# Custom topologies#

As illustrated in Generate transitions, the `StateTransitionManager`

offers you a bit more flexibility than the façade function `generate_transitions()`

used in the main Usage page. In this notebook, we go one step further, by specifying a custom `Topology`

via `StateTransitionManager.topologies`

.

## Show code cell content

```
import graphviz
import qrules
from qrules import InteractionType, StateTransitionManager
from qrules.topology import Edge, Topology
```

## 2-to-2 topology#

As a simple example, we start with a 2-to-2 scattering topology. We define it as follows:

## Show code cell source

```
dot = qrules.io.asdot(
topology,
render_resonance_id=True,
render_node=True,
render_initial_state_id=True,
)
graphviz.Source(dot)
```

First, we construct a `StateTransitionManager`

for the transition \(K^-K^+ \to \pi^+\pi^-\). The constructed `Topology`

can then be inserted via its `topologies`

attribute:

```
stm = StateTransitionManager(
initial_state=["K-", "K+"],
final_state=["pi-", "pi+"],
formalism="canonical",
)
stm.set_allowed_interaction_types([InteractionType.STRONG, InteractionType.EM])
stm.topologies = (topology,) # tuple is immutable
```

For the rest, the process is just the same as in Generate transitions:

```
problem_sets = stm.create_problem_sets()
reaction_kk = stm.find_solutions(problem_sets)
```

## Show code cell source

```
dot = qrules.io.asdot(reaction_kk, collapse_graphs=True)
graphviz.Source(dot)
```

Warning

It is not yet possible to give the initial state a certain energy. So some collider process like \(e^-e^+\to\pi^+\pi\) does not result in a large number of resonances.

```
stm.initial_state = ["e-", "e+"]
problem_sets = stm.create_problem_sets()
reaction_ep = stm.find_solutions(problem_sets)
```

## Show code cell source

```
dot = qrules.io.asdot(reaction_ep, collapse_graphs=True)
graphviz.Source(dot)
```

What can do at most, is switch off `MassConservation`

, either through the constructor of the `StateTransitionManager`

, or by modifying `ProblemSet`

.

```
stm = StateTransitionManager(
initial_state=["e-", "e+"],
final_state=["pi-", "pi+"],
formalism="canonical",
mass_conservation_factor=None,
)
stm.set_allowed_interaction_types([InteractionType.STRONG, InteractionType.EM])
stm.topologies = [topology]
problem_sets = stm.create_problem_sets()
reaction_ep_no_mass = stm.find_solutions(problem_sets)
```

## Show code cell source

```
dot = qrules.io.asdot(reaction_ep_no_mass, collapse_graphs=True)
graphviz.Source(dot)
```