The dynamics of the subatomic fundamental particles, represented by quantum fields, and their interactions are determined uniquely by the assigned transformation properties, i.e., the quantum numbers associated with the underlying symmetry of the model under consideration. These fields constitute a finite number of group invariant operators which are assembled to build a polynomial, known as the Lagrangian of that particular model. The order of the polynomial is determined by the mass dimension. In this paper, we have introduced an automated \({\texttt {Mathematica}}^{\tiny \textregistered }\) package, GrIP, that computes the complete set of operators that form a basis at each such order for a model containing any number of fields transforming under connected compact groups. The spacetime symmetry is restricted to the Lorentz group. The first part of the paper is dedicated to formulating the algorithm of GrIP. In this context, the detailed and explicit construction of the characters of different representations corresponding to connected compact groups and respective Haar measures have been discussed in terms of the coordinates of their respective maximal torus. In the second part, we have documented the user manual of GrIP that captures the generic features of the main program and guides to prepare the input file. We have attached a sub-program CHaar to compute characters and Haar measures for \(SU(N), SO(2N), SO(2N+1), Sp(2N)\). This program works very efficiently to find out the higher mass (non-supersymmetric) and canonical (supersymmetric) dimensional operators relevant to the effective field theory (EFT). We have demonstrated the working principles with two examples: the standard model (SM) and the minimal supersymmetric standard model (MSSM). We have further highlighted important features of GrIP, e.g., identification of effective operators leading to specific rare processes linked with the violation of baryon and lepton numbers, using several beyond standard model (BSM) scenarios. We have also tabulated a complete set of dimension-6 operators for each such model. Some of the operators possess rich flavour structures which are discussed in detail. This work paves the way towards BSM-EFT.

由量子场表示的亚原子基本粒子的动力学及其相互作用是由分配的转换属性（即与所考虑的模型的基本对称性关联的量子数）唯一确定的。这些字段构成有限数量的组不变算子，这些算子被组装以构建多项式，称为该特定模型的拉格朗日算子。多项式的阶数由质量维确定。在本文中，我们介绍了一个自动的\（{\ texttt {Mathematica}} ^ {\ tiny \ textregistered} \）程序包GrIP，它计算完整的一组运算符，这些运算符构成模型的每个此类顺序的基础，该模型包含在连接的紧凑组下转换的任意数量的字段。时空对称仅限于洛伦兹群。本文的第一部分致力于制定GrIP算法。在这种情况下，已经根据它们各自的最大圆环的坐标讨论了与所连接的紧致群和各自的Haar度量相对应的不同表示形式的字符的详细构造。在第二部分中，我们记录了GrIP的用户手册，该手册捕获了主程序的通用功能并指导了如何准备输入文件。我们已经附上了一个子程序CHaar计算\（SU（N），SO（2N），SO（2N + 1），Sp（2N）\）的字符和Haar测度。该程序非常有效地找出与有效场论（EFT）相关的更高质量（非超对称）和规范（超对称）维算子。我们通过两个示例演示了工作原理：标准模型（SM）和最小超对称标准模型（MSSM）。我们进一步强调了GrIP的重要功能例如，使用几种超出标准模型（BSM）的场景来识别导致特定稀有过程的有效操作员，这些过程与重子和轻子数的违反有关。我们还为每个此类模型列出了完整的6维运算符集。一些操作员拥有丰富的风味结构，将对此进行详细讨论。这项工作为实现BSM-EFT铺平了道路。