reduce: Polynomial Simplification

In polynomial: Handling Univariate Polynomials

Description

Simplify a polynomial by removing unwanted coefficients, combining coefficients corresponding to duplicate exponents, and sorting exponents.

Usage

reduce(x, zero.rm = TRUE, na.rm = FALSE, finite = FALSE, dflt.exp = FALSE,
    fix.dup.exp = is.na(dflt.exp) || dflt.exp, decreasing = NA,
    ...)

Arguments

x	a polynomial, or an object which can be coerced by as.polynomial to a polynomial.
zero.rm	logical. Should zero valued coefficients be removed?
na.rm	logical. Should missing valued coefficients (including NaN) be removed?
finite	logical. Should non-finite valued coefficients be removed?
dflt.exp	logical. Should the coefficients be rearranged such that the exponents take on their default values?
fix.dup.exp	logical. Should coefficients corresponding to duplicate exponents be summed?
decreasing	logical. Should the sort order of the exponents be increasing or decreasing?
...	further arguments passed to as.polynomial.

Details

If zero.rm is TRUE, 0 valued coefficients and their corresponding exponents will be removed from the polynomial.

If na.rm is FALSE, NA and NaN valued coefficients will be retained, otherwise NA valued coefficients and their corresponding exponents will be removed from the polynomial.

If finite is TRUE, non-finite valued coefficients and their corresponding exponents will be removed from the polynomial, i.e., finite = TRUE includes na.rm = TRUE.

If fix.dup.exp is TRUE, coefficients corresponding to duplicated exponents will be summed.

If dflt.exp is TRUE, the coefficients are rearranged such that the exponents take on their default values, given by seq(0L, along.with = x). Note that this requires the exponents to be unique (or fix.dup.exp = TRUE).

If decreasing is FALSE, the polynomial is reordered such that the exponents are increasing. If decreasing is TRUE, the polynomial is reordered such that the exponents are decreasing. If decreasing is NA, the polynomial is left as is (the default).

Value

A polynomial object.

Examples

x <- as.polynomial(
    c(1, NA, Inf, 6, 4, 3, 0, 1, 9),
    c(5,  7,   4, 4, 5, 8, 2, 3, 8)
)


reduce(x)                   # 0 valued coefficient is removed
reduce(x, zero.rm = FALSE)  # 0 valued coefficient is not removed
reduce(x, na.rm = TRUE)     # missing valued coefficient is removed
reduce(x, finite = TRUE)    # non-finite valued coefficients are removed


## 'dflt.exp = NA' means that 'reduce' will decide whether the coefficients
## should be rearranged such that the exponents take on their default values.
## In this case, it decides 'dflt.exp = TRUE'
reduce(x, dflt.exp = NA)
reduce(x, dflt.exp = TRUE)  # exponents take on their default values (forced)


## coefficients corresponding to duplicate exponents are summed
reduce(x, fix.dup.exp = TRUE)


reduce(x, decreasing = FALSE)  # increasing exponents
reduce(x, decreasing = TRUE)   # decreasing exponents

polynomial documentation built on Feb. 22, 2021, 5:08 p.m.