Direct Sum of Rings

This is a visualization of the algebraic ring .


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is represented as a circle with equally spaced integers from 0 to . The two circles for and are combined to form a torus, representing the direct sum . Elements of this ring are of the form , where and . Thus form coordinates of a point on the surface of the torus. The two-dimensional grid shows the unwrapped torus. Points A and B represent two elements of and can be dragged in the lower grid to change their values. The sum and product of A and B are both shown.
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