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Analysis of small angle scattering (SAS) data requires intensive modelling toinfer and characterize the structures present in a sample. This iterativeimprovement of models is a time consuming process. Here we present theScattering Equation Builder (SEB), a C++ library that derives exact analyticexpressions for the form factor of complex composite structures. The userwrites a small program that specifies how sub-units should be linked to form acomposite structure and calls SEB to obtain an expression for the form factor.SEB supports e.g. Gaussian polymer chains and loops, thin rods and circles,solid spheres, spherical shells and cylinders, and many different options forhow these can be linked together. In the present paper, we present theformalism behind SEB, and give simple case studies such as block-copolymerswith different types of linkage and more complex examples such as a random walkmodel of $100$ linked sub-units, dendrimers, polymers and rods attached tosurfaces of geometric objects, and finally the scattering from a linear chainof 5 stars, where each star is build by four diblock copolymers. These examplesillustrate how SEB can be used to develop complex models and hence reduce thecost of analyzing SAS data.

A computational tool for symbolic derivation of the small angle scattering from complex composite structures