Solving equation(s):

- Solving an equation
`solve`takes as arguments an equation between two expressions or an expression (`=0`is omitted), and a variable name (by default`x`).`solve`solves this equation. - Solving a system of polynomial equations
`solve`takes as arguments two vectors : a vector of polynomial equations and a vector of variable names.`solve`solves this polynomial equation system.

- In real mode,
`solve`returns only real solutions. To have the complex solutions, switch to complex mode, e.g. by checking`Complex`in the cas configuration, or use the`cSolve`command. - For trigonometric equations,
`solve`returns by default the principal solutions. To have all the solutions check`All_trig_sol`in the cas configuration.

- Solve
*x*^{4}- 1 = 3

Input :`solve(x``^`

4-1=3)`[sqrt(2),-(sqrt(2))]``[sqrt(2),-(sqrt(2)),(i)*sqrt(2),-((i)*sqrt(2))]` - Solve exp(
*x*) = 2

Input :`solve(exp(x)=2)``[log(2)]` - Find
*x*,*y*such that*x*+*y*= 1,*x*-*y*= 0

Input :`solve([x+y=1,x-y],[x,y])``[[1/2,1/2]]` - Find
*x*,*y*such that*x*^{2}+*y*= 2,*x*+*y*^{2}= 2

Input :`solve([x``^`

2+y=2,x+y`^`

2=2],[x,y])`[[-2,-2],[1,1],[(-sqrt(5)+1)/2,(1+sqrt(5))/2],``[(sqrt(5)+1)/2,(1-sqrt(5))/2]]` - Find
*x*,*y*,*z*such that*x*^{2}-*y*^{2}= 0,*x*^{2}-*z*^{2}= 0

Input :`solve([x``^`

2-y`^`

2=0,x`^`

2-z`^`

2=0],[x,y,z])`[[x,x,x],[x,-x,-x],[x,-x,x],[x,x,-x]]` - Solve
cos(2*
*x*) = 1/2

Input :`solve(cos(2*x)=1/2)``[pi/6,(-pi)/6]``All_trig_sol`checked :`[(6*pi*n_0+pi)/6,(6*pi*n_0-pi)/6]` - Find the intersection of a straight line
(given by a list of equations) and a plane.

For example, let*D*be the straight line of cartesian equations [*y*-*z*= 0,*z*-*x*= 0] and let*P*the plane of equation*x*- 1 +*y*+*z*= 0. Find the intersection of*D*and*P*.

Input :`solve([[y-z=0,z-x=0],x-1+y+z=0],[x,y,z])``[[1/3,1/3,1/3]]`