SeQuant is an open-source library for symbolic algebra of tensors over commutative (scalar) and non-commutative (operator) rings. The key innovation supporting most of its functionality is a graph-theoretic tensor network (TN) canonicalizer that can handle tensor networks with symmetries faster than their standard group-theoretic counterparts. The TN canonicalizer is used for routine simplification of conventional tensor expressions, for optimizing application of Wick's theorem (used to canonicalize products of tensors over operator fields), and for manipulation of the intermediate representation leading to the numerical evaluation. Notable features of SeQuant include support for noncovariant tensor networks (which often arise from tensor decompositions) and for tensors with modes that depend parametrically on indices of other tensor modes (such dependencies between degrees of freedom are naturally viewed as nesting of tensors, "tensors of tensors" arising in block-wise data compressions in data science and modern quantum simulation). SeQuant blurs the line between pure symbolic manipulation/code generation and numerical evaluation by including compiler-like components to optimize and directly interpret tensor expressions using external numerical tensor algebra frameworks. The SeQuant source code is available at https://github.com/ValeevGroup/SeQuant.

翻译：SeQuant是一个用于交换（标量）与非交换（算子）环上张量符号代数的开源库。其大部分功能所依赖的关键创新是一个基于图论的张量网络（TN）规范化器，该工具能够比标准群论方法更快速地处理具有对称性的张量网络。该TN规范化器被用于常规简化传统张量表达式、优化维克定理（用于规范化算子域上张量乘积）的应用，以及操控最终导向数值计算的中间表示。SeQuant的显著特性包括：支持非协变张量网络（常源于张量分解）以及支持模态参数化依赖于其他张量模态索引的张量（此类自由度间的依赖关系可自然视为张量的嵌套，即数据科学和现代量子模拟中块状数据压缩产生的“张量的张量”）。SeQuant通过集成类编译器组件来优化并直接借助外部数值张量代数框架解释张量表达式，从而模糊了纯符号操作/代码生成与数值计算之间的界限。SeQuant源代码发布于https://github.com/ValeevGroup/SeQuant。