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 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).