Polynomial components

Compute quantities/expressions related to a multivariate polynomial.

# S3 method for mpoly
[(x, ndx)

LT(x, varorder = vars(x), order = "lex")

LC(x, varorder = vars(x), order = "lex")

LM(x, varorder = vars(x), order = "lex")

multideg(x, varorder = vars(x), order = "lex")

totaldeg(x)

monomials(x)

exponents(x, reduced = FALSE)

Arguments

x	an object of class mpoly
ndx	a subsetting index
varorder	the order of the variables
order	a total order used to order the terms
reduced	if TRUE, don't include zero degrees

Value

An object of class mpoly or mpolyList, depending on the context

Examples

(p <- mp("x y^2 + x (x+1) (x+2) x z + 3 x^10"))
#> x y^2  +  x^4 z  +  3 x^3 z  +  2 x^2 z  +  3 x^10
p[2]
#> x^4 z
p[-2]
#> x y^2  +  3 x^3 z  +  2 x^2 z  +  3 x^10
p[2:3]
#> x^4 z  +  3 x^3 z

LT(p)
#> 3 x^10
LC(p)
#> [1] 3
LM(p)
#> x^10

multideg(p)
#>  x  y  z 
#> 10  0  0 
totaldeg(p)
#> [1] 10
monomials(p)
#> x y^2
#> x^4 z
#> 3 x^3 z
#> 2 x^2 z
#> 3 x^10

exponents(p)
#> [[1]]
#> x y z 
#> 1 2 0 
#> 
#> [[2]]
#> x y z 
#> 4 0 1 
#> 
#> [[3]]
#> x y z 
#> 3 0 1 
#> 
#> [[4]]
#> x y z 
#> 2 0 1 
#> 
#> [[5]]
#>  x  y  z 
#> 10  0  0 
#> 
exponents(p, reduce = TRUE)
#> [[1]]
#> x y 
#> 1 2 
#> 
#> [[2]]
#> x z 
#> 4 1 
#> 
#> [[3]]
#> x z 
#> 3 1 
#> 
#> [[4]]
#> x z 
#> 2 1 
#> 
#> [[5]]
#>  x 
#> 10 
#> 
lapply(exponents(p), is.integer)
#> [[1]]
#> [1] TRUE
#> 
#> [[2]]
#> [1] TRUE
#> 
#> [[3]]
#> [1] TRUE
#> 
#> [[4]]
#> [1] TRUE
#> 
#> [[5]]
#> [1] TRUE
#> 

homogeneous_components(p)
#> 2 x^2 z  +  x y^2
#> 3 x^3 z
#> x^4 z
#> 3 x^10