Differences between revisions 62 and 68 (spanning 6 versions)
Revision 62 as of 2016-05-09 09:56:04
Size: 48431
Editor: akhi
Comment:
Revision 68 as of 2020-06-14 09:10:48
Size: 48543
Editor: chapoton
Comment: fixone
Deletions are marked like this. Additions are marked like this.
Line 79: Line 79:
    html(s)     pretty_print(html(s))
Line 88: Line 88:
def _(N=(100,(2..2000))):
    html("<font color='red'>$\pi(x)$</font> and <font color='blue'>$x/(\log(x)-1)$</font> for $x < %s$"%N)
    show(plot(prime_pi, 0, N, rgbcolor='red') + plot(x/(log(x)-1), 5, N, rgbcolor='blue'))
def _(N=(100,list(range(2,2000)))):
    pretty_print(html(r"<font color='red'>$\pi(x)$</font> and <font color='blue'>$x/(\log(x)-1)$</font> for $x < %s$"%N))
    show(plot(prime_pi, 0, N, color='red') + plot(x/(log(x)-1), 5, N, color='blue'))
Line 115: Line 115:
        else: print 'NaN'         else: print('NaN')
Line 140: Line 140:
    if start < 1 or end <=start: print "invalid start or end value"
    if n > end: print "WARNING: n is larger than the end value"
    if start < 1 or end <=start: print("invalid start or end value")
    if n > end: print("WARNING: n is larger than the end value")
Line 172: Line 172:
    #print x_cord, y_cord
Line 183: Line 182:
        #print x, "=x y=", y, " num =", num
Line 209: Line 207:
        print '(to go from x,y coords to an n, reset by setting n=0)'         print('(to go from x,y coords to an n, reset by setting n=0)')
Line 211: Line 209:
        #print 'if n =', n, 'then (x,y) =', (x_cord, y_cord)

    print
'(x,y) =', (x_cord, y_cord), '<=> n =', find_n(x_cord, y_cord, start)
    print ' '
    print
"SW/NE line"
    if -y_cord<x_cord: print '4*t^2 + 2*t +', -x_cord+y_cord+start
    else: print '4*t^2 + 2*t +', +x_cord-y_cord+start

    print
"NW/SE line"
    if x_cord<y_cord: print '4*t^2 +', -x_cord-y_cord+start
    else: print '4*t^2 + 4*t +', +x_cord+y_cord+start

    print(
'(x,y) =', (x_cord, y_cord), '<=> n =', find_n(x_cord, y_cord, start))
    print(' ')
    print(
"SW/NE line")
    if -y_cord<x_cord: print('4*t^2 + 2*t +', -x_cord+y_cord+start)
    else: print('4*t^2 + 2*t +', +x_cord-y_cord+start)

    print(
"NW/SE line")
    if x_cord<y_cord: print('4*t^2 +', -x_cord-y_cord+start)
    else: print('4*t^2 + 4*t +', +x_cord+y_cord+start)
Line 233: Line 230:

Needs fix for show_factors
Line 239: Line 238:
    if start < 1 or end <=start: print "invalid start or end value"
    if n > end: print "WARNING: n is greater than end value"
    if start < 1 or end <=start: print("invalid start or end value")
    if n > end: print("WARNING: n is greater than end value")
Line 262: Line 261:
        print 'n =', factor(n)         print('n = {}'.format(factor(n)))
Line 284: Line 283:
            print 'Pink Curve: n^2 +', c
            print 'Green Curve: n^2 + n +', c2
            print('Pink Curve: n^2 +', c)
            print('Green Curve: n^2 + n +', c2)
Line 312: Line 311:
    print M; print '\n'*3
    print "Computing basis...\n\n"
    print(M)
    print('\n' * 3)
    print(
"Computing basis...\n\n")
Line 315: Line 315:
         print "Space has dimension 0"          print("Space has dimension 0")
Line 317: Line 317:
        prec = max(prec, M.dimension()+1)         prec = max(prec, M.dimension() + 1)
Line 320: Line 320:
    print "\n\n\nDone computing basis."     print("\n\n\nDone computing basis.")
Line 328: Line 328:
{{{#!sagecell
html('<h1>Cuspidal Subgroups of Modular Jacobians J0(N)</h1>')

ncols not working
{{{#!sagecell
pretty_print(html('<h1>Cuspidal Subgroups of Modular Jacobians J0(N)</h1>'))
Line 333: Line 335:
    print A.cuspidal_subgroup()     print(A.cuspidal_subgroup())
Line 475: Line 477:
                MP += text('$\omega^2$',(i+.5,r-j-.5),rgbcolor='black')                 MP += text(r'$\omega^2$',(i+.5,r-j-.5),rgbcolor='black')
Line 477: Line 479:
                MP += text('$\omega $',(i+.5,r-j-.5),rgbcolor='black')                 MP += text(r'$\omega $',(i+.5,r-j-.5),rgbcolor='black')
Line 486: Line 488:
    MP += text('$ \pi_1$',(r/2,r+2), rgbcolor='black', fontsize=25)
    MP += text('$ \pi_2$',(-2.5,r/2), rgbcolor='black', fontsize=25)

    html('Symmetry of Primary Cubic Residues mod ' \
          + '%d primary primes in $ \mathbf Z[\omega]$.'%r)
    MP += text(r'$ \pi_1$',(r/2,r+2), rgbcolor='black', fontsize=25)
    MP += text(r'$ \pi_2$',(-2.5,r/2), rgbcolor='black', fontsize=25)

    pretty_print(html('Symmetry of Primary Cubic Residues mod ' \
          + r'%d primary primes in $ \mathbf Z[\omega]$.'%r))
Line 644: Line 646:
        html('$$J(%s,%s) = %s$$'%(latex2(e),latex2(f),latex(js)))         pretty_print(html('$$J(%s,%s) = %s$$'%(latex2(e),latex2(f),latex(js))))
Line 664: Line 666:
    html(s)}}}     pretty_print(html(s))
}}}
Line 754: Line 757:
    print "p = %s"%p
    show(E.change_ring(GF(p)).plot(),xmin=0,ymin=0)
    print("p = %s" % p)
    show(E.change_ring(GF(p)).plot(), xmin=0, ymin=0)
Line 778: Line 781:
    html("""     pretty_print(html("""
Line 804: Line 807:
       (g^ b)^a, g^a, b, p, (g^a)^b))        (g^ b)^a, g^a, b, p, (g^a)^b)))
Line 814: Line 817:

crows not working
Line 817: Line 822:
    c = list(continued_fraction(RealField(prec)(number))); print c     c = list(continued_fraction(RealField(prec)(number))); print(c)
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def _(m=selector([1..15],nrows=2), n=(7,(3..10))): def _(m=selector([1..15],nrows=2), n=(7,[3..10])):
Line 828: Line 833:
    s = "<h3>First n=%s Bernoulli numbers attached to characters with modulus m=%s</h3>"%(n,m)
    s += '<table border=1>'
    s += '<tr bgcolor="#edcc9c"><td align=center>$\\chi$</td><td>Conductor</td>' + \
           ''.join('<td>$B_{%s,\chi}$</td>'%k for k in [1..n]) + '</tr>'
    s = r"<h3>First n=%s Bernoulli numbers attached to characters with modulus m=%s</h3>"%(n,m)
    s += r'<table border=1>'
    s += r'<tr bgcolor="#edcc9c"><td align=center>$\chi$</td><td>Conductor</td>' + \
           ''.join(r'<td>$B_{%s,\chi}$</td>'%k for k in [1..n]) + '</tr>'
Line 837: Line 842:
    html(s)     pretty_print(html(s))
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L = [[-0.5, 2.0^(x/100.0) - 1 + sqrt(3.0)/2] for x in xrange(1000, -1, -1)]
R = [[0.5, 2.0^(x/100.0) - 1 + sqrt(3.0)/2] for x in xrange(1000)]
xes = [x/1000.0 for x in xrange(-500,501,1)]
L = [[-0.5, 2.0^(x/100.0) - 1 + sqrt(3.0)/2] for x in range(1000, -1, -1)]
R = [[0.5, 2.0^(x/100.0) - 1 + sqrt(3.0)/2] for x in range(1000)]
xes = [x/1000.0 for x in range(-500,501,1)]
Line 874: Line 879:
== Computing Multiple Zeta values (Euler-Zagier numbers) == == Computing Multiple Zeta values ==
Line 935: Line 940:
  print u   print(u)
Line 1004: Line 1009:
  print u   print(u)
Line 1007: Line 1012:
== Program to Compute Integer Relation between Multiple Zeta Values (Euler-Zagier numbers) == == Program to Compute Integer Relation between Multiple Zeta Values ==
Line 1010: Line 1015:
print "Enter the number of composition" print("Enter the number of composition")
Line 1016: Line 1021:
 print "In each box Enter composition as an array"  print("In each box Enter composition as an array")
Line 1079: Line 1084:
        print "zeta(",a[i],")=",zet[i]         print("zeta(", a[i], ")=", zet[i])
Line 1081: Line 1086:
  print "the Intger Relation between the above zeta values given by the vector"
  print u
  print("the Intger Relation between the above zeta values given by the vector")
  print(u)
Line 1105: Line 1110:
  print "Composition is ",bintocomp(a)   print("Composition is {}".format(bintocomp(a)))
Line 1126: Line 1131:
  print "Word is  ",comptobin(a)   print("Word is {}".format(comptobin(a)))
Line 1148: Line 1153:
  print "Dual word is ",dual(a)   print("Dual word is {}"?format(dual(a)))
Line 1235: Line 1240:
    print c[1][i],"*",c[0][i] ,"+ ",
  print c[1][len(c[0])-1],"*",c[0][len(c[0])-1]
    print(c[1][i],"*",c[0][i] ,"+ ")
  print(c[1][len(c[0])-1],"*",c[0][len(c[0])-1])
Line 1384: Line 1389:
  c=Regshuf0(a)   c = Regshuf0(a)
Line 1387: Line 1392:
      print c[1][i],"*",c[0][i] ,"+ ",       print(c[1][i],"*",c[0][i] ,"+ ")
Line 1389: Line 1394:
    print c[1][len(c[0])-1],"*",c[0][len(c[0])-1]     print(c[1][len(c[0])-1],"*",c[0][len(c[0])-1])
Line 1537: Line 1542:
  c=Regshuf1(a)   c = Regshuf1(a)
Line 1540: Line 1545:
      print c[1][i],"*",c[0][i] ,"+ ",       print(c[1][i],"*",c[0][i] ,"+ ")
Line 1542: Line 1547:
    print c[1][len(c[0])-1],"*",c[0][len(c[0])-1]     print(c[1][len(c[0])-1],"*",c[0][len(c[0])-1])

Integer Factorization

Divisibility Poset

by William Stein

divposet.png

Factor Trees

by William Stein

factortree.png

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

primes.png

Prime Spiral - Square FIXME

by David Runde

SquareSpiral.PNG

Prime Spiral - Polar

by David Runde

Needs fix for show_factors

PolarSpiral.PNG

Modular Forms

Computing modular forms

by William Stein

modformbasis.png

Computing the cuspidal subgroup

by William Stein

ncols not working

cuspgroup.png

A Charpoly and Hecke Operator Graph

by William Stein

heckegraph.png

Modular Arithmetic

Quadratic Residue Table FIXME

by Emily Kirkman

quadres.png

quadresbig.png

Cubic Residue Table FIXME

by Emily Kirkman

cubres.png

Cyclotomic Fields

Gauss and Jacobi Sums in Complex Plane

by Emily Kirkman

jacobising.png

Exhaustive Jacobi Plotter

by Emily Kirkman

jacobiexh.png

Elliptic Curves

Adding points on an elliptic curve

by David Møller Hansen

PointAddEllipticCurve.png

Plotting an elliptic curve over a finite field

ellffplot.png

Cryptography

The Diffie-Hellman Key Exchange Protocol

by Timothy Clemans and William Stein

dh.png

Other

Continued Fraction Plotter

by William Stein

crows not working

contfracplot.png

Computing Generalized Bernoulli Numbers

by William Stein (Sage-2.10.3)

bernoulli.png

Fundamental Domains of SL_2(ZZ)

by Robert Miller

fund_domain.png

Multiple Zeta Values

by Akhilesh P.

Computing Multiple Zeta values

Word Input

akhi1.png

Composition Input

akhi5.png

Program to Compute Integer Relation between Multiple Zeta Values

akhi10.png

Word to composition

akhi2.png

Composition to Word

akhi3.png

Dual of a Word

akhi4.png

Shuffle product of two Words

akhi6.png

Shuffle Regularization at 0

akhi7.png

Shuffle Regularization at 1

akhi8.png

interact/number_theory (last edited 2020-06-14 09:10:48 by chapoton)