Differences between revisions 42 and 68 (spanning 26 versions)
 ⇤ ← Revision 42 as of 2014-12-20 19:27:40 → Size: 33102 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("$\pi(x)$ and $x/(\log(x)-1)$ 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"$\pi(x)$ and $x/(\log(x)-1)$ 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 n =', find_n(x_cord, y_cord, start))    print(' ')    print("SW/NE line")    if -y_cord 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: {{{#!sagecellhtml('

Cuspidal Subgroups of Modular Jacobians J0(N)

') ncols not working{{{#!sagecellpretty_print(html('

Cuspidal Subgroups of Modular Jacobians J0(N)

')) 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) Line 826: Line 831: 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 = "

First n=%s Bernoulli numbers attached to characters with modulus m=%s

"%(n,m)    s += ''    s += '
$\\chi$Conductor$B_{%s,\chi}$
$\chi$Conductor$B_{%s,\chi}$
' + \           ''.join(''%k for k in [1..n]) + '' s = r"

First n=%s Bernoulli numbers attached to characters with modulus m=%s

"%(n,m)    s += r''    s += r'' + \           ''.join(r''%k for k in [1..n]) + '' Line 837: Line 842: html(s) pretty_print(html(s)) Line 846: Line 851: 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 872: Line 877: = Multiple Zeta Values = = Multiple Zeta Values  = Line 874: Line 879: == Word to composition =={{{#!sagecell@interactdef _( weight=(7,(2..30))): n=weight a=[0 for i in range(n-1)] a.append(1) @interact def _(v=('word', input_grid(1, n, default=[a], to_value=lambda x: vector(flatten(x))))):  a=[v[i] for i in range(len(v))]  def bintocomp(a): b=[] count=1 for j in range(len(a)):  if(a[j]==0):   count=count+1  else:   b.append(count)   count=1  return(b)  print "Composition is ",bintocomp(a)}}}{{attachment:akhi2.png}}== Composition to Word =={{{#!sagecell@interactdef _( Depth=(7,(1..30))): n=Depth a=[] a.append(2) a=a+[1 for i in range(1,n)] @interact def _(v=('composition', input_grid(1, n, default=[a], to_value=lambda x: vector(flatten(x))))):  a=[v[i] for i in range(len(v))]  def comptobin(a): word=[] for i in range(len(a)):  word=word+[0]*(a[i]-1)+[1] return(word)  print "Word is is ",comptobin(a)}}}{{attachment:akhi3.png}}== Computing Multiple Zeta values == == Computing Multiple Zeta values ===== Word Input === Line 925: Line 884: def _( weight=(5,(2..20))): def _( weight=(5,(2..100))): Line 978: Line 937: print zeta(a) u=zeta(a)  RIF=RealIntervalField(int(3.321928*D))  u=u/1  print(u) Line 981: Line 943: === Composition Input ==={{{#!sagecellR=RealField(10)@interactdef _( Depth=(5,(2..100))): n=Depth a=[2] a=a+[1 for i in range(n-1)] @interact def _(v=('Composition', input_grid(1, n, default=[a], to_value=lambda x: vector(flatten(x)))), accuracy=(100..100000)):  D=accuracy  a=[v[i] for i in range(len(v))]  def comptobin(a):        word=[]        for i in range(len(a)):                word=word+[0]*(a[i]-1)+[1]        return(word)  a=comptobin(a)  DD=int(3.321928*D)+int(R(log(3.321928*D))/R(log(10)))+4  RIF=RealIntervalField(DD)  def Li(word):        n=int(DD*log(10)/log(2))+1        B=[]        L=[]        S=[]        count=-1        k=len(word)        for i in range(k):                B.append(RIF('0'))                L.append(RIF('0'))                if(word[i]==1 and i

Integer Factorization

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

by William Stein

by David Runde

Prime Spiral - Polar

by David Runde

Needs fix for show_factors

Modular Forms

by William Stein

Computing the cuspidal subgroup

by William Stein

ncols not working

by William Stein

by Emily Kirkman

by Emily Kirkman

by Emily Kirkman

by Emily Kirkman

Elliptic Curves

Adding points on an elliptic curve

by David Møller Hansen

Cryptography

The Diffie-Hellman Key Exchange Protocol

by Timothy Clemans and William Stein

Other

Continued Fraction Plotter

by William Stein

crows not working

Computing Generalized Bernoulli Numbers

by William Stein (Sage-2.10.3)

by Robert Miller

Multiple Zeta Values

by Akhilesh P.

Shuffle Regularization at 1

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