R package for multivariate polynomials with rational coefficients.
library(gmpoly)
Define a polynomial with the gmpoly
function:
<- gmpoly("4 x^(2, 1, 1) + 1/2 x^(0,1,0)")
pol
pol## gmpoly object algebraically equal to
## 1/2 x^(0,1,0) + 4 x^(2,1,1)
Some arithmetic on this polynomial:
-pol
## gmpoly object algebraically equal to
## -1/2 x^(0,1,0) - 4 x^(2,1,1)
2 * pol
## gmpoly object algebraically equal to
## x^(0,1,0) + 8 x^(2,1,1)
/ 2
pol ## gmpoly object algebraically equal to
## 1/4 x^(0,1,0) + 2 x^(2,1,1)
+ 5
pol ## gmpoly object algebraically equal to
## 5 x^(0,0,0) + 1/2 x^(0,1,0) + 4 x^(2,1,1)
- 5
pol ## gmpoly object algebraically equal to
## -5 x^(0,0,0) + 1/2 x^(0,1,0) + 4 x^(2,1,1)
^2
pol## gmpoly object algebraically equal to
## 1/4 x^(0,2,0) + 4 x^(2,2,1) + 16 x^(4,2,2)
Note that you cannot directly use a bigq
scalar,
e.g. you can’t do gmp::as.bigq(5, 3) * pol
. To perform such
an operation, you have to use gmpolyConstant
:
gmpolyConstant(3, "5/3") * pol
## gmpoly object algebraically equal to
## 5/6 x^(0,1,0) + 20/3 x^(2,1,1)
The gmpolyConstant
function converts a scalar to a
constant polynomial, and two polynomials can be added and
multiplied:
<- gmpoly("2 x^(1,1) - 5/3 x^(0,1)")
pol1 <- gmpoly("-2 x^(1,1) + 3 x^(2,1)")
pol2 + pol2
pol1 ## gmpoly object algebraically equal to
## -5/3 x^(0,1) + 3 x^(2,1)
* pol2
pol1 ## gmpoly object algebraically equal to
## 10/3 x^(1,2) - 9 x^(2,2) + 6 x^(3,2)
Use gmpolyEval
to evaluate a polynomial for some values
of the variables:
library(gmp, warn.conflicts = FALSE)
<- gmpoly("5/2 x^(2,3) + 3 x^(1,1)")
pol gmpolyEval(pol, x = as.bigq(c(1, 1)))
## Big Rational ('bigq') :
## [1] 11/2
To evaluate the polynomial for several sets of variables, supply a matrix to the second argument:
<- rbind(
X t(as.bigq(c(1, 1))),
t(as.bigq(c(3, 4), c(4, 3)))
)gmpolyEval(pol, x = X)
## Big Rational ('bigq') object of length 2:
## [1] 11/2 19/3