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MonomialList
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MonomialList

MonomialList[poly]

给出多项式 poly 中所有单项式的列表.

MonomialList[poly,{x1,x2,…}]

给出多项式中关于变量 xi 的单项式的列表.

MonomialList[poly,{x1,x2,…},order]

指定顺序的单项式.

更多信息和选项

  • 无论 poly 是否是展开形式，MonomialList 都起作用.
  • MonomialList[poly] 等价于 MonomialList[poly,Variables[poly]].
  • order 的可能设置是 "Lexicographic"、"DegreeLexicographic"、"DegreeReverseLexicographic"、"NegativeLexicographic"、"NegativeDegreeLexicographic"、"NegativeDegreeReverseLexicographic" 或一个显式权重矩阵.
  • 单项式按照单项式的指数向量的基排序，基是关于变量 xi 的.
  • "NegativeLexicographic" 相当于将 Sort 应用到指数向量列表中.
  • "Lexicographic" 给出 "NegativeLexicographic" 的反向顺序，是 MonomialList 的缺省设置.
  • "DegreeLexicographic" 首先按整个阶排序，然后按照 "Lexicographic" 定义的阶排序.
  • "DegreeReverseLexicographic" 首先按整个阶排序，然后反词典顺序，从最后一个变量开始.
  • "NegativeDegreeLexicographic" 和 "NegativeDegreeReverseLexicographic" 从低阶到高阶排序.
  • 一个显式的权重矩阵 w 定义 w.vi 的 "Lexicographic" 顺序给出的一个顺序，其中 vi 是指数向量.
  • MonomialList[poly,vars,Modulus->m] 计算模 m 的系数.
  • MonomialList[poly,All,order] 等价于 MonomialList[poly,Variables[poly],order].

范例

打开所有单元关闭所有单元

基本范例  (1)常见实例总结

得到单项式列表：

In[1]:=1
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https://wolfram.com/xid/09bep5gvu-ctcwzy
Out[1]=1

范围  (1)标准用法实例范围调查

用 "DegreeLexicographic" 单项式顺序：

In[1]:=1
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https://wolfram.com/xid/09bep5gvu-b8csnn
Out[1]=1

用权重矩阵指定相同的顺序：

In[2]:=2
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https://wolfram.com/xid/09bep5gvu-doqecd
Out[2]=2

选项  (1)各选项的常用值和功能

Modulus  (1)

模 2 化简系数：

In[1]:=1
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https://wolfram.com/xid/09bep5gvu-hlm66i
Out[1]=1

属性和关系  (2)函数的属性及与其他函数的关联

Plus 或 Total 重构原多项式：

In[1]:=1
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https://wolfram.com/xid/09bep5gvu-lspjtq
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09bep5gvu-kocky6
Out[2]=2

CoefficientRules 给出一个不同的表示：

In[3]:=3
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https://wolfram.com/xid/09bep5gvu-bg19ko
Out[3]=3

从 "DegreeLexicographic" 得到 "NegativeDegreeReverseLexicographic"：

In[1]:=1
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https://wolfram.com/xid/09bep5gvu-e5suh4
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09bep5gvu-f7detb
Out[2]=2

可能存在的问题  (1)常见隐患和异常行为

Variables[poly] 给出的列表不总是排好序的：

In[1]:=1
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https://wolfram.com/xid/09bep5gvu-boghg
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09bep5gvu-hj3y5f
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/09bep5gvu-g1uib
Out[3]=3
Wolfram Research (2008)，MonomialList，Wolfram 语言函数，https://reference.wolfram.com/language/ref/MonomialList.html.
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Wolfram Research (2008)，MonomialList，Wolfram 语言函数，https://reference.wolfram.com/language/ref/MonomialList.html.

文本

Wolfram Research (2008)，MonomialList，Wolfram 语言函数，https://reference.wolfram.com/language/ref/MonomialList.html.

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Wolfram Research (2008)，MonomialList，Wolfram 语言函数，https://reference.wolfram.com/language/ref/MonomialList.html.

CMS

Wolfram 语言. 2008. "MonomialList." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/MonomialList.html.

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Wolfram 语言. 2008. "MonomialList." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/MonomialList.html.

APA

Wolfram 语言. (2008). MonomialList. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/MonomialList.html 年

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Wolfram 语言. (2008). MonomialList. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/MonomialList.html 年

BibTeX

@misc{reference.wolfram_2025_monomiallist, author="Wolfram Research", title="{MonomialList}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/MonomialList.html}", note=[Accessed: 02-April-2025 ]}

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@misc{reference.wolfram_2025_monomiallist, author="Wolfram Research", title="{MonomialList}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/MonomialList.html}", note=[Accessed: 02-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_monomiallist, organization={Wolfram Research}, title={MonomialList}, year={2008}, url={https://reference.wolfram.com/language/ref/MonomialList.html}, note=[Accessed: 02-April-2025 ]}

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@online{reference.wolfram_2025_monomiallist, organization={Wolfram Research}, title={MonomialList}, year={2008}, url={https://reference.wolfram.com/language/ref/MonomialList.html}, note=[Accessed: 02-April-2025 ]}