# Analysis along a path

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Informally, traditional analysis can be viewed as an operator theory on function ring over real numbers, and traditional derivatives and integrations are along the additive path. If we consider all possible path over arithmetic expression space in theory construction, we may expand the theoretical space of analysis. And all possible path over arithmetic expression space form a group, with more restrictions on path, this group can be a Lie group.

## A formal description

## Remark on future study

One of the most interesting topic here is how symmetry of the underlying function reflected in the above path group, this may leads to a new way to handle non-linear functions.