About Nemo

Nemo is a library for fast basic arithmetic in various commonly used rings, for the Julia programming language. Our aim is to provide a highly performant package covering

• Commutative Algebra
• Number Theory
• Group Theory

Nemo consists of wrappers of specialised C/C++ libraries:

• Flint http://flintlib.org/
• Arb https://arblib.org/
• Antic https://github.com/wbhart/antic/
• Calcium https://fredrikj.net/calcium/

Nemo also uses AbstractAlgebra.jl to provide generic constructions over the basic rings provided by the above packages.

Why Julia?

Julia is a sophisticated, modern programming language which is designed to be both performant and flexible. It was written by mathematicians, for mathematicians.

The benefits of Julia include

• Familiar imperative syntax
• JIT compilation (provides near native performance, even for highly generic code)
• REPL console (cuts down on development time)
• Parametric types (allows for fast generic constructions over other data types)
• Powerful metaprogramming facilities
• Operator overloading
• Multiple dispatch (dispatch on every argument of a function)
• Efficient native C interface (little or no wrapper overhead)
• Experimental C++ interface
• Dynamic type inference
• Built-in bignums
• Able to be embedded in C programs
• High performance collection types (dictionaries, iterators, arrays, etc.)
• Jupyter support (for web based notebooks)

The main benefits for Nemo are the parametric type system and JIT compilation. The former allows us to model many mathematical types, e.g. generic polynomial rings over an arbitrary base ring. The latter speeds up the runtime performance, even of highly generic mathematical procedures.