The ore_algebra package provides an implementation of Ore algebras for Sage. The main features for the most common instances include basic arithmetic and actions; gcrd and lclm; D-finite closure properties; natural transformations between related algebras; guessing; desingularization; solvers for polynomials, ...

# Dr. Maximilian Jaroschek

## Software

## Publications

### 2014

### Ore Polynomials in Sage

#### Manuel Kauers, Maximilian Jaroschek, Fredrik Johansson

In: Computer Algebra and Polynomials, Jaime Gutierrez, Josef Schicho, Martin Weimann (ed.), Lecture Notes in Computer Science , pp. ?-?. 2014. tba. [pdf] [ps]@

author = {Manuel Kauers and Maximilian Jaroschek and Fredrik Johansson},

title = {{Ore Polynomials in Sage}},

booktitle = {{Computer Algebra and Polynomials}},

language = {english},

abstract = {We present a Sage implementation of Ore algebras. The main features for the mostcommon instances include basic arithmetic and actions; GCRD and LCLM; D-finiteclosure properties; natural transformations between related algebras; guessing;desingularization; solvers for polynomials, rational functions and (generalized)power series. This paper is a tutorial on how to use the package.},

series = {Lecture Notes in Computer Science},

pages = {?--?},

isbn_issn = {tba},

year = {2014},

editor = {Jaime Gutierrez and Josef Schicho and Martin Weimann},

refereed = {yes},

length = {17}

}

**inproceedings**{RISC4944,author = {Manuel Kauers and Maximilian Jaroschek and Fredrik Johansson},

title = {{Ore Polynomials in Sage}},

booktitle = {{Computer Algebra and Polynomials}},

language = {english},

abstract = {We present a Sage implementation of Ore algebras. The main features for the mostcommon instances include basic arithmetic and actions; GCRD and LCLM; D-finiteclosure properties; natural transformations between related algebras; guessing;desingularization; solvers for polynomials, rational functions and (generalized)power series. This paper is a tutorial on how to use the package.},

series = {Lecture Notes in Computer Science},

pages = {?--?},

isbn_issn = {tba},

year = {2014},

editor = {Jaime Gutierrez and Josef Schicho and Martin Weimann},

refereed = {yes},

length = {17}

}

### Radicals of Ore Polynomials

#### Maximilian Jaroschek

In: Proceedings of EACA 2014, , pp. -. 2014. to appear. [pdf]@

author = {Maximilian Jaroschek},

title = {{Radicals of Ore Polynomials}},

booktitle = {{Proceedings of EACA 2014}},

language = {english},

pages = {--},

isbn_issn = {?},

year = {2014},

note = {to appear},

editor = {?},

refereed = {yes},

length = {4}

}

**inproceedings**{RISC4979,author = {Maximilian Jaroschek},

title = {{Radicals of Ore Polynomials}},

booktitle = {{Proceedings of EACA 2014}},

language = {english},

pages = {--},

isbn_issn = {?},

year = {2014},

note = {to appear},

editor = {?},

refereed = {yes},

length = {4}

}

### 2013

### Desingularization Explains Order-Degree Curves for Ore Operators

#### Shaoshi Chen, Maximilian Jaroschek, Manuel Kauers, Michael F. Singer

In: Proceedings of ISSAC'13, Manuel Kauers (ed.), pp. 157-164. 2013. isbn 978-1-4503-2059-7/13/06. [pdf] [ps]@

author = {Shaoshi Chen and Maximilian Jaroschek and Manuel Kauers and Michael F. Singer},

title = {{Desingularization Explains Order-Degree Curves for Ore Operators}},

booktitle = {{Proceedings of ISSAC'13}},

language = {english},

abstract = { Desingularization is the problem of finding a left multiple of a given Ore operator in which some factor of the leading coefficient of the original operator is removed. An order-degree curve for a given Ore operator is a curve in the $(r,d)$-plane such that for all points $(r,d)$ above this curve, there exists a left multiple of order~$r$ and degree~$d$ of the given operator. We give a new proof of a desingularization result by Abramov and van Hoeij for the shift case, and show how desingularization implies order-degree curves which are extremely accurate in examples. },

pages = {157--164},

isbn_issn = {isbn 978-1-4503-2059-7/13/06},

year = {2013},

editor = {Manuel Kauers},

refereed = {yes},

length = {8}

}

**inproceedings**{RISC4706,author = {Shaoshi Chen and Maximilian Jaroschek and Manuel Kauers and Michael F. Singer},

title = {{Desingularization Explains Order-Degree Curves for Ore Operators}},

booktitle = {{Proceedings of ISSAC'13}},

language = {english},

abstract = { Desingularization is the problem of finding a left multiple of a given Ore operator in which some factor of the leading coefficient of the original operator is removed. An order-degree curve for a given Ore operator is a curve in the $(r,d)$-plane such that for all points $(r,d)$ above this curve, there exists a left multiple of order~$r$ and degree~$d$ of the given operator. We give a new proof of a desingularization result by Abramov and van Hoeij for the shift case, and show how desingularization implies order-degree curves which are extremely accurate in examples. },

pages = {157--164},

isbn_issn = {isbn 978-1-4503-2059-7/13/06},

year = {2013},

editor = {Manuel Kauers},

refereed = {yes},

length = {8}

}

### Improved Polynomial Remainder Sequences for Ore Polynomials

#### Maximilian Jaroschek

Journal of Symbolic Computation 58, pp. 64-76. 2013. ISSN 0747-7171. [url]@

author = {Maximilian Jaroschek},

title = {{Improved Polynomial Remainder Sequences for Ore Polynomials}},

language = {english},

journal = {Journal of Symbolic Computation},

volume = {58},

pages = {64--76},

isbn_issn = {ISSN 0747-7171},

year = {2013},

refereed = {yes},

length = {14},

url = {http://www.sciencedirect.com/science/article/pii/S0747717113000849}

}

**article**{RISC4726,author = {Maximilian Jaroschek},

title = {{Improved Polynomial Remainder Sequences for Ore Polynomials}},

language = {english},

journal = {Journal of Symbolic Computation},

volume = {58},

pages = {64--76},

isbn_issn = {ISSN 0747-7171},

year = {2013},

refereed = {yes},

length = {14},

url = {http://www.sciencedirect.com/science/article/pii/S0747717113000849}

}

### Removable Singularities of Ore Operators

#### Maximilian Jaroschek

RISC. PhD Thesis. November 2013. [pdf]@

author = {Maximilian Jaroschek},

title = {{Removable Singularities of Ore Operators}},

language = {english},

year = {2013},

month = {November},

translation = {0},

school = {RISC},

length = {115}

}

**phdthesis**{RISC4848,author = {Maximilian Jaroschek},

title = {{Removable Singularities of Ore Operators}},

language = {english},

year = {2013},

month = {November},

translation = {0},

school = {RISC},

length = {115}

}