Interface to 'Maxima', Enabling Symbolic Computation

An interface to the powerful and fairly complete computer algebra system 'Maxima'. It can be used to start and control 'Maxima' from within R by entering 'Maxima' commands. Results from 'Maxima' can be parsed and evaluated in R. It facilitates outputting results from 'Maxima' in 'LaTeX' and 'MathML'. 2D and 3D plots can be displayed directly. This package also registers a 'knitr'-engine enabling 'Maxima' code chunks to be written in 'RMarkdown' documents.

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;")
r <- maxima.get("sum(1/x^2, x, 1, 10000)")

## Warning in value[[3L]](cond): Caught error while parsing
## input buffer overflow (<input>:1:8193)
## Returning NA.

print(r)
iprint(r)

## [1] "(%i2) sum(1/x^2, x, 1, 10000)"

maxima.isInstalled()

## [1] TRUE

maxima.version()

## [1] '5.47.0'

maxima.options

##  Option        Value 
##  -------------:-----------------------------------------------------------------
##  format        linear
##                (Printing format of returned object from maxima.get())
##  engine.format latex 
##                (Same as 'format', but for maxima code chunks in
##                'RMarkdown' documents.)
##  inline.format inline
##                (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  FALSE 
##                (Same as 'label', but for inline code chunks)

maxima.options(format = "ascii")
maxima.apropos("int")
maxima.get("integrate(1 / (x^4 + 1), x);")
maxima.get("jacobian( [alpha / (alpha + beta), 1 / sqrt(alpha + beta)], [alpha, beta] )")
l <- maxima.get("%;")
maxima.eval(l, code = TRUE, envir = list(alpha = 0.3, beta = 2.5))

##             [,1]       [,2]
## [1,]  0.31887755 -0.1067168
## [2,] -0.03826531 -0.1067168
## attr(,"maxima")
## matrix(data = c(((-1L * alpha * ((alpha + beta)^-2L)) + ((alpha + 
##     beta)^-1L)), (-1L * alpha * ((alpha + beta)^-2L)), ((-1L/2L) * 
##     ((alpha + beta)^(-3L/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)],"
## [2] "             [-(1/(2*(beta+alpha)^(3/2))),-(1/(2*(beta+alpha)^(3/2)))])"    
## 
## $wtl$ascii
## [1] "           [      1              alpha                alpha        ]"
## [2] "           [ ------------ - ---------------    - ---------------   ]"
## [3] "           [ beta + alpha                 2                    2   ]"
## [4] "           [                (beta + alpha)       (beta + alpha)    ]"
## [5] "(%o6)      [                                                       ]"
## [6] "           [                1                           1          ]"
## [7] "           [     - -------------------       - ------------------- ]"
## [8] "           [                       3/2                         3/2 ]"
## [9] "           [       2 (beta + alpha)            2 (beta + alpha)    ]"
## 
## $wtl$latex
## [1] "$$\\mathtt{(\\textit{\\%o}_{6})}\\quad \\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\left(\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2}\\right) \\\\ -\\left(\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}}\\right) & -\\left(\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}}\\right) \\\\ \\end{pmatrix}$$"
## 
## $wtl$inline
## [1] "$\\mathtt{(\\textit{\\%o}_{6})}\\quad \\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\left(\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2}\\right) \\\\ -\\left(\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}}\\right) & -\\left(\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}}\\right) \\\\ \\end{pmatrix}$"
## 
## $wtl$mathml
##  [1] " <math xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mi>mlabel</mi> " 
##  [2] " <mfenced separators=\"\"><msub><mi>%o</mi> <mn>6</mn></msub> "        
##  [3] " <mo>,</mo><mfenced separators=\"\" open=\"(\" close=\")\"><mtable>"   
##  [4] " <mtr><mtd><mfrac><mrow><mn>1</mn> </mrow> <mrow><mi>&beta;</mi> "     
##  [5] " <mo>+</mo> <mi>&alpha;</mi> </mrow></mfrac> <mo>-</mo> <mfrac><mrow>" 
##  [6] " <mi>&alpha;</mi> </mrow> <mrow><msup><mrow><mfenced separators=\"\">" 
##  [7] " <mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> </mfenced> </mrow> "      
##  [8] " <mn>2</mn> </msup> </mrow></mfrac> </mtd><mtd><mo>-</mo>"             
##  [9] " <mfrac><mrow><mi>&alpha;</mi> </mrow> <mrow><msup><mrow>"             
## [10] " <mfenced separators=\"\"><mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> "
## [11] " </mfenced> </mrow> <mn>2</mn> </msup> </mrow></mfrac> </mtd></mtr> "  
## [12] " <mtr><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>"           
## [13] " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>"             
## [14] " <mfenced separators=\"\"><mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> "
## [15] " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>"      
## [16] " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> "           
## [17] " </mtd><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>"          
## [18] " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>"             
## [19] " <mfenced separators=\"\"><mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> "
## [20] " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>"      
## [21] " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> "           
## [22] " </mtd></mtr> </mtable></mfenced> </mfenced> </math>"                  
## 
## 
## $wol
## $wol$linear
## [1] "matrix([1/(beta+alpha)-alpha/(beta+alpha)^2,-(alpha/(beta+alpha)^2)],"
## [2] "       [-(1/(2*(beta+alpha)^(3/2))),-(1/(2*(beta+alpha)^(3/2)))])"    
## 
## $wol$ascii
## [1] "[      1              alpha                alpha        ]"
## [2] "[ ------------ - ---------------    - ---------------   ]"
## [3] "[ beta + alpha                 2                    2   ]"
## [4] "[                (beta + alpha)       (beta + alpha)    ]"
## [5] "[                                                       ]"
## [6] "[                1                           1          ]"
## [7] "[     - -------------------       - ------------------- ]"
## [8] "[                       3/2                         3/2 ]"
## [9] "[       2 (beta + alpha)            2 (beta + alpha)    ]"
## 
## $wol$latex
## [1] "$$\\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\left(\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2}\\right) \\\\ -\\left(\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}}\\right) & -\\left(\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}}\\right) \\\\ \\end{pmatrix}$$"
## 
## $wol$inline
## [1] "$\\begin{pmatrix}\\frac{1}{\\beta+\\alpha}-\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2} & -\\left(\\frac{\\alpha}{\\left(\\beta+\\alpha\\right)^2}\\right) \\\\ -\\left(\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}}\\right) & -\\left(\\frac{1}{2\\,\\left(\\beta+\\alpha\\right)^{\\frac{3}{2}}}\\right) \\\\ \\end{pmatrix}$"
## 
## $wol$mathml
##  [1] " <math xmlns=\"http://www.w3.org/1998/Math/MathML\"> "                 
##  [2] " <mfenced separators=\"\" open=\"(\" close=\")\"><mtable><mtr><mtd>"   
##  [3] " <mfrac><mrow><mn>1</mn> </mrow> <mrow><mi>&beta;</mi> <mo>+</mo> "    
##  [4] " <mi>&alpha;</mi> </mrow></mfrac> <mo>-</mo> <mfrac><mrow>"            
##  [5] " <mi>&alpha;</mi> </mrow> <mrow><msup><mrow><mfenced separators=\"\">" 
##  [6] " <mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> </mfenced> </mrow> "      
##  [7] " <mn>2</mn> </msup> </mrow></mfrac> </mtd><mtd><mo>-</mo>"             
##  [8] " <mfrac><mrow><mi>&alpha;</mi> </mrow> <mrow><msup><mrow>"             
##  [9] " <mfenced separators=\"\"><mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> "
## [10] " </mfenced> </mrow> <mn>2</mn> </msup> </mrow></mfrac> </mtd></mtr> "  
## [11] " <mtr><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>"           
## [12] " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>"             
## [13] " <mfenced separators=\"\"><mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> "
## [14] " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>"      
## [15] " <mn>2</mn> </mrow></mfrac> </mrow></msup> </mrow></mfrac> "           
## [16] " </mtd><mtd><mo>-</mo><mfrac><mrow><mn>1</mn> </mrow> <mrow>"          
## [17] " <mn>2</mn> <mspace width=\"thinmathspace\"/><msup><mrow>"             
## [18] " <mfenced separators=\"\"><mi>&beta;</mi> <mo>+</mo> <mi>&alpha;</mi> "
## [19] " </mfenced> </mrow> <mrow><mfrac><mrow><mn>3</mn> </mrow> <mrow>"      
## [20] " <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 * alpha * ((alpha + beta) ^ -2L)), ((-1L / 2L) * ((alpha + beta) ^ (-3L / 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 * alpha * ((alpha + beta)^-2L)), ((-1L/2L) * 
##     ((alpha + beta)^(-3L/2L))), ((-1L/2L) * ((alpha + beta)^(-3L/2L)))), 
##     ncol = 2, nrow = 2)
## attr(,"from_engine")
## [1] FALSE

maxima.load("abs_integrate")
maxima.stop()