……代数结构是有意义的（比如刘维尔结构定理）。参考例如：- https://billcookmath.com/courses/math4010-spring2016/math401... (2016) 的第 2 页及接下来的例子 - Ritt 的《Integration in Finite Terms: Liouville's Theory of Elementary Methods》(1948) 分析学书籍很少会严格定义初等函数这一类别。
…algebraic structure is meaningful (like Liouvillian structure theorems). See e.g. - Page 2 and the following example of https://billcookmath.com/courses/math4010-spring2016/math401... (2016) - Ritt's Integration in Finite Terms: Liouville's Theory of Elementary Methods (1948) It's not frequent that analysis books will define the class of elementary functions rigorously.
……Variable.”《符号逻辑学期刊》（Journal of Symbolic Logic）, 33(4)。——微分是一个简单的递归算法；而判定用初等项的可积性在一般情况下是不可判定的。[2] Risch, R. H. (1969). “The Problem of Integration in Finite Terms.”《美国数学会汇刊》（Transactions of the American Mathematical Society）, 139。——部分挽救：针对受限类别的（半）判定算法。[3] Guilford, J. P. (1967). 《The Nature of Human Intelligence》. McGraw-Hill.……
…Variable." Journal of Symbolic Logic, 33(4). — Differentiation is a simple recursive algorithm; deciding integrability in elementary terms is undecidable in general. [2] Risch, R. H. (1969). "The Problem of Integration in Finite Terms." Transactions of the American Mathematical Society, 139. — The partial recovery: a (semi-)decision procedure for a restricted class. [3] Guilford, J. P. (1967). The Nature of Human Intelligence. McGraw-Hill.…
……代数结构是有意义的（比如刘维尔结构定理）。参考例如：- https://billcookmath.com/courses/math4010-spring2016/math401... (2016) 的第 2 页及接下来的例子 - Ritt 的《Integration in Finite Terms: Liouville's Theory of Elementary Methods》(1948) 分析学书籍很少会严格定义初等函数这一类别。
…algebraic structure is meaningful (like Liouvillian structure theorems). See e.g. - Page 2 and the following example of https://billcookmath.com/courses/math4010-spring2016/math401... (2016) - Ritt's Integration in Finite Terms: Liouville's Theory of Elementary Methods (1948) It's not frequent that analysis books will define the class of elementary functions rigorously.
……Variable.”《符号逻辑学期刊》（Journal of Symbolic Logic）, 33(4)。——微分是一个简单的递归算法；而判定用初等项的可积性在一般情况下是不可判定的。[2] Risch, R. H. (1969). “The Problem of Integration in Finite Terms.”《美国数学会汇刊》（Transactions of the American Mathematical Society）, 139。——部分挽救：针对受限类别的（半）判定算法。[3] Guilford, J. P. (1967). 《The Nature of Human Intelligence》. McGraw-Hill.……
…Variable." Journal of Symbolic Logic, 33(4). — Differentiation is a simple recursive algorithm; deciding integrability in elementary terms is undecidable in general. [2] Risch, R. H. (1969). "The Problem of Integration in Finite Terms." Transactions of the American Mathematical Society, 139. — The partial recovery: a (semi-)decision procedure for a restricted class. [3] Guilford, J. P. (1967). The Nature of Human Intelligence. McGraw-Hill.…