CommonPolynom: GCD and LCM for polynomial matrices

Description

The greatest common divisor of polynomial that keeps the elements of the given polynomial matrix.

Usage

# S3 method for polyMatrix
GCD(x, type=OPERATION_TYPE_TOTAL, ...)
  # S3 method for polyMatrix
LCM(x, type=OPERATION_TYPE_TOTAL, ...)

Arguments

an polyMatrix class object

type

calculates the common polynom column-wise (type="col"), row-wise (type="row") or for the total matrix (type="total", by-default)

…

additional arguments

Value

A polynom matrix which is the greatest common divisor or the least common multiple for all the elements of the given polynomial matrix or for the columns or for the rows, depending on the value of the 'type' parameter.

Details

Calculates the greatest common divisor or the least common divisor of the total matrix, or row-wise or column-wise, depending on the parameter type.

Possible operator types: OPERATION_TYPE_TOTAL="total", OPERATION_TYPE_COLUMN="col", OPERATION_TYPE_ROW="row"

Examples

Run this code

# NOT RUN {
p1 <- ch2pn("1 - x")
p2 <- ch2pn("x - x^2")
p3 <- ch2pn("1 - x^2")
p4 <- ch2pn("1 + x")
p5 <- ch2pn("1 + 2*x + x^2")
p6 <- ch2pn("1 - 2*x + x^2")
A <- polyMgen.d(2, 3, rawData=list(p1, p2, p3, p4, p5, p6))
A
# 1 - x     1 - x^2   1 + 2*x + x^2
# x - x^2   1 + x     1 - 2*x + x^2

l<-function(...) structure(list(...), class = "polylist")

GCD(A) # 1
polynom::GCD(l(p1, p2, p3, p4, p5, p6)) # 1

GCD(A, "col") # 1
list(
  polynom::GCD(l(p1, p2)),
  polynom::GCD(l(p3, p4)),
  polynom::LCM(l(p5, p6))
)
# 1 - x; 1 + x; 1 - 2*x^2 + x^4

polynom::GCD(l(p1, p2))
polynom::GCD(l(p3, p4))
polynom::LCM(l(p5, p6))


GCD(A, "row") # 1; 1
polynom::GCD(l(p1, p3, p5))
polynom::GCD(l(p2, p4, p6)) # 1; 1

# ---

LCM(A)
polynom::LCM(l(p1, p2, p3, p4, p5, p6))
# 0.25*x - 0.5*x^3 + 0.25*x^5

LCM(A, "col") # x - x^3
list(
  polynom::LCM(l(p1, p2)),
  polynom::LCM(l(p3, p4)),
  polynom::LCM(l(p5, p6))
)
# x - x^2; 1 - x^2; 1 - 2*x^2 + x^4

LCM(A, "row") # x - x^3
list(
  polynom::LCM(l(p1, p3, p5)),
  polynom::LCM(l(p2, p4, p6))
)
# 0.5 + 0.5*x - 0.5*x^2 - 0.5*x^3; 0.5*x - 0.5*x^2 - 0.5*x^3 + 0.5*x^4

# clean up
# rm(A, p1, p2, p3, p4, p5, p6, l)
# }