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| = Sage Interactions = | #Choose the size D of the square matrix: D = 3 |
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| Post code that demonstrates the use of the interact command in Sage here. It should be easy to just scroll through and paste examples out of here into their own sage notebooks.If you have suggestions on how to improve interact, add them [:interactSuggestions: here] or email [email protected]. | example = [[1 if k==j else 0 for k in range(D)] for j in range(D)] example[0][-1] = 2 example[-1][0] = 3 |
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| * [:interact/graph_theory:Graph Theory] * [:interact/calculus:Calculus] * [:interact/diffeq:Differential Equations] * [:interact/linear_algebra:Linear Algebra] * [:interact/algebra:Algebra] * [:interact/number_theory:Number Theory] * [:interact/web:Web Applications] * [:interact/bio:Bioinformatics] * [:interact/graphics:Drawing Graphics] == Miscellaneous == == Profile a snippet of code == {{{ html('<h2>Profile the given input</h2>') import cProfile; import profile |
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| def _(cmd = ("Statement", '2 + 2'), do_preparse=("Preparse?", True), cprof =("cProfile?", False)): if do_preparse: cmd = preparse(cmd) print "<html>" # trick to avoid word wrap if cprof: cProfile.run(cmd) else: profile.run(cmd) print "</html>" }}} attachment:profile.png === Evaluate a bit of code in a given system === by William Stein (there is no way yet to make the text box big): {{{ @interact def _(system=selector([('sage0', 'Sage'), ('gp', 'PARI'), ('magma', 'Magma')]), code='2+2'): print globals()[system].eval(code) }}} attachment:evalsys.png === A Random Walk === by William Stein {{{ html('<h1>A Random Walk</h1>') vv = []; nn = 0 @interact def foo(pts = checkbox(True, "Show points"), refresh = checkbox(False, "New random walk every time"), steps = (50,(10..500))): # We cache the walk in the global variable vv, so that # checking or unchecking the points checkbox doesn't change # the random walk. html("<h2>%s steps</h2>"%steps) global vv if refresh or len(vv) == 0: s = 0; v = [(0,0)] for i in range(steps): s += random() - 0.5 v.append((i, s)) vv = v elif len(vv) != steps: # Add or subtract some points s = vv[-1][1]; j = len(vv) for i in range(steps - len(vv)): s += random() - 0.5 vv.append((i+j,s)) v = vv[:steps] else: v = vv L = line(v, rgbcolor='#4a8de2') if pts: L += points(v, pointsize=10, rgbcolor='red') show(L, xmin=0, figsize=[8,3]) }}} attachment:randomwalk.png === 3D Random Walk === {{{ @interact def rwalk3d(n=(50,1000), frame=True): pnt = [0,0,0] v = [copy(pnt)] for i in range(n): pnt[0] += random()-0.5 pnt[1] += random()-0.5 pnt[2] += random()-0.5 v.append(copy(pnt)) show(line3d(v,color='black'),aspect_ratio=[1,1,1],frame=frame) }}} attachment:randomwalk3d.png |
def _(M=input_grid(D,D, default = example, label='Matrix to invert', to_value=matrix), tt = text_control('Enter the bits of precision used' ' (only if you entered floating point numbers)'), precision = slider(5,100,5,20), auto_update=False): if det(M)==0: print 'Failure: Matrix is not invertible' return if M.base_ring() == RR: M = M.apply_map(RealField(precision)) N=M M=M.augment(identity_matrix(D)) print 'We construct the augmented matrix' show(M) for m in range(0,D-1): if M[m,m] == 0: lista = [(M[j,m],j) for j in range(m,D)] maxi, c = max(lista) M[c,:],M[m,:]=M[m,:],M[c,:] print 'We permute rows %d and %d'%(m+1,c+1) show(M) for n in range(m+1,D): a=M[m,m] if M[n,m]!=0: print "We add %s times row %d to row %d"%(-M[n,m]/a, m+1, n+1) M=M.with_added_multiple_of_row(n,m,-M[n,m]/a) show(M) for m in range(D-1,-1,-1): for n in range(m-1,-1,-1): a=M[m,m] if M[n,m]!=0: print "We add %s times row %d to the row %d"%(-M[n,m]/a, m+1, n+1) M=M.with_added_multiple_of_row(n,m,-M[n,m]/a) show(M) for m in range(0,D): if M[m,m]!=1: print 'We divide row %d by %s'%(m+1,M[m,m]) M = M.with_row_set_to_multiple_of_row(m,m,1/M[m,m]) show(M) M=M.submatrix(0,D,D) print 'We keep the right submatrix, which contains the inverse' html('$$M^{-1}=%s$$'%latex(M)) print 'We check it actually is the inverse' html('$$M^{-1}*M=%s*%s=%s$$'%(latex(M),latex(N),latex(M*N))) |
D = 3
example = [[1 if k==j else 0 for k in range(D)] for j in range(D)] example[0][-1] = 2 example[-1][0] = 3
@interact def _(M=input_grid(D,D, default = example,
- label='Matrix to invert', to_value=matrix),
- tt = text_control('Enter the bits of precision used'
- ' (only if you entered floating point numbers)'),
- if det(M)==0:
- print 'Failure: Matrix is not invertible' return
M = M.apply_map(RealField(precision))
- if M[m,m] == 0:
- lista = [(M[j,m],j) for j in range(m,D)] maxi, c = max(lista) M[c,:],M[m,:]=M[m,:],M[c,:] print 'We permute rows %d and %d'%(m+1,c+1) show(M)
- a=M[m,m] if M[n,m]!=0:
- print "We add %s times row %d to row %d"%(-M[n,m]/a, m+1, n+1) M=M.with_added_multiple_of_row(n,m,-M[n,m]/a) show(M)
- for n in range(m-1,-1,-1):
- a=M[m,m] if M[n,m]!=0:
- print "We add %s times row %d to the row %d"%(-M[n,m]/a, m+1, n+1) M=M.with_added_multiple_of_row(n,m,-M[n,m]/a) show(M)
- a=M[m,m] if M[n,m]!=0:
- if M[m,m]!=1:
- print 'We divide row %d by %s'%(m+1,M[m,m]) M = M.with_row_set_to_multiple_of_row(m,m,1/M[m,m]) show(M)
html('
M^{-1}=%s'%latex(M)) print 'We check it actually is the inverse' html('M^{-1}*M=%s*%s=%s'%(latex(M),latex(N),latex(M*N)))