def check_dim(n): a=identity_matrix(n) do_with(a) a[0,0]=1+2*randint(-99,99) do_with(a) a[n-1,n-1]=1+2*randint(-99,99) do_with(a) a[0,0], a[0,n-1] =0,1 a[n-1,0],a[n-1,n-1]=1,0 do_with(a) for i in range(5): do_with( unimodular_triL(n,9) ) do_with( unimodular_triU(n,9) ) do_with( odd_hermite(n,4) ) do_with( odd_hermite(n,4).T ) do_with( unimodular(n)*odd_hermite(n,99) ) do_with( unimodular(n)*unimodular_diag(n)*odd_hermite(n,99) )
def test_serie_1(dim,vol,loud):
if dim<20:
max_k=dim+1
else:
max_k=21
for k in range(1,max_k):
assert k <= dim
for x in range(vol):
' create matrice with abs(det)<2**63 and diagonal with k entries>1 '
nums=small_nums(k)
A=sage.all.identity_matrix(ZZ,dim)
for i in range(k-1):
A[i,i]=nums[i]
A[dim-1,dim-1]=nums[k-1]
A *= unimodular(dim)
A *= unimodular(dim)
A=left_trans(A,dim)
A=left_trans(A,dim)
test(A,loud)
def test_serie_1(be, m, c, vol):
if c < 30:
max_k = c + 1
else:
max_k = 30
for x in range(vol):
for k in range(1, max_k):
assert k <= c
" create matrice with abs(det)<2**128 and diagonal with k entries>1 "
nums = small_nums(k)
A = identity_matrix(ZZ, c)
if m > c:
A = A.stack(matrix(m - c, c))
for i in range(k - 1):
A[i, i] = nums[i]
A[c - 1, c - 1] = nums[k - 1]
A *= unimodular(c)
A = left_trans(A, m)
d = three_det_divisors(nums)
test_serie_2(be, A, d)
# don't start new iteration if too many experiments done
if be[-1] >= 1000:
return
def test_serie_1(m,c,vol,loud):
if c<30:
max_k=c+1
else:
max_k=30
for k in range(1,max_k):
assert k <= c
for x in range(vol):
' create matrice with abs(det)<2**128 and diagonal with k entries>1 '
nums=small_nums(k)
A=identity_matrix(ZZ,c)
if m>c:
A=A.stack( matrix( m-c, c ) )
for i in range(k-1):
A[i,i]=nums[i]
A[c-1,c-1]=nums[k-1]
A *= unimodular(c)
A=left_trans(A,m)
d=three_det_divisors( nums )
if 1:
write('.')
else:
print 'nums=%s divisors=%s' % (nums,d)
test_serie_2(A,d,loud)
def matrix_with_det(n, d):
x = identity_matrix(n)
x[0, 0] = d
return x * unimodular(n)
def matrix_with_det( n, d ): if n==5 and LOUD_5: print 'testing matrice with det=%d' % d x=identity_matrix(n) x[0,0]=d return x * unimodular(n)