Solve Symbolic Equations

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

solve(a, b, ...)

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

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

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

Arguments

a, b	Objects, see details.
...	Not used.

Value

A VecBasic or DenseMatrix S4 object.

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.

Examples

## Inverse of a symbolic matrix
mat <- Matrix(c("A", "B", "C", "D"), 2)
solve(mat)
#> DenseMatrix of dim 2 x 2
#> [(1 + B*C/(A*(D - B*C/A)))/A, -C/(A*(D - B*C/A))]
#> [-B/(A*(D - B*C/A)), (D - B*C/A)**(-1)]

## 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)
#> DenseMatrix of dim 2 x 1
#> [(b1 - a12*(b2 - b1*a21/a11)/(a22 - a21*a12/a11))/a11]
#> [(b2 - b1*a21/a11)/(a22 - a21*a12/a11)]

## 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
#> VecBasic of length 2
#> V( 1, 6 )