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I am looking for an advanced 3d mathematics geometry software where I can create equations of geometry,trace rays as in Optics,create equations of rays(Ray tracing),create different types of 3D and 2D geometry(shapes) and their equations, etc.

To be more specific, for example as I am sitting in a room, I want to create my room(simple 3d objects) not too Complex, and then I want to draw lines(light rays) coming from light source and where they will go, and then create equations about light rays.

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Blender is not a mathematics oriented software but it answers the needs you describe in your example. You can write plugins in Python and run them within Blender to fill up your mathematical needs.

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