sage: phi = K.gen()
sage: P0 = PolyhedronPartition.jeandel_rao_tilings_partition()
sage: Gamma0 = matrix.column([(phi,0), (1,phi+3)])
sage: fundamental_domain = polytopes.parallelotope([(phi,0), (0,phi+3)])
sage: R0e2 = PET.toral_translation(Gamma0, vector((0,1)), fundamental_domain)
sage: y_le_1 = [1, 0, -1] # syntax for the inequality y <= 1
sage:
sage: %time P1,beta0 = R0e2.induced_partition(y_le_1, P0, substitution_type='column')
CPU times: user 4.6 s, sys: 84 ms, total: 4.68 s
Wall time: 4.64 s
sage: %prun P1,beta0 = R0e2.induced_partition(y_le_1, P0, substitution_type='column')
3059637 function calls (3058959 primitive calls) in 5.373 seconds
Ordered by: internal time
ncalls tottime percall cumtime percall filename:lineno(function)
4878 0.619 0.000 1.713 0.000 {method 'right_kernel' of 'sage.matrix.matrix2.Matrix' objects}
4184 0.392 0.000 0.489 0.000 {method 'solve_right' of 'sage.matrix.matrix2.Matrix' objects}
43084 0.253 0.000 0.280 0.000 matrix_space.py:720(__call__)
9756 0.209 0.000 0.294 0.000 number_field.py:3081(_repr_)
30698 0.191 0.000 0.253 0.000 matrix_space.py:103(get_matrix_class)
4184 0.166 0.000 0.182 0.000 {method 'pivots' of 'sage.matrix.matrix0.Matrix' objects}
4184 0.166 0.000 0.205 0.000 {method 'pivot_rows' of 'sage.matrix.matrix2.Matrix' objects}
5243 0.152 0.000 0.171 0.000 {method 'rank' of 'sage.matrix.matrix0.Matrix' objects}
5005 0.146 0.000 0.325 0.000 free_module.py:662(__init__)
54383 0.140 0.000 0.200 0.000 free_module.py:973(_element_constructor_)
14168 0.138 0.000 0.197 0.000 sequence.py:80(Sequence)
435687 0.122 0.000 0.122 0.000 {isinstance}
35194 0.115 0.000 0.127 0.000 representation.py:1181(evaluated_on)
30698 0.113 0.000 0.367 0.000 matrix_space.py:432(__classcall__)
4184 0.106 0.000 1.284 0.000 double_description.py:641(initial_pair)
54383 0.102 0.000 0.304 0.000 free_module.py:5569(_element_constructor_)
9637 0.101 0.000 0.312 0.000 {sage.modules.free_module_element.vector}
8368 0.080 0.000 0.169 0.000 {method 'rows' of 'sage.matrix.matrix1.Matrix' objects}
41111 0.072 0.000 0.149 0.000 misc.py:295(cputime)
10231 0.070 0.000 0.072 0.000 double_description.py:313(R_by_sign)
35194 0.066 0.000 0.247 0.000 representation.py:694(contains)
41111 0.057 0.000 0.057 0.000 {resource.getrusage}
52510 0.051 0.000 0.051 0.000 free_module.py:328(create_key)
4593 0.050 0.000 0.112 0.000 {method 'columns' of 'sage.matrix.matrix1.Matrix' objects}
4878 0.045 0.000 0.156 0.000 free_module.py:1593(basis_matrix)
2092 0.043 0.000 0.408 0.000 double_description_inhomogeneous.py:273(_extract_Vrep)
4878 0.042 0.000 0.443 0.000 free_module.py:5643(__init__)
19512 0.038 0.000 0.038 0.000 {method 'sub' of '_sre.SRE_Pattern' objects}
14168 0.036 0.000 0.039 0.000 sequence.py:405(__init__)
2965 0.036 0.000 0.057 0.000 representation.py:330(_set_data)
2092 0.036 0.000 2.732 0.001 double_description_inhomogeneous.py:154(__init__)
43834 0.032 0.000 0.281 0.000 base.py:587(<genexpr>)
1882 0.031 0.000 0.063 0.000 number_field.py:1554(_element_constructor_)
5005 0.030 0.000 0.042 0.000 free_module.py:7218(element_class)
6983 0.028 0.000 0.030 0.000 {method 'inner_product' of 'sage.modules.free_module_element.FreeModuleElement' objects}
35194 0.028 0.000 0.028 0.000 backend_field.py:92(_is_nonneg)
2965 0.028 0.000 0.084 0.000 representation.py:311(__init__)
10231 0.024 0.000 0.193 0.000 double_description.py:689(add_inequality)
41111 0.023 0.000 0.173 0.000 misc.py:525(verbose)
19512 0.023 0.000 0.023 0.000 re.py:230(_compile)
1882 0.023 0.000 0.025 0.000 polynomial_ring.py:320(_element_constructor_)
5010 0.022 0.000 0.085 0.000 modules.py:112(__classcall_private__)
347 0.022 0.000 0.328 0.001 point_configuration.py:1827(contained_simplex)
31 0.021 0.001 4.147 0.134 polyhedron_partition.py:1204(refinement)
47132 0.020 0.000 0.020 0.000 number_field.py:3792(pari_polynomial)
1745 0.019 0.000 3.565 0.002 backend_field.py:214(_init_from_Hrepresentation)
6276 0.019 0.000 0.020 0.000 double_description.py:112(__init__)
409 0.018 0.000 0.027 0.000 {method 'inverse' of 'sage.matrix.matrix2.Matrix' objects}
7979 0.018 0.000 0.037 0.000 fields.py:63(__contains__)
2092 0.018 0.000 0.747 0.000 double_description_inhomogeneous.py:451(_init_Vrep)
93 0.018 0.000 0.041 0.000 point_configuration.py:332(__init__)
4878 0.017 0.000 0.481 0.000 free_module.py:3794(span)
5629 0.017 0.000 0.017 0.000 {hasattr}
9675 0.017 0.000 0.018 0.000 free_module.py:2371(zero_vector)
┌────────────────────────────────────────────────────────────────────┐