# mvp v1.0-8

Monthly downloads

## Fast Symbolic Multivariate Polynomials

Fast manipulation of symbolic multivariate polynomials
using the 'Map' class of the Standard Template Library. The package
uses print and coercion methods from the 'mpoly' package (Kahle 2013,
"Multivariate polynomials in R". The R Journal, 5(1):162), but offers
speed improvements. It is comparable in speed to the 'spray' package
for sparse arrays, but retains the symbolic benefits of 'mpoly'.

## Readme

# Fast symbolic multivariate polynomials in R

# Overview

Multivariate polynomials are intereresting and useful objects. Here I
present the `mvp`

package which hopefully improves upon previous R
functionality provided by the packages `multipol`

, `mpoly`

, and `spray`

.
The `mvp`

package follows `mpoly`

in using a symbolic, rather than
numeric, representation of a multivariate polynomial; but it offers
speed advantages over `mpoly`

. `mvp`

uses the excellent print and
coercion methods of the `mpoly`

package. `mvp`

includes some pleasing
substitution idiom not found elsewhere; it is theoretically comparable
in speed to the `spray`

package and I present some timings in the
package vignette.

The `mvp`

package uses `C++`

’s STL `map`

class for efficiency, which has
the downside that the order of the terms, and the order of the symbols
within each term, is undefined. This does not matter as the mathematical
value of a multivariate polynomial is unaffected by reordering; and the
print method (taken from `mpoly`

) does a good job in producing
human-readable output.

# Installation

You can install the released version of `mvp`

from
CRAN with:

```
# install.packages("mvp") # uncomment this to install the package
library("mvp")
```

# The `mvp`

package in use

Creating a multivariate polynomial is straightforward:

```
X <- as.mvp("1 + a^2 + a*b*c^3")
X
#> mvp object algebraically equal to
#> 1 + a b c^3 + a^2
```

and arithmetic operations work as expected:

```
Y <- as.mvp("12*a^2 + b - c^2 + 4*d")
X+Y
#> mvp object algebraically equal to
#> 1 + a b c^3 + 13 a^2 + b - c^2 + 4 d
X-3*Y
#> mvp object algebraically equal to
#> 1 + a b c^3 - 35 a^2 - 3 b + 3 c^2 - 12 d
X^2
#> mvp object algebraically equal to
#> 1 + 2 a b c^3 + 2 a^2 + a^2 b^2 c^6 + 2 a^3 b c^3 + a^4
```

Substitution uses the `subs()`

function:

```
X
#> mvp object algebraically equal to
#> 1 + a b c^3 + a^2
subs(X,a=1)
#> mvp object algebraically equal to
#> 2 + b c^3
subs(X,a=1,b=2)
#> mvp object algebraically equal to
#> 2 + 2 c^3
subs(X,a=1,b=2,c=3)
#> [1] 56
subs(X+Y,a="1+x^2",b="x+y",c=0)
#> mvp object algebraically equal to
#> 14 + 4 d + x + 26 x^2 + 13 x^4 + y
```

# Further information

For more detail, see the package vignette

`vignette("mvp")`

## Functions in mvp

Name | Description | |

deriv | Differentiation of mvp objects | |

ooom | One over one minus a multivariate polynomial | |

mvp | Multivariate polynomials, mvp objects | |

summary | Summary methods for mvp objects | |

lose | Drop empty variables | |

zero | The zero polynomial | |

lowlevel | Low level functions | |

spray | Spray functionality | |

rmvp | Random multivariate polynomials | |

subs | Substitution | |

Print methods for mvp objects | ||

series | Decomposition of multivariate polynomials by powers | |

special | Various functions to create simple multivariate polynomials | |

mpoly | Conversion to and from mpoly form | |

mvp-package | mvp | |

horner | Horner's method | |

as.function.mvp | Functional form for multivariate polynomials | |

constant | The constant term | |

kahle | A sparse multivariate polynomial | |

allvars | All variables in a multivariate polynomial | |

invert | Replace symbols with their reciprocals | |

Ops.mvp | Arithmetic Ops Group Methods for mvp objects | |

knight | Chess knight | |

accessor | Accessor methods for mvp objects | |

No Results! |

## Vignettes of mvp

Name | ||

mvp.Rmd | ||

poly.bib | ||

No Results! |

## Last month downloads

## Details

Type | Package |

VignetteBuilder | knitr |

License | GPL (>= 2) |

LinkingTo | Rcpp |

SystemRequirements | C++11 |

URL | https://github.com/RobinHankin/mvp.git |

BugReports | https://github.com/RobinHankin/mvp/issues |

NeedsCompilation | yes |

Packaged | 2019-09-04 21:41:02 UTC; rhankin |

Repository | CRAN |

Date/Publication | 2019-09-05 04:40:09 UTC |

suggests | knitr , microbenchmark , rmarkdown , spray , testthat |

imports | magic , mpoly (>= 1.1.0) , partitions , Rcpp (>= 0.12.3) |

depends | magrittr , methods |

Contributors |

#### Include our badge in your README

```
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```