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Symbolic solution of algebraic equations.
g = solve(eq) g = solve(eq,var) g =solve(eq1,eq2,...,eqn)g =solve(eq1,eq2,...,eqn,var1,var2,...,varn)
solve can be either symbolic expressions or strings. If eq is a symbolic expression (x^2-2*x+1) or a string that does not contain an equal sign ('x^2-2*x+1'), then solve(eq) solves the equation eq=0 for its default variable (as determined by findsym).
solve(eq,var) solves the equation eq (or eq=0 in the two cases cited above) for the variable var.
solve(eq1,eq2,...,eqn) solves the system of equations implied by eq1,eq2,...,eqn in the n variables determined by applying findsym to the system.
Three different types of output are possible. For one equation and one output, the resulting solution is returned with multiple solutions for a nonlinear equation. For a system of equations and an equal number of outputs, the results are sorted alphabetically and assigned to the outputs. For a system of equations and a single output, a structure containing the solutions is returned.
For both a single equation and a system of equations, numeric solutions are returned if symbolic solutions cannot be determined.
solve('a*x^2 + b*x + c') returns
[ 1/2/a*(-b+(b^2-4*a*c)^(1/2)), 1/2/a*(-b-(b^2-4*a*c)^(1/2))]
solve('a*x^2 + b*x + c','b') returns
-(a*x^2+c)/x
solve('x + y = 1','x - 11*y = 5') returns
y = -1/3, x = 4/3
A = solve('a*u^2 + v^2', 'u - v = 1', 'a^2 - 5*a + 6')
returns
A =
a: [1x4 sym]
u: [1x4 sym]
v: [1x4 sym]
where
A.a =
[ 2, 2, 3, 3]
A.u =
[ 1/3+1/3*i*2^(1/2), 1/3-1/3*i*2^(1/2),
1/4+1/4*i*3^(1/2), 1/4-1/4*i*3^(1/2)]
A.v =
[ -2/3+1/3*i*2^(1/2), -2/3-1/3*i*2^(1/2),
-3/4+1/4*i*3^(1/2), -3/4-1/4*i*3^(1/2)]
arithmetic operators, dsolve, findsym