The theory of persistence modules on the commutative ladders $CL_n(\tau)$provides an extension of persistent homology. However, an efficient algorithmto compute the generalized persistence diagrams is still lacking. In this work,we view a persistence module $M$ on $CL_n(\tau)$ as a morphism between zigzagmodules, which can be expressed in a block matrix form. For the representationfinite case ($n\leq 4)$, we provide an algorithm that uses certain permissiblerow and column operations to compute a normal form of the block matrix. In thisform an indecomposable decomposition of $M$, and thus its persistence diagram,is obtained.
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机译：交换阶梯$ CL_n（\ tau）$上的持久性模块理论提供了持久同源性的扩展。但是，仍然缺少一种有效的算法来计算广义持久性图。在这项工作中，我们将$ CL_n（\ tau）$上的持久性模块$ M $视为之字形模块之间的态射，可以以块矩阵形式表示。对于表示形式有限的情况（$ n \ leq 4）$，我们提供了一种算法，该算法使用某些允许的行和列运算来计算块矩阵的正常形式。以这种形式获得了$ M $的不可分解的分解，并因此获得了其持久性图。
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