We describe an essential improvement of our recent algorithm for computingcohomology of Lie (super)algebra based on partition of the whole cochaincomplex into minimal subcomplexes. We replace the arithmetic of rationalnumbers or integers by a much cheaper arithmetic of a modular field and use theinequality between the dimensions of cohomology H over any modular field F_p =Z/pZ and over Q: dim H(F_p) >= dim H(Q). With this inequality we can, bycomputing over arbitrary F_p, quickly find the (usually, rare) subcomplexes forwhich dim H(F_p) > 0 and then carry out the full computation over Q withinthese subcomplexes. We also present the results of application of thecorresponding C program to the Lie superalgebra of special vector fieldspreserving an "odd-symplectic" structure on the (2|2)-dimensionalsupermanifold. For this algebra, we found some new basis elements of thecohomology in the trivial module.
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机译：我们描述了基于整个共链复合体划分为最小子复合体的李（代）代数计算同构关系的最新算法的本质改进。我们用一个便宜得多的模场算术代替有理数或整数算术，并在任何模场F_p = Z / pZ和Q上使用同调H的维数之间的不等式：dim H（F_p）> = dim H（Q ）。利用这种不等式，我们可以通过对任意F_p进行计算，快速找到其H（F_p）> 0暗的（通常是稀有的）子复合体，然后在这些子复合体中对Q进行完整的计算。我们还介绍了将相应的C程序应用到在（2 | 2）维超流形上保留“奇-渐近”结构的特殊矢量场的Lie超代数的应用结果。对于这个代数，我们在平凡的模块中发现了同调的一些新的基础元素。
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