def test__get_mat_1(self):
#
# Permute a block matrices to obtain rotation along x-axis.
#
print(get_mat('I', 'Oprpp', 'I'))
e_lst = [1, 4, 2, 3, 5, 6, 7, 8]
i_lst = sage_Permutation(e_lst).inverse()
A_str = 'E' + str(i_lst)
B_str = 'Oprpp'
C_str = 'E' + str(e_lst)
tup = (A_str, B_str, C_str)
print(tup)
mati = get_emat(A_str)
mate = get_emat(C_str)
assert mate * mati == sage_identity_matrix(9)
out = get_mat(*tup)
print(out)
print(list(out))
assert str(
list(out)
) == '[(1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, c0, -s0, 0, 0, 0, 0, 0), (0, 0, s0, c0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1)]'
def set( self, p_tup, o_tup, v_tup ):
'''
Parameters
----------
p_tup : tuple<string>
A 3-tuple of strings with format as in the docs of "orb_matrices.get_mat()".
o_tup : tuple<string>
Same specs as "p_tup".
v_tup : tuple<string>
Same specs as "p_tup".
Returns
-------
self
Sets "self.pmat", "self.omat" and "self.vmat"
according "p_tup", "o_tup" and "v_tup" respectively.
The matrices are obtained with "orb_matrices.get_mat()".
Set "self.info_dct" with info about the decomposition
of the matrices:
"self.info_dct['pmat'] = p_tup"
"self.info_dct['omat'] = o_tup"
"self.info_dct['vmat'] = v_tup"
'''
self.pmat = get_mat( p_tup[0], p_tup[1], p_tup[2] )
self.omat = get_mat( o_tup[0], o_tup[1], o_tup[2] )
self.vmat = get_mat( v_tup[0], v_tup[1], v_tup[2] )
self.info_dct['pmat'] = p_tup
self.info_dct['omat'] = o_tup
self.info_dct['vmat'] = v_tup
return self
def test__get_imp( self ):
omat = get_mat( 'T[1, 0, 0, 0, 0, 0, 0]', 'Orppp', 'T[-1, 0, 0, 0, 0, 0, 0]' )
vmat = get_mat( 'T[0, 1, 1, 0, 0, 0, 0]', 'Rrrrs[37, 0, 0, 0]', 'T[0, -1, -1, 0, 0, 0, 0]' )
imp_lst = get_imp( omat, vmat ) # ideal of Perseus cyclide
print( imp_lst )
assert str( imp_lst ) == '[x7, x6, x5, x4, 100*x1^2 - 4*x0*x3 - 40*x1*x3 + 9*x3^2 - 200*x1*x8 + 44*x3*x8 + 100*x8^2, 100*x0^2 - 100*x2^2 - 4*x0*x3 - 40*x1*x3 - 91*x3^2 - 200*x1*x8 + 44*x3*x8]'
def test__get_mat__I_Orppp_I(self):
out = get_mat('I', 'Orppp', 'I')
print(out)
print(list(out))
assert str(
list(out)
) == '[(1, 0, 0, 0, 0, 0, 0, 0, 0), (0, c0, -s0, 0, 0, 0, 0, 0, 0), (0, s0, c0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1)]'
def random( self, coef_bnd = 3, random_pmat = True ):
'''
Sets (restricted) random values for "self.omat",
"self.vmat" and "self.pmat".
Parameters
----------
coef_bnd : int
Positive integer.
random_pmat : boolean
Returns
-------
self
Notes
-----
The translation coefficients of "self.vmat"
are in the interval: [-coef_bnd, +coef_bnd].
If "random_pmat== True", then "self.pmat"
is set to a random value (P1), and
otherwise "self.pmat" is set to a standard
projection (P0).
'''
ch_lst = ['r', 's', 'p', 'm', 'a']
#
# random self.pmat
#
Pn = {True:'P1', False:'P0'}[random_pmat]
self.pmat = get_mat( Pn, 'I', 'I' )
self.info_dct['pmat'] = ( Pn, 'I', 'I' )
#
# random self.omat
#
rnd = OrbRing.random_elt( [0, 1] )
if rnd == 0:
ch_str = ''.join( [OrbRing.random_elt( ch_lst ) for i in range( 4 ) ] )
B_str = 'O' + ch_str
rnd2 = OrbRing.random_elt( [0, 1] )
if rnd2 == 0:
A_str = 'I'
C_str = 'I'
else:
p = sage_Permutations( range( 1, 8 + 1 ) )
rp = p.random_element()
rpI = sage_Permutation( rp ).inverse()
A_str = 'E' + str( list( rpI ) )
C_str = 'E' + str( list( rp ) )
elif rnd == 1:
A_str = 'I'
B_str = 'tT'
C_str = 'I'
self.omat = get_mat( A_str, B_str, C_str )
self.info_dct['omat'] = ( A_str, B_str, C_str )
#
# random self.vmat
#
# All the coefficients are bound by coef_size-n for some integer n.
coef_size = OrbRing.random_elt( range( 1, coef_bnd + 1 ) )
# A -- self.vmat
t_lst = [OrbRing.random_int( coef_size ) for i in range( 7 )]
A_str = 'T' + str( t_lst )
# B -- self.vmat"
# note that small angles means small coefficients
angle_lst = [ OrbRing.random_elt( range( 0, 360 ) ) for i in range( 4 ) ]
ch_str = ''.join( [OrbRing.random_elt( ch_lst ) for i in range( 4 ) ] )
B_str = 'R' + ch_str + str( angle_lst )
# C -- self.vmat
rnd = OrbRing.random_elt( [0, 1, 2] )
if rnd == 0:
C_str = 'T' + str( [-t_lst[i] for i in range( 7 )] ) # inverse
elif rnd == 1:
C_str = 'T' + str( [OrbRing.random_int( coef_size ) for i in range( 7 )] )
elif rnd == 2:
C_str = 'I'
# A*B*C -- self.vmat
self.vmat = get_mat( A_str, B_str, C_str )
self.info_dct['vmat'] = ( A_str, B_str, C_str )
return self