This white paper highlights current limitations in the algebraic closure Unified Form Language (UFL). UFL currently represents forms over finite element spaces, however finite element problems naturally result in objects in the dual to a finite element space, and operators mapping between primal and dual finite element spaces. This document sketches the relevant mathematical areas and proposes changes to the UFL language to support dual spaces as first class types in UFL.

中文翻译：

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UFL Dual Spaces，一项提案

本白皮书重点介绍了代数闭包统一格式语言（UFL）的当前限制。UFL当前表示的是有限元空间上的形式，但是有限元问题自然会导致对偶到有限元空间中的对象，以及原始和对偶有限元空间之间的运算符映射。本文概述了相关的数学领域，并提出了对UFL语言的更改，以支持双重空间作为UFL中的头等舱类型。