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| Deletions are marked like this. | Additions are marked like this. |
| Line 549: | Line 549: |
| S = circle((0,0),1,rgbcolor='yellow') \ + line([e_pt,e_gs_pt], rgbcolor='red', thickness=4) \ + line([f_pt,f_gs_pt], rgbcolor='blue', thickness=3) \ + line([ef_pt,ef_gs_pt], rgbcolor='purple',thickness=2) \ + point(e_pt,pointsize=50, rgbcolor='red') \ + point(f_pt,pointsize=50, rgbcolor='blue') \ + point(ef_pt,pointsize=50,rgbcolor='purple') \ + point(f_gs_pt,pointsize=75, rgbcolor='black') \ + point(e_gs_pt,pointsize=75, rgbcolor='black') \ + point(ef_gs_pt,pointsize=75, rgbcolor='black') \ + point(js_pt,pointsize=100,rgbcolor='green') |
S = circle((0,0),1,rgbcolor='yellow') S += line([e_pt,e_gs_pt], rgbcolor='red', thickness=4) S += line([f_pt,f_gs_pt], rgbcolor='blue', thickness=3) S += line([ef_pt,ef_gs_pt], rgbcolor='purple',thickness=2) S += point(e_pt,pointsize=50, rgbcolor='red') S += point(f_pt,pointsize=50, rgbcolor='blue') S += point(ef_pt,pointsize=50,rgbcolor='purple') S += point(f_gs_pt,pointsize=75, rgbcolor='black') S += point(e_gs_pt,pointsize=75, rgbcolor='black') S += point(ef_gs_pt,pointsize=75, rgbcolor='black') S += point(js_pt,pointsize=100,rgbcolor='green') |
| Line 561: | Line 561: |
| S += text('$J(%s,%s) = %s$'%(latex2(e),latex2(f),latex(js)), \ | S += text('$J(%s,%s) = %s$'%(latex2(e),latex2(f),latex(js)), |
| Line 629: | Line 629: |
| S = circle((0,0),1,rgbcolor='yellow') \ + line([e_pt,e_gs_pt], rgbcolor='red', thickness=4) \ + line([f_pt,f_gs_pt], rgbcolor='blue', thickness=3) \ + line([ef_pt,ef_gs_pt], rgbcolor='purple',thickness=2) \ + point(e_pt,pointsize=50, rgbcolor='red') \ + point(f_pt,pointsize=50, rgbcolor='blue') \ + point(ef_pt,pointsize=50,rgbcolor='purple') \ + point(f_gs_pt,pointsize=75, rgbcolor='black') \ + point(e_gs_pt,pointsize=75, rgbcolor='black') \ + point(ef_gs_pt,pointsize=75, rgbcolor='black') \ + point(js_pt,pointsize=100,rgbcolor='green') |
S = circle((0,0),1,rgbcolor='yellow') S += line([e_pt,e_gs_pt], rgbcolor='red', thickness=4) S += line([f_pt,f_gs_pt], rgbcolor='blue', thickness=3) S += line([ef_pt,ef_gs_pt], rgbcolor='purple',thickness=2) S += point(e_pt,pointsize=50, rgbcolor='red') S += point(f_pt,pointsize=50, rgbcolor='blue') S += point(ef_pt,pointsize=50,rgbcolor='purple') S += point(f_gs_pt,pointsize=75, rgbcolor='black') S += point(e_gs_pt,pointsize=75, rgbcolor='black') S += point(ef_gs_pt,pointsize=75, rgbcolor='black') S += point(js_pt,pointsize=100,rgbcolor='green') |
| Line 641: | Line 641: |
| S += text('$J(%s,%s) = %s$'%(latex2(e),latex2(f),latex(js)), \ | S += text('$J(%s,%s) = %s$'%(latex2(e),latex2(f),latex(js)), |
| Line 653: | Line 653: |
| ga[i].save('j%d.PNG'%i,figsize=4,aspect_ratio=1, \ | ga[i].save('j%d.png'%i,figsize=4,aspect_ratio=1, |
| Line 659: | Line 659: |
| html('<table bgcolor=lightgrey cellpadding=2>') | s='<table bgcolor=lightgrey cellpadding=2>' |
| Line 661: | Line 661: |
| html('<tr><td align="center"><img src="cell://j%d.PNG"></td>'%(2*i)) html('<td align="center"><img src="cell://j%d.PNG"></td></tr>'%(2*i+1)) html('</table>') }}} |
s+='<tr><td align="center"><img src="cell://j%d.png"></td>'%(2*i) s+='<td align="center"><img src="cell://j%d.png"></td></tr>'%(2*i+1) s+='</table>' html(s)}}} |
| Line 670: | Line 670: |
| == Adding points on an elliptic curve == | == Adding points on an elliptic curve FIXME == |
| Line 777: | Line 777: |
| print """ <html> |
html(""" |
| Line 802: | Line 801: |
| </ol></html> | </ol> |
| Line 804: | Line 803: |
| (g^ b)^a, g^a, b, p, (g^a)^b) | (g^ b)^a, g^a, b, p, (g^a)^b)) |
Contents
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 FIXME
by William Stein
Computing the cuspidal subgroup
by William Stein
A Charpoly and Hecke Operator Graph FIXME
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 FIXME
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
