Solve Symbolic Equations

Description

Solve system of symbolic equations or solve a polynomial equation. Depending on types of arguments, it supports different modes. See Details and Examples.

Usage

solve(a, b, ...)

## S4 method for signature 'DenseMatrix'
solve(a, b, ...)

## S4 method for signature 'VecBasic'
solve(a, b, ...)

## S4 method for signature 'Basic'
solve(a, b, ...)

Arguments

Details

solve is a generic function dispatched on the class of the first argument.

• If a is a (square) DenseMatrix, it solves the equation a %*% x = b for x. (similar to solve.default())

• If a is a DenseMatrix and b is missing, b is taken to be an identity matrix and solve will return the inverse of a. (similar to solve.default())

• If a is a VecBasic, it solves the system of linear equations represented by a with regards to symbols represented in b.

• If a is a Basic, it solves the polynomial equation represented by a with regards to the symbol represented in b.

Value

A VecBasic or DenseMatrix S4 object.

Examples

## Inverse of a symbolic matrix
mat <- Matrix(c("A", "B", "C", "D"), 2)
solve(mat)

## Solve a %*% x == b
a <- Matrix(c("a11", "a21", "a12", "a22"), 2) # a is a 2x2 matrix
b <- Vector("b1", "b2")                       # b is a length 2 vector
solve(a, b)                                   # Solution of x (2x1 matrix)

## Solve the system of linear equations represented by a with regards to
## symbols in b
a <- Vector(~ -2*x + y - 4,  # A system of linear equations
            ~  3*x + y - 9)
b <- Vector(~x, ~y)          # Symbols to solve (x and y)
solve(a, b)                  # Solution of x and y