|
|
from sympy.core.sorting import ordered, default_sort_key |
|
|
from sympy.combinatorics.partitions import (Partition, IntegerPartition, |
|
|
RGS_enum, RGS_unrank, RGS_rank, |
|
|
random_integer_partition) |
|
|
from sympy.testing.pytest import raises |
|
|
from sympy.utilities.iterables import partitions |
|
|
from sympy.sets.sets import Set, FiniteSet |
|
|
|
|
|
|
|
|
def test_partition_constructor(): |
|
|
raises(ValueError, lambda: Partition([1, 1, 2])) |
|
|
raises(ValueError, lambda: Partition([1, 2, 3], [2, 3, 4])) |
|
|
raises(ValueError, lambda: Partition(1, 2, 3)) |
|
|
raises(ValueError, lambda: Partition(*list(range(3)))) |
|
|
|
|
|
assert Partition([1, 2, 3], [4, 5]) == Partition([4, 5], [1, 2, 3]) |
|
|
assert Partition({1, 2, 3}, {4, 5}) == Partition([1, 2, 3], [4, 5]) |
|
|
|
|
|
a = FiniteSet(1, 2, 3) |
|
|
b = FiniteSet(4, 5) |
|
|
assert Partition(a, b) == Partition([1, 2, 3], [4, 5]) |
|
|
assert Partition({a, b}) == Partition(FiniteSet(a, b)) |
|
|
assert Partition({a, b}) != Partition(a, b) |
|
|
|
|
|
def test_partition(): |
|
|
from sympy.abc import x |
|
|
|
|
|
a = Partition([1, 2, 3], [4]) |
|
|
b = Partition([1, 2], [3, 4]) |
|
|
c = Partition([x]) |
|
|
l = [a, b, c] |
|
|
l.sort(key=default_sort_key) |
|
|
assert l == [c, a, b] |
|
|
l.sort(key=lambda w: default_sort_key(w, order='rev-lex')) |
|
|
assert l == [c, a, b] |
|
|
|
|
|
assert (a == b) is False |
|
|
assert a <= b |
|
|
assert (a > b) is False |
|
|
assert a != b |
|
|
assert a < b |
|
|
|
|
|
assert (a + 2).partition == [[1, 2], [3, 4]] |
|
|
assert (b - 1).partition == [[1, 2, 4], [3]] |
|
|
|
|
|
assert (a - 1).partition == [[1, 2, 3, 4]] |
|
|
assert (a + 1).partition == [[1, 2, 4], [3]] |
|
|
assert (b + 1).partition == [[1, 2], [3], [4]] |
|
|
|
|
|
assert a.rank == 1 |
|
|
assert b.rank == 3 |
|
|
|
|
|
assert a.RGS == (0, 0, 0, 1) |
|
|
assert b.RGS == (0, 0, 1, 1) |
|
|
|
|
|
|
|
|
def test_integer_partition(): |
|
|
|
|
|
raises(ValueError, lambda: IntegerPartition(list(range(3)))) |
|
|
|
|
|
raises(ValueError, lambda: IntegerPartition(100, list(range(1, 3)))) |
|
|
a = IntegerPartition(8, [1, 3, 4]) |
|
|
b = a.next_lex() |
|
|
c = IntegerPartition([1, 3, 4]) |
|
|
d = IntegerPartition(8, {1: 3, 3: 1, 2: 1}) |
|
|
assert a == c |
|
|
assert a.integer == d.integer |
|
|
assert a.conjugate == [3, 2, 2, 1] |
|
|
assert (a == b) is False |
|
|
assert a <= b |
|
|
assert (a > b) is False |
|
|
assert a != b |
|
|
|
|
|
for i in range(1, 11): |
|
|
next = set() |
|
|
prev = set() |
|
|
a = IntegerPartition([i]) |
|
|
ans = {IntegerPartition(p) for p in partitions(i)} |
|
|
n = len(ans) |
|
|
for j in range(n): |
|
|
next.add(a) |
|
|
a = a.next_lex() |
|
|
IntegerPartition(i, a.partition) |
|
|
for j in range(n): |
|
|
prev.add(a) |
|
|
a = a.prev_lex() |
|
|
IntegerPartition(i, a.partition) |
|
|
assert next == ans |
|
|
assert prev == ans |
|
|
|
|
|
assert IntegerPartition([1, 2, 3]).as_ferrers() == '###\n##\n#' |
|
|
assert IntegerPartition([1, 1, 3]).as_ferrers('o') == 'ooo\no\no' |
|
|
assert str(IntegerPartition([1, 1, 3])) == '[3, 1, 1]' |
|
|
assert IntegerPartition([1, 1, 3]).partition == [3, 1, 1] |
|
|
|
|
|
raises(ValueError, lambda: random_integer_partition(-1)) |
|
|
assert random_integer_partition(1) == [1] |
|
|
assert random_integer_partition(10, seed=[1, 3, 2, 1, 5, 1] |
|
|
) == [5, 2, 1, 1, 1] |
|
|
|
|
|
|
|
|
def test_rgs(): |
|
|
raises(ValueError, lambda: RGS_unrank(-1, 3)) |
|
|
raises(ValueError, lambda: RGS_unrank(3, 0)) |
|
|
raises(ValueError, lambda: RGS_unrank(10, 1)) |
|
|
|
|
|
raises(ValueError, lambda: Partition.from_rgs(list(range(3)), list(range(2)))) |
|
|
raises(ValueError, lambda: Partition.from_rgs(list(range(1, 3)), list(range(2)))) |
|
|
assert RGS_enum(-1) == 0 |
|
|
assert RGS_enum(1) == 1 |
|
|
assert RGS_unrank(7, 5) == [0, 0, 1, 0, 2] |
|
|
assert RGS_unrank(23, 14) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2] |
|
|
assert RGS_rank(RGS_unrank(40, 100)) == 40 |
|
|
|
|
|
def test_ordered_partition_9608(): |
|
|
a = Partition([1, 2, 3], [4]) |
|
|
b = Partition([1, 2], [3, 4]) |
|
|
assert list(ordered([a,b], Set._infimum_key)) |
|
|
|
