If I is an independent set I, and e is an element such that $I \cup \{e\}$ is dependent (in particular e is not in I), then there is a unique circuit contained in $I \cup \{e\}$, called the fundamental circuit of e with respect to I, which moreover contains e. Every circuit is the fundamental circuit of some element with respect to some basis.





This method does not perform any checks (e.g. whether $I$ is independent, or if $e$ is not in $I$). If $I \cup \{e\}$ is independent, then (if debugLevel is greater than 0) a warning is printed, and null is returned. In the example below, the elements with indices 2 and 3 are parallel (indeed, both are equal to the column vector (1, 1)). Thus in general it is safer to refer to a subset by its indices, rather than its elements.






The object fundamentalCircuit is a method function.