# Sylver

Sylver solves simultaneous Sylverster equations $AX+BY=C$ in as fast a way as currently possible.

Linear Sylvester systems $AX+BY=C$ appear as a primitive linear equations across mathematics, physics, and engineering. **Concurrent Sylvester Systems** batch together multiple Sylvester Systems into Tensor Sylvester systems and solves them concurrently with provably nearly optimal speed and minimal memory usage.

e.g. finding solutions $(X,Y)$ that simultaneously solve:
These, and general higher-dimensional Tensor Sylvester Systems, can be solved with minimum space and in time just slightly more than linear in the input size. They also admit natural parallelism and randomized solutions. **Sylver** is our library of routines to solve Sylvester Systems.

### Sylver

**Sylver** and its dependent libraries is available on GitHub. Follow the installation instructions.
- **Sylver** for Magma available here.
- **Sylver** for GAP (coming soon).
- **Sylver** for Scala (coming soon).