GiNaC
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GiNaC is a free computer algebra system released under the GNU General Public License. The name is a recursive acronym for GiNaC is Not a CAS (Computer Algebra System). This misleading name is an allusion to the GNU project.
What distinguishes GiNaC from most other computer algebra systems is that it does not provide a high-level interface for user interaction. Rather, it encourages its users to write symbolic algorithms directly in C++, which is GiNaC's implementation programming language. Algebraic syntax is achieved through the use of operator overloading.