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>&beta;</mi> "     
##  [5] " <mo>+</mo> <mi>&alpha;</mi> </mrow></mfrac> <mo>-</mo> <mfrac><mrow>"  " <mi>&alpha;</mi> </mrow> <mrow><msup><mrow><mfenced separators=\"\">" 
##  [7] " <mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> </mfenced> </mrow> "       " <mn>2</mn> </msup> </mrow></mfrac> </mtd><mtd><mo>-</mo>"             
##  [9] " <mfrac><mrow><mi>&alpha;</mi> </mrow> <mrow><msup><mrow>"              " <mfenced separators=\"\"><mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</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>&beta;</mi> <mo>+</mo> <mi>&alpha;</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>&beta;</mi> <mo>+</mo> <mi>&alpha;</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>&beta;</mi> <mo>+</mo> "     " <mi>&alpha;</mi> </mrow></mfrac> <mo>-</mo> <mfrac><mrow>"            
##  [5] " <mi>&alpha;</mi> </mrow> <mrow><msup><mrow><mfenced separators=\"\">"  " <mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> </mfenced> </mrow> "      
##  [7] " <mn>2</mn> </msup> </mrow></mfrac> </mtd><mtd><mo>-</mo>"              " <mfrac><mrow><mi>&alpha;</mi> </mrow> <mrow><msup><mrow>"             
##  [9] " <mfenced separators=\"\"><mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</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>&beta;</mi> <mo>+</mo> <mi>&alpha;</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>&beta;</mi> <mo>+</mo> <mi>&alpha;</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()