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Carsten Schneider
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2020 – today
- 2024
- [j32]Evans Doe Ocansey, Carsten Schneider
:
Representation of hypergeometric products of higher nesting depths in difference rings. J. Symb. Comput. 120: 102220 (2024) - [i52]Peter Paule, Carsten Schneider:
Creative Telescoping for Hypergeometric Double Sums. CoRR abs/2401.16314 (2024) - 2023
- [j31]Johannes Blümlein, Marco Saragnese, Carsten Schneider
:
Hypergeometric structures in Feynman integrals. Ann. Math. Artif. Intell. 91(5): 591-649 (2023) - [j30]Johannes Blümlein, Nikolai Fadeev, Carsten Schneider:
Computing Mellin Representations and Asymptotics of Nested Binomial Sums in a Symbolic Way: The RICA Package. ACM Commun. Comput. Algebra 57(2): 31-34 (2023) - [c12]Carsten Schneider
:
Refined telescoping algorithms in RΠΣ -extensions to reduce the degrees of the denominators✱. ISSAC 2023: 498-507 - [i51]Carsten Schneider:
Refined telescoping algorithms in RΠΣ-extensions to reduce the degrees of the denominators. CoRR abs/2302.03563 (2023) - [i50]Johannes Blümlein, Nikolai Fadeev, Carsten Schneider:
Computing Mellin representations and asymptotics of nested binomial sums in a symbolic way: the RICA package. CoRR abs/2308.06042 (2023) - 2022
- [i49]Johannes Blümlein, Carsten Schneider:
The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals. CoRR abs/2203.13015 (2022) - [i48]Johannes Blümlein, Marco Saragnese, Carsten Schneider:
Computer Algebra and Hypergeometric Structures for Feynman Integrals. CoRR abs/2207.08524 (2022) - [i47]Koustav Banerje, Peter Paule, Cristian-Silviu Radu, Carsten Schneider:
Error bounds for the asymptotic expansion of the partition function. CoRR abs/2209.07887 (2022) - 2021
- [j29]Sergei A. Abramov, Manuel Bronstein, Marko Petkovsek, Carsten Schneider
:
On rational and hypergeometric solutions of linear ordinary difference equations in ΠΣ⁎-field extensions. J. Symb. Comput. 107: 23-66 (2021) - [j28]Carsten Schneider
:
The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra. Math. Comput. Sci. 15(4): 577-588 (2021) - [c11]Jakob Ablinger, Carsten Schneider
:
Solving Linear Difference Equations with Coefficients in Rings with Idempotent Representations. ISSAC 2021: 27-34 - [e1]Carsten Schneider, Mircea Marin, Viorel Negru, Daniela Zaharie:
23rd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2021, Timisoara, Romania, December 7-10, 2021. IEEE 2021, ISBN 978-1-6654-0650-5 [contents] - [i46]Carsten Schneider:
Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation. CoRR abs/2102.01471 (2021) - [i45]Jakob Ablinger, Carsten Schneider:
Solving linear difference equations with coefficients in rings with idempotent representations. CoRR abs/2102.03307 (2021) - [i44]Jakob Ablinger, Johannes Blümlein, Carsten Schneider:
Iterated integrals over letters induced by quadratic forms. CoRR abs/2103.08330 (2021) - [i43]Johannes Blümlein, Marco Saragnese, Carsten Schneider:
Hypergeometric Structures in Feynman Integrals. CoRR abs/2111.15501 (2021) - 2020
- [j27]Carsten Schneider
:
Minimal Representations and Algebraic Relations for Single Nested Products. Program. Comput. Softw. 46(2): 133-161 (2020) - [i42]Carsten Schneider:
The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra. CoRR abs/2003.01921 (2020) - [i41]Carsten Schneider, Wadim Zudilin:
A case study for ζ(4). CoRR abs/2004.08158 (2020) - [i40]Sergei A. Abramov, Manuel Bronstein, Marko Petkovsek, Carsten Schneider:
On Rational and Hypergeometric Solutions of Linear Ordinary Difference Equations in $Π\mathbfΣ^*$-field extensions. CoRR abs/2005.04944 (2020) - [i39]Evans Doe Ocansey, Carsten Schneider:
Representation of hypergeometric products of higher nesting depths in difference rings. CoRR abs/2011.08775 (2020)
2010 – 2019
- 2019
- [j26]Jakob Ablinger, Johannes Blümlein, Mark Round, Carsten Schneider
:
Numerical implementation of harmonic polylogarithms to weight w = 8. Comput. Phys. Commun. 240: 189-201 (2019) - [i38]Carsten Schneider:
Minimal representations and algebraic relations for single nested products. CoRR abs/1911.04837 (2019) - [i37]Johannes Blümlein, Peter Marquard, Carsten Schneider:
A refined machinery to calculate large moments from coupled systems of linear differential equations. CoRR abs/1912.04390 (2019) - 2018
- [j25]Johannes Middeke
, Carsten Schneider
:
Towards a direct method for finding hypergeometric solutions of linear first order recurrence systems. ACM Commun. Comput. Algebra 52(3): 89-91 (2018) - [i36]Johannes Blümlein, Carsten Schneider:
Computer algebra tools for Feynman integrals and related multi-sums. CoRR abs/1809.06168 (2018) - [i35]Peter Paule, Carsten Schneider:
Towards a symbolic summation theory for unspecified sequences. CoRR abs/1809.06578 (2018) - 2017
- [j24]Carsten Schneider, Robin Sulzgruber:
Asymptotic and Exact Results on the Complexity of the Novelli-Pak-Stoyanovskii Algorithm. Electron. J. Comb. 24(2): 2 (2017) - [j23]Carsten Schneider
:
Summation Theory II: Characterizations of RΠΣ⁎-extensions and algorithmic aspects. J. Symb. Comput. 80: 616-664 (2017) - [i34]Johannes Blümlein, Carsten Schneider:
The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory. CoRR abs/1701.04614 (2017) - [i33]Johannes Middeke, Carsten Schneider:
Denominator Bounds for Systems of Recurrence Equations using $ΠΣ$-Extensions. CoRR abs/1705.00280 (2017) - [i32]Evans Doe Ocansey, Carsten Schneider:
Representing ($q$-)hypergeometric products and mixed versions in difference rings. CoRR abs/1705.01368 (2017) - [i31]Jakob Ablinger, Johannes Blümlein, Abilio De Freitas, Mark van Hoeij, Erdal Imamoglu, Clemens G. Raab, Cristian-Silviu Radu, Carsten Schneider
:
Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams. CoRR abs/1706.01299 (2017) - [i30]Johannes Blümlein, Mark Round, Carsten Schneider:
Refined Holonomic Summation Algorithms in Particle Physics. CoRR abs/1706.03677 (2017) - 2016
- [j22]Evans Doe Ocansey, Carsten Schneider
:
Representation of hypergeometric products in difference rings. ACM Commun. Comput. Algebra 50(4): 161-163 (2016) - [j21]Johannes Middeke
, Carsten Schneider
:
Denominator bounds for higher order systems of linear recurrence equations. ACM Commun. Comput. Algebra 50(4): 185-187 (2016) - [j20]Jakob Ablinger, Arnd Behring
, Johannes Blümlein, Abilio De Freitas, Andreas von Manteuffel, Carsten Schneider
:
Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra. Comput. Phys. Commun. 202: 33-112 (2016) - [j19]Carsten Schneider
:
A difference ring theory for symbolic summation. J. Symb. Comput. 72: 82-127 (2016) - [c10]Carsten Schneider
:
Symbolic Summation in Difference Rings and Applications. ISSAC 2016: 9-12 - [i29]Jakob Ablinger, Johannes Blümlein, Abilio De Freitas, Carsten Schneider
:
A toolbox to solve coupled systems of differential and difference equations. CoRR abs/1601.01856 (2016) - [i28]Carsten Schneider:
Summation Theory II: Characterizations of RΠΣ*-extensions and algorithmic aspects. CoRR abs/1603.04285 (2016) - [i27]Carsten Schneider, Robin Sulzgruber:
Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithm. CoRR abs/1606.07597 (2016) - [i26]Christian Krattenthaler, Carsten Schneider:
Evaluation of binomial double sums involving absolute values. CoRR abs/1607.05314 (2016) - [i25]Jakob Ablinger, Arnd Behring
, Johannes Blümlein, Abilio De Freitas, Carsten Schneider:
Algorithms to solve coupled systems of differential equations in terms of power series. CoRR abs/1608.05376 (2016) - 2015
- [p2]Carsten Schneider
:
Fast Algorithms for Refined Parameterized Telescoping in Difference Fields. Computer Algebra and Polynomials 2015: 157-191 - [i24]Jakob Ablinger, Arnd Behring
, Johannes Blümlein, Abilio De Freitas, Andreas von Manteuffel, Carsten Schneider
:
Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra. CoRR abs/1509.08324 (2015) - [i23]Jakob Ablinger, Carsten Schneider
:
Algebraic independence of (cyclotomic) harmonic sums. CoRR abs/1510.03692 (2015) - 2014
- [c9]Carsten Schneider
:
A Streamlined Difference Ring Theory: Indefinite Nested Sums, the Alternating Sign, and the Parameterized Telescoping Problem. SYNASC 2014: 26-33 - [i22]Johannes Blümlein, Abilio De Freitas, Carsten Schneider
:
Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations. CoRR abs/1407.2537 (2014) - [i21]Jakob Ablinger, Johannes Blümlein, Clemens G. Raab, Carsten Schneider
:
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams. CoRR abs/1407.4721 (2014) - [i20]Carsten Schneider:
A Difference Ring Theory for Symbolic Summation. CoRR abs/1408.2776 (2014) - [i19]Carsten Schneider:
A streamlined difference ring theory: Indefinite nested sums, the alternating sign and the parameterized telescoping problem. CoRR abs/1412.2782 (2014) - 2013
- [i18]Jakob Ablinger, Johannes Blümlein, Carsten Schneider
:
Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms. CoRR abs/1302.0378 (2013) - [i17]Carsten Schneider:
Simplifying Multiple Sums in Difference Fields. CoRR abs/1304.4134 (2013) - [i16]Stefan Gerhold, Manuel Kauers, Christoph Koutschan
, Peter Paule, Carsten Schneider, Burkhard Zimmermann:
Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order. CoRR abs/1305.4818 (2013) - [i15]Carsten Schneider:
Fast Algorithms for Refined Parameterized Telescoping in Difference Fields. CoRR abs/1307.7887 (2013) - [i14]Carsten Schneider
:
Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction. CoRR abs/1310.0160 (2013) - 2012
- [j18]Johannes Blümlein, Sebastian Klein, Carsten Schneider
, Flavia Stan:
A symbolic summation approach to Feynman integral calculus. J. Symb. Comput. 47(10): 1267-1289 (2012) - [i13]Johannes Blümlein, Alexander Hasselhuhn, Carsten Schneider
:
Evaluation of Multi-Sums for Large Scale Problems. CoRR abs/1202.4303 (2012) - [i12]Jakob Ablinger, Johannes Blümlein, Mark Round, Carsten Schneider
:
Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals. CoRR abs/1210.1685 (2012) - 2011
- [j17]Helmut Prodinger, Carsten Schneider
, Stephan G. Wagner:
Unfair permutations. Eur. J. Comb. 32(8): 1282-1298 (2011) - [c8]Manuel Kauers, Carsten Schneider
:
A refined denominator bounding algorithm for multivariate linear difference equations. ISSAC 2011: 201-208 - [i11]Manuel Kauers, Carsten Schneider:
A Refined Denominator Bounding Algorithm for Multivariate Linear Difference Equations. CoRR abs/1101.2803 (2011) - [i10]Jakob Ablinger, Johannes Blümlein, Carsten Schneider
:
Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials. CoRR abs/1105.6063 (2011) - 2010
- [j16]Carsten Schneider
:
Structural theorems for symbolic summation. Appl. Algebra Eng. Commun. Comput. 21(1): 1-32 (2010) - [j15]Johannes Blümlein, Sebastian Klein, Carsten Schneider
, Flavia Stan:
A symbolic summation approach to feynman integrals. ACM Commun. Comput. Algebra 44(3/4): 95-96 (2010) - [c7]Manuel Kauers, Carsten Schneider
:
Partial denominator bounds for partial linear difference equations. ISSAC 2010: 211-218 - [c6]Carsten Schneider:
Towards an Eclipse Ontology Framework: Integrating OWL and the Eclipse Modeling Framework. TWOMDE@TOOLS 2010 - [i9]Manuel Kauers, Carsten Schneider:
Partial Denominator Bounds for Partial Linear Difference Equations. CoRR abs/1005.0602 (2010) - [i8]Johannes Blümlein, Sebastian Klein, Carsten Schneider
, Flavia Stan:
A Symbolic Summation Approach to Feynman Integral Calculus. CoRR abs/1011.2656 (2010)
2000 – 2009
- 2009
- [j14]Johannes Blümlein, Manuel Kauers, Sebastian Klein, Carsten Schneider
:
Determining the closed forms of the O(sS3) anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra. Comput. Phys. Commun. 180(11): 2143-2165 (2009) - [j13]Robert Osburn, Carsten Schneider
:
Gaussian Hypergeometric series and supercongruences. Math. Comput. 78(265): 275-292 (2009) - [p1]Peter Paule, Bruno Buchberger, Lena Kartashova, Manuel Kauers, Carsten Schneider
, Franz Winkler:
Algorithms in Symbolic Computation. Hagenberg Research 2009: 5-62 - [i7]Johannes Blümlein, Manuel Kauers, Sebastian Klein, Carsten Schneider
:
Determining the closed forms of the $O(a_s^3)$ anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra. CoRR abs/0902.4091 (2009) - [i6]Johannes Blümlein, Manuel Kauers, Sebastian Klein, Carsten Schneider
:
From Moments to Functions in Quantum Chromodynamics. CoRR abs/0902.4095 (2009) - [i5]Carsten Schneider:
A Symbolic Summation Approach to Find Optimal Nested Sum Representations. CoRR abs/0904.2323 (2009) - 2008
- [j12]Carsten Schneider
:
Multi-summation in difference fields (abstract only). ACM Commun. Comput. Algebra 42(1-2): 19 (2008) - [j11]Manuel Kauers, Carsten Schneider:
Automated Proofs for Some Stirling Number Identities. Electron. J. Comb. 15(1) (2008) - [j10]Carsten Schneider
:
A refined difference field theory for symbolic summation. J. Symb. Comput. 43(9): 611-644 (2008) - [i4]Carsten Schneider:
A Refined Difference Field Theory for Symbolic Summation. CoRR abs/0808.2543 (2008) - [i3]Carsten Schneider
:
Parameterized Telescoping Proves Algebraic Independence of Sums. CoRR abs/0808.2596 (2008) - 2007
- [j9]Carsten Schneider:
Apery's Double Sum is Plain Sailing Indeed. Electron. J. Comb. 14(1) (2007) - [j8]Robin Pemantle, Carsten Schneider:
When Is 0.999... Equal to 1? Am. Math. Mon. 114(4): 344-350 (2007) - [c5]Manuel Kauers, Carsten Schneider
:
Symbolic summation with radical expressions. ISSAC 2007: 219-226 - [i2]I. Bierenbaum, Johannes Blümlein, Sebastian Klein, Carsten Schneider
:
Difference Equations in Massive Higher Order Calculations. CoRR abs/0707.4659 (2007) - 2006
- [j7]A. Becirovic, Peter Paule, Veronika Pillwein, Axel Riese, Carsten Schneider
, Joachim Schöberl:
Hypergeometric Summation Algorithms for High-order Finite Elements. Computing 78(3): 235-249 (2006) - [j6]Manuel Kauers, Carsten Schneider
:
Indefinite summation with unspecified summands. Discret. Math. 306(17): 2073-2083 (2006) - [c4]Carsten Schneider, Gerhard Arminger:
Factor Analysis for Extraction of Structural Components and Prediction in Time Series. GfKl 2006: 273-280 - [c3]Manuel Kauers, Carsten Schneider
:
Application of unspecified sequences in symbolic summation. ISSAC 2006: 177-183 - 2005
- [j5]Carsten Schneider
:
Degree Bounds to Find Polynomial Solutions of Parameterized Linear Difference Equations in Pi-Sigma-Fields. Appl. Algebra Eng. Commun. Comput. 16(1): 1-32 (2005) - [j4]George E. Andrews, Peter Paule, Carsten Schneider
:
Plane partitions VI: Stembridge's TSPP theorem. Adv. Appl. Math. 34(4): 709-739 (2005) - [j3]Carsten Schneider
:
A new Sigma approach to multi-summation. Adv. Appl. Math. 34(4): 740-767 (2005) - [c2]Carsten Schneider
:
Finding telescopers with minimal depth for indefinite nested sum and product expressions. ISSAC 2005: 285-292 - [i1]Carsten Schneider:
Some Notes On "When is 0.999... equal to 1?". Mathematics, Algorithms, Proofs 2005 - 2004
- [j2]Carsten Schneider
:
The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application. Discret. Math. Theor. Comput. Sci. 6(2): 365-386 (2004) - [c1]Carsten Schneider
:
Symbolic summation with single-nested sum extensions. ISSAC 2004: 282-289 - 2003
- [j1]Peter Paule, Carsten Schneider
:
Computer proofs of a new family of harmonic number identities. Adv. Appl. Math. 31(2): 359-378 (2003)
Coauthor Index
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