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| = Multiple Zeta Values = | = Multiple Zeta Values = |
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| == Computing Multiple Zeta values == | == Computing Multiple Zeta values (Euler-Zagier numbers) == |
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| def _( weight=(5,(2..20))): | def _( weight=(5,(2..100))): |
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| print zeta(a) | u=zeta(a) RIF=RealIntervalField(int(3.321928*D)) u=u/1 print u |
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| def _( Depth=(5,(2..20))): | def _( Depth=(5,(2..100))): |
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print zeta(a) |
u=zeta(a) RIF=RealIntervalField(int(3.321928*D)) u=u/1 print u |
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| == Program to Compute Integer Relation between Multiple Zeta Values == | == Program to Compute Integer Relation between Multiple Zeta Values (Euler-Zagier numbers) == |
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| def _( n=(5,(2..20))): | def _( n=(5,(2..100))): |
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| mp.dps=D for i in range(n): zet[i]=zet[i]/1 |
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| def _( weight=(7,(2..30))): | def _( weight=(7,(2..100))): |
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| def _( Depth=(7,(1..30))): | def _( Depth=(7,(1..100))): |
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| def _( weight=(7,(2..30))): | def _( weight=(7,(2..100))): |
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| def _( w1=(2,(2..20)), w2=(2,(2..20))): | def _( w1=(2,(2..100)), w2=(2,(2..100))): |
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| def _( w=(2,(2..20))): | def _( w=(2,(2..100))): |
Contents
- Integer Factorization
- Prime Numbers
- Modular Forms
- Modular Arithmetic
- Cyclotomic Fields
- Elliptic Curves
- Cryptography
- Other
- Multiple Zeta Values
Integer Factorization
Divisibility Poset
by William Stein
Factor Trees
by William Stein
More complicated demonstration using Mathematica: http://demonstrations.wolfram.com/FactorTrees/
Factoring an Integer
by Timothy Clemans
Sage implementation of the Mathematica demonstration of the same name. http://demonstrations.wolfram.com/FactoringAnInteger/
Prime Numbers
Illustrating the prime number theorem
by William Stein
Prime Spiral - Square FIXME
by David Runde
Prime Spiral - Polar
by David Runde
Modular Forms
Computing modular forms
by William Stein
Computing the cuspidal subgroup
by William Stein
A Charpoly and Hecke Operator Graph
by William Stein
Modular Arithmetic
Quadratic Residue Table FIXME
by Emily Kirkman
Cubic Residue Table FIXME
by Emily Kirkman
Cyclotomic Fields
Gauss and Jacobi Sums in Complex Plane
by Emily Kirkman
Exhaustive Jacobi Plotter
by Emily Kirkman
Elliptic Curves
Adding points on an elliptic curve
by David Møller Hansen
Plotting an elliptic curve over a finite field
Cryptography
The Diffie-Hellman Key Exchange Protocol
by Timothy Clemans and William Stein
Other
Continued Fraction Plotter
by William Stein
Computing Generalized Bernoulli Numbers
by William Stein (Sage-2.10.3)
Fundamental Domains of SL_2(ZZ)
by Robert Miller
Multiple Zeta Values
by Akhilesh P.
Computing Multiple Zeta values (Euler-Zagier numbers)
Word Input
Composition Input
Program to Compute Integer Relation between Multiple Zeta Values (Euler-Zagier numbers)
Word to composition
Composition to Word
Dual of a Word
Shuffle product of two Words
Shuffle Regularization at 0
Shuffle Regularization at 1
