All exceptions generated by the Hipparchus code are unchecked (i.e. they inherit from the standard RuntimeException class). The main rationale supporting this design decision is that the exceptions generated in the library are not recoverable: They most of the time result from bad input parameters or some failure due to numerical problems.
All Hipparchus exceptions are inherit from a common root, org.hipparchus.exception.MathRuntimeException.
The detailed error messages (i.e. the string returned by the getLocalizedMessage method) can be localized. However, besides the American/English default, French is the only language for which a translation resource is available.
Exceptions generated by public methods are advertised and documented in javadoc.