Junctions and thin shells in general relativity using computer algebra. I: The Darmois-Israel formalism. We present the GRjunction computer algebra program which allows the study of non-null boundary surfaces and thin shells in general relativity. Implementing the Darmois-Israel thin-shell formalism requires a careful selection of definitions and algorithms to ensure that results are generated in a straightforward way. We have used the package to correctly reproduce a wide variety of examples from the literature. In this paper GRjunction is used to perform two new calculations: joining two Kerr solutions with differing masses and angular momenta along a thin shell in the slow rotation limit, and the calculation of the stress-energy of a Curzon wormhole. The Curzon wormhole has the interesting property that shells located at radius $R < 2m$ have regions which satisfy the weak energy condition.