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Type:

Package

Title:

Multivariate Polynomials with Rational Coefficients

Version:

1.1.0

Date:

2022-02-21

Author:

Stéphane Laurent

Maintainer:

Stéphane Laurent <laurent_step@outlook.fr>

Description:

Symbolic calculation (addition or multiplication) and evaluation of multivariate polynomials with rational coefficients.

License:

GPL-3

Encoding:

UTF-8

Imports:

gmp, purrr, mvp, english

RoxygenNote:

7.1.2

URL:

https://github.com/stla/gmpoly

BugReports:

https://github.com/stla/gmpoly/issues

Suggests:

testthat (≥ 3.0.0)

Config/testthat/edition:

NeedsCompilation:

Packaged:

2022-03-20 04:27:56 UTC; SDL96354

Repository:

CRAN

Date/Publication:

2022-03-20 04:40:02 UTC

Arithmetic operators for multivariate polynomials

Description

Arithmetic operators for multivariate polynomials

Usage

## S3 method for class 'gmpoly'
Ops(e1, e2 = NULL)

Arguments

e1, e2

for an unary operator, only e1 must be given, a gmpoly object; for a binary operator, at least one of e1 and e2 must be a gmpoly object, and the other must a gmpoly object as well or a scalar; the power operator (^) is an exception: one can only raise a gmpoly object to a positive integer power

Value

A gmpoly object.

Examples

library(gmpoly)
pol <- gmpoly("4 x^(2, 1, 1) + 1/2 x^(0,1,0)")
+pol
-pol
2 * pol
pol / 2
pol + 5
pol - 5
pol^2
pol1 <- gmpoly("2 x^(1,1) - 5/3 x^(0,1)")
pol2 <- gmpoly("-2 x^(1,1) + 3 x^(2,1)")
pol1 + pol2
pol1 * pol2
pol1 == pol2
pol1 != pol2

Define a multivariate polynomial

Description

Define a multivariate polynomial from a string or from its coefficients and powers.

Usage

gmpoly(string, coeffs = NULL, powers = NULL)

Arguments

string

a string such as "x^(1,2,1) + 4 x^(0,2,3)", or you can define the polynomial with coeffs and powers; in this case set string to NULL or to nothing (i.e. missing)

coeffs

the coefficients of the polynomial, in case you don't define it with the string argument; this must be a vector of bigq numbers

powers

the powers of the polynomial, in case you don't define it with the string argument; this must be a matrix of integers, one row for each term (hence nrow(powers) must equal length(coeffs)), and the number of columns is the number of variables

Value

A gmpoly object.

Examples

library(gmpoly)
gmpoly("5/2 x^(2,3) + 3 x^(1,1)")
gmpoly("5/2 x^(2,3) - 3 x^(1,1)")
gmpoly("-x^(1,2,3) + 4/7 x^(3,1,1)")
library(gmp)
gmpoly(
  coeffs = as.bigq(c(5, 7), c(8, 9)), 
  powers = rbind(c(1, 1, 1), c(2, 2, 2))
)

Conversion to 'mvp' polynomial

Description

Convert a gmpoly polynomial to a mvp polynomial.

Usage

gmpoly2mvp(pol)

Arguments

pol

a gmpoly object

Value

A mvp object.

Examples

library(gmpoly)
pol <- gmpoly("5/2 x^(2,2,3) + 3 x^(1,0,1)")
gmpoly2mvp(pol)

Constant multivariate polynomial

Description

Constructs a constant multivariate polynomial.

Usage

gmpolyConstant(m, value)

Arguments

m

number of variables, a strictly positive integer

value

the constant value of the polynomial; the as.bigq function is applied to this argument, so it can be e.g. an integer or a character string such as "2/3" (avoid decimal numbers)

Value

A gmpoly object.

Examples

library(gmpoly)
gmpolyConstant(3, "2/3")

Evaluation of a multivariate polynomial

Description

Evaluates a gmpoly multivariate polynomial for given values of the variables.

Usage

gmpolyEval(pol, x)

Arguments

pol

a gmpoly object

x

either a bigq vector, or a bigq matrix; in the later case, the evaluation is performed for each row of the matrix

Value

A bigq number or vector.

Examples

library(gmpoly)
library(gmp)
pol <- gmpoly("5/2 x^(2,3) + 3 x^(1,1)")
gmpolyEval(pol, as.bigq(c(1, 1)))
x <- rbind(
  t(as.bigq(c(1, 1))),
  t(as.bigq(c(3, 4), c(4, 3)))
)
gmpolyEval(pol, x)

Grow polynomial

Description

Grow a multivariate polynomial by including a new variable.

Usage

gmpolyGrow(pol)

Arguments

pol

a gmpoly object

Value

The "same" multivariate polynomial as pol, except that it has an additional variable.

Examples

library(gmpoly)
pol <- gmpoly("3 x^(1,2) - 1/7 x^(5,3)")
gmpolyGrow(pol)

Print a multivariate polynomial

Description

Print a multivariate polynomial of class gmpoly.

Usage

## S3 method for class 'gmpoly'
print(x, ...)

Arguments

x

a gmpoly object

...

ignored

Value

No value, just prints the polynomial.