# Constraints definition and system solving

A system in Kiwi is defined by a set of constraints that can be either equalities or inequalities (>= and <= only, strict inequalities are not accepted), each of which can have an associated strength making more or less important to respect when solving the problem. The next sections will cover how to define those constraints and extract the result from the solver.

## Defining variables and constraints

The first things that need to be defined are variables. Variables represent the values which the solver will be trying to determine. Variables are represented by `Variable` objects which can be created as follow:

```from kiwisolver import Variable

x1 = Variable('x1')
x2 = Variable('x2')
xm = Variable('xm')
```

Note

Naming your variables is not mandatory but it is recommended since it will help the solver in providing more meaningful error messages.

Now that we have some variables we can define our constraints.

```constraints = [x1 >= 0, x2 <= 100, x2 >= x1 + 10, xm == (x1 + x2) / 2]
```

The next step is to add them to our solver, which is an instance of `Solver`:

```from kiwisolver import Solver

solver = Solver()

for cn in constraints:
```

Note

You do not have to create all your variables before starting adding constraints to the solver.

So far we have defined a system representing three points on the segment [0, 100], with one of them being the middle of the others which cannot get closer than 10. All those constraints have to be satisfied, in the context of cassowary they are “required” constraints.

Note

Cassowary (and Kiwi) supports to have redundant constraints, meaning that even if having two constraints (x == 10, x + y == 30) is equivalent to a third one (y == 20), all three can be added to the solver without issue.

However, one should not add multiple times the same constraint (in the same form) to the solver.

## Managing constraints strength

Cassowary also supports constraints that are not required. Those are only respected on a best effort basis. To express that a constraint is not required we need to assign it a strength. Kiwi defines three standard strengths in addition of the “required” strength: strong, medium, weak. A strong constraint will always win over a medium constraints which will always win over a weak constraint 1 .

Lets assume than in our example x1 would like to be at 40, but it does not have to. This is translated as follow:

```solver.addConstraint((x1 == 40) | "weak")
```

## Adding edit variables

So far our system is pretty static, we have no way of trying to find solutions for a particular value of xm lets say. This is a problem. In a real application (for a GUI layout), we would like to find the size of the widgets based on the top window but also react to the window resizing so actually adding and removing constraints all the time wouldn’t be optimal. And there is a better way: edit variables.

Edit variables are variables for which you can suggest values. Edit variable have a strength which can be at most strong (the value of a edit variable can never be required).

For the sake of our example we will make “xm” editable:

```solver.addEditVariable(xm, 'strong')
```

Once a variable has been added as an edit variable, you can suggest a value for it and the solver will try to solve the system with it.

```solver.suggestValue(xm, 60)
```

This gives the following solution: `xm == 60, x1 == 40, x2 == 80`.

## Solving and updating variables

Kiwi solves the system each time a constraint is added or removed, or a new value is suggested for an edit variable. Solving the system each time make for faster updates and allow to keep the solver in a consinstent state. However, the variable values are not updated automatically and you need to ask the solver to perform this operation before reading the values as illustrated below:

```solver.suggestValue(xm, 90)
solver.updateVariables()
print(xm.value(), x1.value(), x2.value())
```

This last update creates an infeasible situation by pushing x2 further than 100 if we keep x1 where it would like to be and as a consequence we get the following solution: `xm == 90, x1 == 80, x2 == 100`

Note

To know if a non-required constraint was violated when solving the system, you can use the constraint `violated` method.

New in version 1.4.

## Footnotes

1

Actually there are some corner cases in which this can be violated. See Solver internals and tips