degree

The <dfn>degree</dfn> of a monomial weyl object
 \(x^a\partial^b\) is defined as \(a+b\). The degree
 of a general weyl object expressed as a linear combination of
 monomials is the maximum of the degrees of these monomials. Following
 Coutinho we have:
<ul>
<li>\(\mathrm{deg}(d_1+d_2)\leq\max(\mathrm{deg}(d_1)+
 \mathrm{deg}(d_2))\)</li>
<li>\(\mathrm{deg}(d_1d_2) = \mathrm{deg}(d_1)+
 \mathrm{deg}(d_2)\)</li>
<li>\(\mathrm{deg}(d_1d_2-d_2d_1)\leq\mathrm{deg}(d_1)+
 \mathrm{deg}(d_2)-2\)</li>
</ul>

A suite of routines for Weyl algebras. Notation follows
Coutinho (1995, ISBN 0-521-55119-6, "A Primer of Algebraic
D-Modules"). Uses 'disordR' discipline
(Hankin 2022 <doi:10.48550/arXiv.2210.03856>). To cite
the package in publications, use Hankin
2022 <doi:10.48550/arXiv.2212.09230>.

Robin K S Hankin

weyl

The Weyl Algebra

degree function

<dl>
<dt>S</dt>
<dd>Object of class <code>weyl</code></dd>
</dl>

Arguments

Author

The <dfn>degree</dfn> of a monomial weyl object
 \(x^a\partial^b\) is defined as \(a+b\). The degree
 of a general weyl object expressed as a linear combination of
 monomials is the maximum of the degrees of these monomials. Following
 Coutinho we have:
<ul>
<li>\(\mathrm{deg}(d_1+d_2)\leq\max(\mathrm{deg}(d_1)+
 \mathrm{deg}(d_2))\)</li>
<li>\(\mathrm{deg}(d_1d_2) = \mathrm{deg}(d_1)+
 \mathrm{deg}(d_2)\)</li>
<li>\(\mathrm{deg}(d_1d_2-d_2d_1)\leq\mathrm{deg}(d_1)+
 \mathrm{deg}(d_2)-2\)</li>
</ul>

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degree: The degree of a `weyl` object

Description

Usage

Value

Arguments

Author

Examples