This generic function solves the equation $a x = b$ for $x$.
# S3 method for yac_symbol
solve(a, b, ...)A yac_symbol
A yac_symbol or a value, see details and examples.
See details and examples.
When a is a matrix and b not provided,
this finds the inverse of a.
When a is a matrix and a vector b is provided, the
linear system of equations is solved.
Note that solving non-linear equations:
solve(a, b): find roots of a for variable b, i.e. yacas Solve(a == 0, b)
solve(a, b, v): find solutions to a == b for variable v, i.e. yacas Solve(a == b, v)
This also works for a system of equations (when a is a vector)
A <- outer(0:3, 1:4, "-") + diag(2:5)
a <- 1:4
B <- ysym(A)
b <- ysym(a)
solve(A)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.18316832 0.02970297 0.20297030 0.30693069
#> [2,] -0.16831683 0.29702970 0.02970297 0.06930693
#> [3,] -0.09405941 -0.06930693 0.19306931 -0.04950495
#> [4,] -0.04950495 -0.08910891 -0.10891089 0.07920792
solve(B)
#> {{ 37/202, 3/101, 41/202, 31/101},
#> {(-17)/101, 30/101, 3/101, 7/101},
#> {(-19)/202, (-7)/101, 39/202, (-5)/101},
#> { (-5)/101, (-9)/101, (-11)/101, 8/101}}
solve(A, a)
#> [1] 2.0792079 0.7920792 0.1485149 -0.2376238
solve(B, b)
#> {210/101, 80/101, 15/101, (-24)/101}
poly <- ysym("x^2 - x - 6")
solve(poly, "x") # Solve(poly == 0, x)
#> {x==(-2), x==3}
solve(poly, 3, "x") # Solve(poly == 3, x)
#> {x==(Sqrt(37)+1)/2, x==(1-Sqrt(37))/2}