface to the
powerful and fairly complete maxima computer algebra system
This repository is a fork from RMaxima, the original version created by
Kseniia Shumelchyk and Hans W. Borcher
shumelchyk/rmaxima, which is
currently not maintained.
Installation
install.packages("rim")
Requirements
- Maxima (https://sourceforge.net/projects/maxima/, tested with
versions >=5.42.1), needs to be on PATH
Latest Version
If you want to install the latest version install the R package
remotes first and then install the package from this github repo:
install.packages("remotes")
remotes::install_github("rcst/rim")
Usage
This section only demonstrates the package’s R-function directly
accessible to the user. On how to use the package’s knitr engine see
this page.
library(rim)
maxima.start(restart = TRUE)
maxima.get("1+1;")
## (%o1) 2
r <- maxima.get("sum(1/x^2, x, 1, 10000)")
## Warning in value[[3L]](cond): Caught error while parsing
## Überlauf des Eingabebuffers in Zeile 1
## Returning NA.
print(r)
## (%o2) 54714423173933343999582177160129362529870283624174963297531328605746589773430778183198620050736675427362803973347189596920858374826198299243875944018790714269022039209429246957120164226897122221467774889383041528298564231525726005885733604890567741863788282223101091820040246774500899582880738779441903043993446797207474982772365818204209418017874472746075929430402719315899195398091579911840793724334501466809497514690646349026417408657798612724412146815881907468466138871837138164123922629387751665906831009172724807380344362641581163733346203555718850891948260773752299205407726870601562897167876485357851589965396280602666157317110387959451092855487589490685186018122043775191659379508292628762992096830369387377564339210809700754302538398507252386941602236810441631669594849503782189852039566430411366575909380827769724447338940111761588124004276515786306137226537894846082264669311720594628838458236534704442082294084133019729052294375893488930238771136044176775587032445127166320941961770547230342282891720711094680202323745272645863298738706071559533479377820073676651860866476014981202902915165425984274917243253526013326104533936418682251997405429350574846738597941596465847889444363702434675773342527460766142607487599035002858371082612263524228218717418382091490999753564503938592826918552223027205803181181888741408228059697739547051812861769394298478975745066997066788703540179782594827175983300181264325697248430726629456282185376474013917829429243519811721072662085485111045703987412094220689686673634241955047247609854041200778578542832459371567518406936908136456278580855326355096792872324174145562813303949605379230174018494117853603702152059335440764083293322471807283069472531202462722202917551408494598048677137074200859816690275986663030277286569976460908346358904422964424746645104732745352326121282910390649387427416055754359188091700147618060211231503082679247785691660641065431271701057523938788707846180991151470917443986898990696238399554440903455233022468088651148799684030267146193796334043119080594644322358796906759836770505103557429631622296333030266327046011619967776159634366887279937028243689380001409729105518639839675945116128815330668016315503185899714161216687671230574073946303172784011192584424549790851949628053757067125708116500923344172251805167855674009789352798000845818461242899224835938000020378170885269055841255490568216829243335871796252244109330529902983716481736108361446573154715062745211442983313584589859718458201409644684427903762533836045799364210919834689625426037370437764039595607214082990598178228046116112630636040001663147483205019386481519822689029391114522931957183171963601512521439959563534069438676951975087909832523209070515108411852576337766181331210245202556778537611245618032446627001987176726069215070633346030796232494244019728751779926096081430988292745260805874652716348627255093805602013625670873133828325514622056327230677993441485202456141624053594915112957418286324951364793572836369723116492808563095213991319047761945317187869248729375289646267504478167028273396579524813913334151803023358073522405222549035123864804815678071618740638054974112593483726390502113599929647317259818412046014321600804441793135484014715991040128640051384584336103707601446933382393773627271309500975826400733339412405476577984912684169457984989567273831263186466544309763153431065963866240968246813680236626161775578250353653632304278658916659205865168664633596162571073255555785527047441982726477428415441608391620914299858924649341080842414427042884773862327960684379853819918113906923732799168708234502574103035248876408173859907743983277977179889939690429027728899836034303103846198087243860133694609495003085594474285042927122313337572294151335513419111029590872832714904180393358701596366385951443810672106202469574018799513459696965569155880094143095244341376943866450111670328409290239406024323584249461010638411786389182375518466075581091820058065184342719352703433649383541885319070885434140096435888895915838399889468766955213317926658229843966956015883000989184322171710713223649126536034372588359814912282338149828331742475288776165758624668302616582826157942988548761128057396876656217465326482735010879330795681553493747259618459826243669763540270027708731304870445825284361682698093387761793742048304278104093500532463894820462859057282396283759525305867486353270235939534246792138612608840528996034304412039332005879449134846209923941893166636009769500421980450818388532886689781787068817196712858933448063045608771626658106014788519330242475177372495165820226543420903872341980336920464845619553623926915434440577108858461813046669675213100608647130957218743496405831782804948156306093884408227146007099300059879697593185055729716721089763708268661326778789153938771996075981554131700962184855700361219028651893129459248410229172748625837731140325878800075436691689542794858719884224083845593868131724898886440575779158384233204867975224464329634148174423778660117199058743344643347405140437467793625685821216020779247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iprint(r)
## [1] "(%i2) sum(1/x^2, x, 1, 10000)"
maxima.isInstalled()
## [1] TRUE
maxima.version()
## [1] '5.44.0'
maxima.options
## Option Value
## -------------:------------------------------------------------------------------------------------------------------
## format linear
## (Printing format of returned object from maxima.get())
## engine.format linear
## (Same as 'format', but for maxima code chunks in 'RMarkdown' documents.)
## inline.format linear
## (Same as 'engine.format', but for printing output inline via maxima.inline(). Cannot be set to 'ascii'.)
## label TRUE
## (Sets whether a maxima reference label should be printed when printing a maxima return object.)
## engine.label TRUE
## (Same as 'label', but for maxima code chunks.)
## inline.label TRUE
## (Same as 'label', but for inline code chunks)
maxima.options(format = "ascii")
maxima.apropos("int")
## (%o3) [adjoint, adjoint-impl, askinteger, askinteger-impl,
## beta_args_sum_to_integer, cint, defint, defint-impl, disjointp,
## disjointp-impl, display_format_internal, expint, expint-impl, expintegral_chi,
## expintegral_chi-impl, expintegral_ci, expintegral_ci-impl, expintegral_e,
## expintegral_e-impl, expintegral_e1, expintegral_e1-impl, expintegral_ei,
## expintegral_ei-impl, expintegral_hyp, expintegral_li, expintegral_li-impl,
## expintegral_shi, expintegral_shi-impl, expintegral_si, expintegral_si-impl,
## expintegral_trig, expintexpand, expintrep, factor_max_degree_print_warning,
## floatint, fpprintprec, gcprint, intanalysis, integer, integer_partitions,
## integer_partitions-impl, integerp, integerp-impl, integervalued, integral,
## integrate, integrate-impl, integrate_use_rootsof, integration_constant,
## integration_constant_counter, interaction, interpolate, intersect,
## intersect-impl, intersection, intersection-impl, intervalp, intfaclim,
## intopois, intopois-impl, intosum, intosum-impl, invert_by_adjoint,
## invert_by_adjoint-impl, invert_by_adjoint_size_limit, ldefint, ldefint-impl,
## linespoints, lisp_print, loadprint, lognegint, mapprint, maxfpprintprec,
## maxpsinegint, maxpsiposint, mdebug_print_length, ninth, nointegrate,
## noninteger, nonnegintegerp, noprint, point_type, pointbound, points, poisint,
## poisint-impl, print, print-impl, printf, printfile, printfile-impl, printpois,
## printpois-impl, printprops, printvarlist, printvarlist-impl, ratprint,
## require_integer, require_posinteger, require_selfadjoint_matrix, specint,
## specint-impl, sprint, tldefint, tldefint-impl, e-integer-coeff]
maxima.get("integrate(1 / (x^4 + 1), x);")
## 2 x + sqrt(2)
## 2 2 atan(-------------)
## log(x + sqrt(2) x + 1) log(x - sqrt(2) x + 1) sqrt(2)
## (%o4) ----------------------- - ----------------------- + -------------------
## 5/2 5/2 3/2
## 2 2 2
## 2 x - sqrt(2)
## atan(-------------)
## sqrt(2)
## + -------------------
## 3/2
## 2
maxima.get("jacobian( [alpha / (alpha + beta), 1 / sqrt(alpha + beta)], [alpha, beta] )")
## [ 1 alpha alpha ]
## [ ------------ - --------------- - --------------- ]
## [ beta + alpha 2 2 ]
## [ (beta + alpha) (beta + alpha) ]
## (%o5) [ ]
## [ 1 1 ]
## [ - ------------------- - ------------------- ]
## [ 3/2 3/2 ]
## [ 2 (beta + alpha) 2 (beta + alpha) ]
l <- maxima.get("%;")
maxima.eval(l, code = TRUE, envir = list(alpha = 0.3, beta = 2.5))
## [,1] [,2]
## [1,] 0.3188776 -0.03826531
## [2,] -0.1067168 -0.10671684
## attr(,"maxima")
## matrix(data = c(((-1L * alpha * ((alpha + beta)^-2L)) + ((alpha +
## beta)^-1L)), ((-1L/2L) * ((alpha + beta)^(-3L/2L))), (-1L *
## alpha * ((alpha + beta)^-2L)), ((-1L/2L) * ((alpha + beta)^(-3L/2L)))),
## ncol = 2, nrow = 2)
unclass(l)
## $wtl
## $wtl$linear
## [1] "(%o6) matrix([1/(beta+alpha)-alpha/(beta+alpha)^2,-alpha/(beta+alpha)^2]," " [-1/(2*(beta+alpha)^(3/2)),-1/(2*(beta+alpha)^(3/2))])"
##
## $wtl$ascii
## [1] " [ 1 alpha alpha ]" " [ ------------ - --------------- - --------------- ]"
## [3] " [ beta + alpha 2 2 ]" " [ (beta + alpha) (beta + alpha) ]"
## [5] "(%o6) [ ]" " [ 1 1 ]"
## [7] " [ - ------------------- - ------------------- ]" " [ 3/2 3/2 ]"
## [9] " [ 2 (beta + alpha) 2 (beta + alpha) ]"
##
## $wtl$latex
## [1] "$$\\mathtt{(\\textit{\\%o}_{6})}\\quad \\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} \\\\ -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} & -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} \\\\ \\end{pmatrix}$$"
##
## $wtl$inline
## [1] "$\\mathtt{(\\textit{\\%o}_{6})}\\quad \\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} \\\\ -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} & -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} \\\\ \\end{pmatrix}$"
##
## $wtl$mathml
## [1] " <math xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mi>mlabel</mi> " " <mfenced separators=\"\"><msub><mi>%o</mi> <mn>6</mn></msub> "
## [3] " <mo>,</mo><mfenced separators=\"\" open=\"(\" close=\")\"><mtable>" " <mtr><mtd><mfrac><mrow><mn>1</mn> </mrow> <mrow><mi>β</mi> "
## [5] " <mo>+</mo> <mi>α</mi> </mrow></mfrac> <mo>-</mo> <mfrac><mrow>" " <mi>α</mi> </mrow> <mrow><msup><mrow><mfenced separators=\"\">"
## [7] " <mi>β</mi> <mo>+</mo> <mi>α</mi> </mfenced> </mrow> " " <mn>2</mn> </msup> </mrow></mfrac> </mtd><mtd><mo>-</mo>"
## [9] " <mfrac><mrow><mi>α</mi> </mrow> <mrow><msup><mrow>" " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> "
## [11] " </mfenced> </mrow> <mn>2</mn> </msup> </mrow></mfrac> </mtd></mtr> " " <mtr><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>"
## [13] " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>" " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> "
## [15] " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>" " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> "
## [17] " </mtd><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>" " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>"
## [19] " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> " " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>"
## [21] " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> " " </mtd></mtr> </mtable></mfenced> </mfenced> </math>"
##
##
## $wol
## $wol$linear
## [1] "matrix([1/(beta+alpha)-alpha/(beta+alpha)^2,-alpha/(beta+alpha)^2]," " [-1/(2*(beta+alpha)^(3/2)),-1/(2*(beta+alpha)^(3/2))])"
##
## $wol$ascii
## [1] "[ 1 alpha alpha ]" "[ ------------ - --------------- - --------------- ]" "[ beta + alpha 2 2 ]"
## [4] "[ (beta + alpha) (beta + alpha) ]" "[ ]" "[ 1 1 ]"
## [7] "[ - ------------------- - ------------------- ]" "[ 3/2 3/2 ]" "[ 2 (beta + alpha) 2 (beta + alpha) ]"
##
## $wol$latex
## [1] "$$\\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} \\\\ -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} & -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} \\\\ \\end{pmatrix}$$"
##
## $wol$inline
## [1] "$\\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} \\\\ -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} & -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} \\\\ \\end{pmatrix}$"
##
## $wol$mathml
## [1] " <math xmlns=\"http://www.w3.org/1998/Math/MathML\"> " " <mfenced separators=\"\" open=\"(\" close=\")\"><mtable><mtr><mtd>"
## [3] " <mfrac><mrow><mn>1</mn> </mrow> <mrow><mi>β</mi> <mo>+</mo> " " <mi>α</mi> </mrow></mfrac> <mo>-</mo> <mfrac><mrow>"
## [5] " <mi>α</mi> </mrow> <mrow><msup><mrow><mfenced separators=\"\">" " <mi>β</mi> <mo>+</mo> <mi>α</mi> </mfenced> </mrow> "
## [7] " <mn>2</mn> </msup> </mrow></mfrac> </mtd><mtd><mo>-</mo>" " <mfrac><mrow><mi>α</mi> </mrow> <mrow><msup><mrow>"
## [9] " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> " " </mfenced> </mrow> <mn>2</mn> </msup> </mrow></mfrac> </mtd></mtr> "
## [11] " <mtr><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>" " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>"
## [13] " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> " " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>"
## [15] " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> " " </mtd><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>"
## [17] " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>" " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> "
## [19] " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>" " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> "
## [21] " </mtd></mtr> </mtable></mfenced> </math>"
##
## $wol$rstr
## [1] "matrix(data = c(((-1L * alpha * ((alpha + beta) ^ -2L)) + ((alpha + beta) ^ -1L)), ((-1L / 2L) * ((alpha + beta) ^ (-3L / 2L))), (-1L * alpha * ((alpha + beta) ^ -2L)), ((-1L / 2L) * ((alpha + beta) ^ (-3L / 2L)))), ncol = 2, nrow = 2)"
##
##
## attr(,"input.label")
## [1] "%i6"
## attr(,"output.label")
## [1] "%o6"
## attr(,"command")
## [1] "%;"
## attr(,"suppressed")
## [1] FALSE
## attr(,"parsed")
## matrix(data = c(((-1L * alpha * ((alpha + beta)^-2L)) + ((alpha +
## beta)^-1L)), ((-1L/2L) * ((alpha + beta)^(-3L/2L))), (-1L *
## alpha * ((alpha + beta)^-2L)), ((-1L/2L) * ((alpha + beta)^(-3L/2L)))),
## ncol = 2, nrow = 2)
maxima.load("abs_integrate")
maxima.stop()
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rim - R’s interface to Maxima
Development version of CRAN package. rim provides an interface to the
powerful and fairly complete maxima computer algebra system
This repository is a fork from RMaxima, the original version created by Kseniia Shumelchyk and Hans W. Borcher shumelchyk/rmaxima, which is currently not maintained.
Installation
install.packages("rim")
Requirements
- Maxima (https://sourceforge.net/projects/maxima/, tested with versions >=5.42.1), needs to be on PATH
Latest Version
If you want to install the latest version install the R package
remotes first and then install the package from this github repo:
install.packages("remotes")
remotes::install_github("rcst/rim")
Usage
This section only demonstrates the package’s R-function directly
accessible to the user. On how to use the package’s knitr engine see
this page.
library(rim)
maxima.start(restart = TRUE)
maxima.get("1+1;")
## (%o1) 2
r <- maxima.get("sum(1/x^2, x, 1, 10000)")
## Warning in value[[3L]](cond): Caught error while parsing
## Überlauf des Eingabebuffers in Zeile 1
## Returning NA.
print(r)
## (%o2) 54714423173933343999582177160129362529870283624174963297531328605746589773430778183198620050736675427362803973347189596920858374826198299243875944018790714269022039209429246957120164226897122221467774889383041528298564231525726005885733604890567741863788282223101091820040246774500899582880738779441903043993446797207474982772365818204209418017874472746075929430402719315899195398091579911840793724334501466809497514690646349026417408657798612724412146815881907468466138871837138164123922629387751665906831009172724807380344362641581163733346203555718850891948260773752299205407726870601562897167876485357851589965396280602666157317110387959451092855487589490685186018122043775191659379508292628762992096830369387377564339210809700754302538398507252386941602236810441631669594849503782189852039566430411366575909380827769724447338940111761588124004276515786306137226537894846082264669311720594628838458236534704442082294084133019729052294375893488930238771136044176775587032445127166320941961770547230342282891720711094680202323745272645863298738706071559533479377820073676651860866476014981202902915165425984274917243253526013326104533936418682251997405429350574846738597941596465847889444363702434675773342527460766142607487599035002858371082612263524228218717418382091490999753564503938592826918552223027205803181181888741408228059697739547051812861769394298478975745066997066788703540179782594827175983300181264325697248430726629456282185376474013917829429243519811721072662085485111045703987412094220689686673634241955047247609854041200778578542832459371567518406936908136456278580855326355096792872324174145562813303949605379230174018494117853603702152059335440764083293322471807283069472531202462722202917551408494598048677137074200859816690275986663030277286569976460908346358904422964424746645104732745352326121282910390649387427416055754359188091700147618060211231503082679247785691660641065431271701057523938788707846180991151470917443986898990696238399554440903455233022468088651148799684030267146193796334043119080594644322358796906759836770505103557429631622296333030266327046011619967776159634366887279937028243689380001409729105518639839675945116128815330668016315503185899714161216687671230574073946303172784011192584424549790851949628053757067125708116500923344172251805167855674009789352798000845818461242899224835938000020378170885269055841255490568216829243335871796252244109330529902983716481736108361446573154715062745211442983313584589859718458201409644684427903762533836045799364210919834689625426037370437764039595607214082990598178228046116112630636040001663147483205019386481519822689029391114522931957183171963601512521439959563534069438676951975087909832523209070515108411852576337766181331210245202556778537611245618032446627001987176726069215070633346030796232494244019728751779926096081430988292745260805874652716348627255093805602013625670873133828325514622056327230677993441485202456141624053594915112957418286324951364793572836369723116492808563095213991319047761945317187869248729375289646267504478167028273396579524813913334151803023358073522405222549035123864804815678071618740638054974112593483726390502113599929647317259818412046014321600804441793135484014715991040128640051384584336103707601446933382393773627271309500975826400733339412405476577984912684169457984989567273831263186466544309763153431065963866240968246813680236626161775578250353653632304278658916659205865168664633596162571073255555785527047441982726477428415441608391620914299858924649341080842414427042884773862327960684379853819918113906923732799168708234502574103035248876408173859907743983277977179889939690429027728899836034303103846198087243860133694609495003085594474285042927122313337572294151335513419111029590872832714904180393358701596366385951443810672106202469574018799513459696965569155880094143095244341376943866450111670328409290239406024323584249461010638411786389182375518466075581091820058065184342719352703433649383541885319070885434140096435888895915838399889468766955213317926658229843966956015883000989184322171710713223649126536034372588359814912282338149828331742475288776165758624668302616582826157942988548761128057396876656217465326482735010879330795681553493747259618459826243669763540270027708731304870445825284361682698093387761793742048304278104093500532463894820462859057282396283759525305867486353270235939534246792138612608840528996034304412039332005879449134846209923941893166636009769500421980450818388532886689781787068817196712858933448063045608771626658106014788519330242475177372495165820226543420903872341980336920464845619553623926915434440577108858461813046669675213100608647130957218743496405831782804948156306093884408227146007099300059879697593185055729716721089763708268661326778789153938771996075981554131700962184855700361219028651893129459248410229172748625837731140325878800075436691689542794858719884224083845593868131724898886440575779158384233204867975224464329634148174423778660117199058743344643347405140437467793625685821216020779247523666721758801733589747337849247346899425349147268152461678125906071471834676112405343343956698976393725993977695617708488484909616454320408236182254100663514392663988532469781250088749171558917572313626520320178676148544919877041358098554483954790172091138185361565655261012863907079644076228772780748351151926491215503647185415971443705202181767609730806089770801035429749998043792312851884644743752813258139875276310149574144396379172372433319740886535397849571861903477542572434740208689196188897381758130683224720946734486870662993972958242564498642289481257673061271646154799451748897408440149105922652489081901881190687295443602490373855311584574590569819672287646003467989460539878700753688516834744400655248098721042798094922853807034173937553014758910903166723693219094324958985538822226275412837868767849455864993908045703165812516453925106076720925664553211297349630885657515014079813436986731838509436367169544767983588348172639936282163815402727935993699213679304559824496017851460676697897561329983501996510963688138874655152475344904323788272122634729260781509246326358372566482432472194713353700628497335073777469597999790082549366484067173305172474929907836440985423540565767243778594081828708945224070163357648368651464839780435877072249325792168345131643285292301344844968174212466176541002362066701716438334393602510379752410453535501774417268612253289131889040539333102428437613225420554729020100465702534065578988787694649021448405621508669423820835999946793329162317636529741456662520053535310703552737556758998800108529809665211831386755353866127149625163666779521322727930638163656890122830323910546848030636543332249360303039404438910588249720932306541563590770596925332441479321749157111249066406550557696231957852075133719500736203578650066813155988760390174715181370216345598412623392598864950301027169922675662182959278772058241220076908068561820691331178873268044491717169569011045123586361336089584037973586874622600834671824806671811098540809367330724392994098844290463613143289532328775319183024595903171732536374124988795744073909040413308180261874890993381644921381274607102275620405042127210382719983082685633866484392100738884373676686979899044294781411673631215505276518116221540575820837344924985303468053846195655413116266031120844021436834615165161472761479297894656802478387122781254486866876028528475220274133079206008736124537893667972984881218229985926338252796260887834458813714575859009379935614974051839193281981297824005736639857016030291148184720157796439522000826862540346487723465189977369189882601926042049659661063643206563237843559200905087283130352202990209189223108945473494240717500360891066395194741480745156765009222906935515433358682588895905416741543996511360937592478388725605389719306466810380027885711190100698281872210494382939688609171235794755465526434836854853832912247923196199966028777141052554294671972317063437414723165040433612516879993128928872841172738808153392441022928739731085880277177493185489461756392591259000087065681837528998559187231981473331080573187926672726930585739939888272495695285777375302525902472988714375966921511442117458516678245895080868501740982654276036044560620520065518030631867236770513316758754103689961254256359861141701271540896101025082179652139128056988035169507273892915247469263858016614803662933936230160620854212420346408215267232249922568522099691758589620507335724997813111105030641744067465593772218513211477334999346130140206221426772875328790818589390667159108462025159490124949540066157019389321256733646476754426996654717162188226741532138935795707734537510573574153893253425413281031566662480032673914324808453322722499260898566901940251790312824537149175649667700005717
## 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7768956889327480435267432510190501177515725808362421019160229086420362092967948491793634153703214463588506996558499722779629923668094605915423195631572470764238633590255662125991835866355941842332198480913676625450188569960308451906289527117969094587824814470058885056081417133412767443339670896413969830537619538970176124887841696308216810943296383559500134949665993684928873627638699525791956398577734738994891596400994844249726102400944716525461712485203259398296485102557311636680484477552730814681845987476342273189477508739378373121352983539924761597482504364519321088456402274911461181514144830638556514696656847114340044778831826180982709021038305150445967243015955163912943126218632586487956271430395743890720548471837484731949814734485523523998727547393899605823924385089991318450121081178528243764673256161706784775854196446900973979672782753497517567985383313134414846684670387662643538721087547173295763830033198259702065595263039968305694259042822085142235103285993782978615887428173092189977846684761838363721490671386488846048408200918150803901198053890796285689694323167048240376786488600906735478814959460899161883137618579846359798418294209436649286559925662103975491713598755617015934110547768284554944478036488859390163205373042832190923808964631989146651072692491006811396402738795366557398341911218977614695670815730533569809694824196890006055878006454108489936668911082741607188988463196571428652073639554751575232389071210793434612825330805437992585615237827050636793497381238153484089205286860770633219792429961782976462193366367866791864719508480982292217534264549738584007068775735480394416835481403455817589920031201290556253536456036610688217111644491171269193561162398786454710716183190114899487341528476773882186512310827069112494481912585593360293453345205620122988419303457331674163827617236935071659762909831466360008440141555324932144952971274474537376264554687854379678628034748170796612684104505881097033772586636808929594109962393683728837371021778692307565437884189525703187497742739990243925011600363197093423965985115356578555432404021897972588598036476773451067161509135663143450811411986213361049161516465445773298837516589129787104314541601579417501236864492550766578261048370032013161070726860032209214134931342985987629142820893274771434806903214787375372778373370706103857998979941153374806575871083415439042230462963103634053847109972645460439720828415003193524703979383370133072534900668546683235995478363653653195114262237020838649504970998021249362492168196239186603983767942097894916755461694307551477154681114831402126069473779539970316039319986720036446305432725174898264760816423873714389780315904921963418760894889610952095835066891394318524364729100362458731755867661527245519850209107298781078041399724377569864732449895875542557219164511267995824339480872731173499186782391832829564918280937833935927611404299888631265559539486723814521074677744446633385106520472438884215545943530388553006662382424129871601979026884378569431849646272074539539584660768204573450044406445190866516025008258454344958749612909545168167640200038030904814229214358370820446197819040500716555513500536640814823879805431577609790132049303870745004630414173903227918192132116798703961633720220159794695895892129620885189962065533528870545023650911936062839656491987620337222408560457872872488559448946173026871601759807326578999201633410398565099094020751344023413680048350699713441437881843014697501248387719839832864530039699146049618899448561805422839678172391612177718904777699104987723632979965333342423421020715661865014763847773042161439279283022603223015527076982157542643853382180549104283340100656314099214441929166761859014799586372485120000000000
iprint(r)
## [1] "(%i2) sum(1/x^2, x, 1, 10000)"
maxima.isInstalled()
## [1] TRUE
maxima.version()
## [1] '5.44.0'
maxima.options
## Option Value
## -------------:------------------------------------------------------------------------------------------------------
## format linear
## (Printing format of returned object from maxima.get())
## engine.format linear
## (Same as 'format', but for maxima code chunks in 'RMarkdown' documents.)
## inline.format linear
## (Same as 'engine.format', but for printing output inline via maxima.inline(). Cannot be set to 'ascii'.)
## label TRUE
## (Sets whether a maxima reference label should be printed when printing a maxima return object.)
## engine.label TRUE
## (Same as 'label', but for maxima code chunks.)
## inline.label TRUE
## (Same as 'label', but for inline code chunks)
maxima.options(format = "ascii")
maxima.apropos("int")
## (%o3) [adjoint, adjoint-impl, askinteger, askinteger-impl,
## beta_args_sum_to_integer, cint, defint, defint-impl, disjointp,
## disjointp-impl, display_format_internal, expint, expint-impl, expintegral_chi,
## expintegral_chi-impl, expintegral_ci, expintegral_ci-impl, expintegral_e,
## expintegral_e-impl, expintegral_e1, expintegral_e1-impl, expintegral_ei,
## expintegral_ei-impl, expintegral_hyp, expintegral_li, expintegral_li-impl,
## expintegral_shi, expintegral_shi-impl, expintegral_si, expintegral_si-impl,
## expintegral_trig, expintexpand, expintrep, factor_max_degree_print_warning,
## floatint, fpprintprec, gcprint, intanalysis, integer, integer_partitions,
## integer_partitions-impl, integerp, integerp-impl, integervalued, integral,
## integrate, integrate-impl, integrate_use_rootsof, integration_constant,
## integration_constant_counter, interaction, interpolate, intersect,
## intersect-impl, intersection, intersection-impl, intervalp, intfaclim,
## intopois, intopois-impl, intosum, intosum-impl, invert_by_adjoint,
## invert_by_adjoint-impl, invert_by_adjoint_size_limit, ldefint, ldefint-impl,
## linespoints, lisp_print, loadprint, lognegint, mapprint, maxfpprintprec,
## maxpsinegint, maxpsiposint, mdebug_print_length, ninth, nointegrate,
## noninteger, nonnegintegerp, noprint, point_type, pointbound, points, poisint,
## poisint-impl, print, print-impl, printf, printfile, printfile-impl, printpois,
## printpois-impl, printprops, printvarlist, printvarlist-impl, ratprint,
## require_integer, require_posinteger, require_selfadjoint_matrix, specint,
## specint-impl, sprint, tldefint, tldefint-impl, e-integer-coeff]
maxima.get("integrate(1 / (x^4 + 1), x);")
## 2 x + sqrt(2)
## 2 2 atan(-------------)
## log(x + sqrt(2) x + 1) log(x - sqrt(2) x + 1) sqrt(2)
## (%o4) ----------------------- - ----------------------- + -------------------
## 5/2 5/2 3/2
## 2 2 2
## 2 x - sqrt(2)
## atan(-------------)
## sqrt(2)
## + -------------------
## 3/2
## 2
maxima.get("jacobian( [alpha / (alpha + beta), 1 / sqrt(alpha + beta)], [alpha, beta] )")
## [ 1 alpha alpha ]
## [ ------------ - --------------- - --------------- ]
## [ beta + alpha 2 2 ]
## [ (beta + alpha) (beta + alpha) ]
## (%o5) [ ]
## [ 1 1 ]
## [ - ------------------- - ------------------- ]
## [ 3/2 3/2 ]
## [ 2 (beta + alpha) 2 (beta + alpha) ]
l <- maxima.get("%;")
maxima.eval(l, code = TRUE, envir = list(alpha = 0.3, beta = 2.5))
## [,1] [,2]
## [1,] 0.3188776 -0.03826531
## [2,] -0.1067168 -0.10671684
## attr(,"maxima")
## matrix(data = c(((-1L * alpha * ((alpha + beta)^-2L)) + ((alpha +
## beta)^-1L)), ((-1L/2L) * ((alpha + beta)^(-3L/2L))), (-1L *
## alpha * ((alpha + beta)^-2L)), ((-1L/2L) * ((alpha + beta)^(-3L/2L)))),
## ncol = 2, nrow = 2)
unclass(l)
## $wtl
## $wtl$linear
## [1] "(%o6) matrix([1/(beta+alpha)-alpha/(beta+alpha)^2,-alpha/(beta+alpha)^2]," " [-1/(2*(beta+alpha)^(3/2)),-1/(2*(beta+alpha)^(3/2))])"
##
## $wtl$ascii
## [1] " [ 1 alpha alpha ]" " [ ------------ - --------------- - --------------- ]"
## [3] " [ beta + alpha 2 2 ]" " [ (beta + alpha) (beta + alpha) ]"
## [5] "(%o6) [ ]" " [ 1 1 ]"
## [7] " [ - ------------------- - ------------------- ]" " [ 3/2 3/2 ]"
## [9] " [ 2 (beta + alpha) 2 (beta + alpha) ]"
##
## $wtl$latex
## [1] "$$\\mathtt{(\\textit{\\%o}_{6})}\\quad \\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} \\\\ -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} & -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} \\\\ \\end{pmatrix}$$"
##
## $wtl$inline
## [1] "$\\mathtt{(\\textit{\\%o}_{6})}\\quad \\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} \\\\ -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} & -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} \\\\ \\end{pmatrix}$"
##
## $wtl$mathml
## [1] " <math xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mi>mlabel</mi> " " <mfenced separators=\"\"><msub><mi>%o</mi> <mn>6</mn></msub> "
## [3] " <mo>,</mo><mfenced separators=\"\" open=\"(\" close=\")\"><mtable>" " <mtr><mtd><mfrac><mrow><mn>1</mn> </mrow> <mrow><mi>β</mi> "
## [5] " <mo>+</mo> <mi>α</mi> </mrow></mfrac> <mo>-</mo> <mfrac><mrow>" " <mi>α</mi> </mrow> <mrow><msup><mrow><mfenced separators=\"\">"
## [7] " <mi>β</mi> <mo>+</mo> <mi>α</mi> </mfenced> </mrow> " " <mn>2</mn> </msup> </mrow></mfrac> </mtd><mtd><mo>-</mo>"
## [9] " <mfrac><mrow><mi>α</mi> </mrow> <mrow><msup><mrow>" " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> "
## [11] " </mfenced> </mrow> <mn>2</mn> </msup> </mrow></mfrac> </mtd></mtr> " " <mtr><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>"
## [13] " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>" " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> "
## [15] " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>" " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> "
## [17] " </mtd><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>" " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>"
## [19] " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> " " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>"
## [21] " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> " " </mtd></mtr> </mtable></mfenced> </mfenced> </math>"
##
##
## $wol
## $wol$linear
## [1] "matrix([1/(beta+alpha)-alpha/(beta+alpha)^2,-alpha/(beta+alpha)^2]," " [-1/(2*(beta+alpha)^(3/2)),-1/(2*(beta+alpha)^(3/2))])"
##
## $wol$ascii
## [1] "[ 1 alpha alpha ]" "[ ------------ - --------------- - --------------- ]" "[ beta + alpha 2 2 ]"
## [4] "[ (beta + alpha) (beta + alpha) ]" "[ ]" "[ 1 1 ]"
## [7] "[ - ------------------- - ------------------- ]" "[ 3/2 3/2 ]" "[ 2 (beta + alpha) 2 (beta + alpha) ]"
##
## $wol$latex
## [1] "$$\\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} \\\\ -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} & -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} \\\\ \\end{pmatrix}$$"
##
## $wol$inline
## [1] "$\\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} \\\\ -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} & -\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}} \\\\ \\end{pmatrix}$"
##
## $wol$mathml
## [1] " <math xmlns=\"http://www.w3.org/1998/Math/MathML\"> " " <mfenced separators=\"\" open=\"(\" close=\")\"><mtable><mtr><mtd>"
## [3] " <mfrac><mrow><mn>1</mn> </mrow> <mrow><mi>β</mi> <mo>+</mo> " " <mi>α</mi> </mrow></mfrac> <mo>-</mo> <mfrac><mrow>"
## [5] " <mi>α</mi> </mrow> <mrow><msup><mrow><mfenced separators=\"\">" " <mi>β</mi> <mo>+</mo> <mi>α</mi> </mfenced> </mrow> "
## [7] " <mn>2</mn> </msup> </mrow></mfrac> </mtd><mtd><mo>-</mo>" " <mfrac><mrow><mi>α</mi> </mrow> <mrow><msup><mrow>"
## [9] " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> " " </mfenced> </mrow> <mn>2</mn> </msup> </mrow></mfrac> </mtd></mtr> "
## [11] " <mtr><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>" " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>"
## [13] " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> " " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>"
## [15] " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> " " </mtd><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>"
## [17] " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>" " <mfenced separators=\"\"><mi>β</mi> <mo>+</mo> <mi>α</mi> "
## [19] " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>" " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> "
## [21] " </mtd></mtr> </mtable></mfenced> </math>"
##
## $wol$rstr
## [1] "matrix(data = c(((-1L * alpha * ((alpha + beta) ^ -2L)) + ((alpha + beta) ^ -1L)), ((-1L / 2L) * ((alpha + beta) ^ (-3L / 2L))), (-1L * alpha * ((alpha + beta) ^ -2L)), ((-1L / 2L) * ((alpha + beta) ^ (-3L / 2L)))), ncol = 2, nrow = 2)"
##
##
## attr(,"input.label")
## [1] "%i6"
## attr(,"output.label")
## [1] "%o6"
## attr(,"command")
## [1] "%;"
## attr(,"suppressed")
## [1] FALSE
## attr(,"parsed")
## matrix(data = c(((-1L * alpha * ((alpha + beta)^-2L)) + ((alpha +
## beta)^-1L)), ((-1L/2L) * ((alpha + beta)^(-3L/2L))), (-1L *
## alpha * ((alpha + beta)^-2L)), ((-1L/2L) * ((alpha + beta)^(-3L/2L)))),
## ncol = 2, nrow = 2)
maxima.load("abs_integrate")
maxima.stop()
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