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What is cosmomathica?

Wolfram Mathematica is a powerful and convenient software package used by many cosmologists everywhere. However, since it is not always the most efficient for low-level computing, most popular algorithms for numerical computations in cosmology have been written in C or Fortran, since these languages are typically much better suited for the task at hand. This package bundles the functionality of some of these algorithms in a Mathematica package, which makes them easier to use and avoids the need to learn C or Fortran.

It makes use of the MathLink technology, which means that the original source code remains untouched. The algorithms are not reimplemented either, because that would negate the advantage of having them implemented in a lower level language in terms of efficiency. On top of that, it would inevitably introduce new bugs given the complexity of these algorithms.

For further details on how MathLink works, see


  • Wolfram Mathematica version >=8

  • For CosmicEmulator and FrankenEmu: GSL (GNU Scientific Library)

  • For CAMB: Possibly cfitsio, healpix

  • For Copter: The Boost C++ library headers

  • The GNU Compiler Compilation (gcc) version >=4.6

External programs

Due to copyright issues, the external packages cannot be delivered as part of this package. You need to download the source code of the following programs yourself. To make sure you got the right version, the MD5 sums of the files in question are given here.

The (extracted) files need to placed in directories with names tf, halofit, camb, CosmicEmulator, FrankenEmu, class_v2.3.2 and copter-0.8.7, respectively, inside the ext directory.

If you wish to use a different version of CAMB, for instance, cosmomathica may still work, but it has not been tested for it. If you use a modified version of CAMB, the same applies. In general, if you modify things like the type CAMBparams, you almost certainly will have to modify cosmomathica as well.

How to compile the MathLink

The paths to the required Mathematica libraries are often different on every system, so first you should adjust the Mathematica-related lines in the Makefile, which is located in the ext directory. Next, change into the ext directory and type make.

CAMB uses the Intel Fortran compiler by default. Due to compatibility issues with linking the different object files, CAMB needs to be compiled with GNU gfortran. When building the MathLink, CAMB's Makefile is automatically changed accordingly.

Note that all warnings and errors that you see may be cause by the external programs. Make sure the warning is not from compiling the MathLink and contact the respective authors if you have concerns. Otherwise, feel free to file a bug report on GitHub.

How to use Cosmomathica

In general, each one of the functions CAMB, Transfer, Halofit, Class and CosmicEmu returns a list of replacement rules containing the raw data as computed by the respective program. See the notebook demo.nb for a demonstration.


This is version 0.3. Since this is an alpha status, backwards compatibility may be broken in future releases.

Copyright and licensing

Cosmomathica is released under the GPL2. Contributions are welcome. Note that the copyright of the external software packages belong to their respective owners. Read their copyright remarks before using them.


A Mathematica package to call other programs commonly used in cosmology




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