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diagram.py
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diagram.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
from sage.rings.integer import Integer
class Diagram():
r"""
A list of cells in the grid $\mathbb{N} \times \mathbb{N}$ :
$[(a_1, b_1), (a_2, b_2), ..., (a_n, b_n)]$.
EXAMPLES ::
sage: d = Diagram([(0,0),(3,0),(6,0)])
sage: d = Diagram([(0,0),(1,0),(2,0),(3,0),(0,1),(2,1)])
"""
def __init__(self, cells):
c = True
for cell in cells:
if len(cell) != 2:
c = False
self._cells = []
if c:
for cell in cells:
self._cells += [(cell[1],cell[0])]
self._cells.sort()
else:
print("Wrong format for class Diagram")
def size(self) :
"""
The size of the diagram, which is the number of cells.
OUTPUT: The number of cells of the diagram.
EXAMPLES:
sage: d = Diagram([(0,0),(3,0),(6,0)])
sage: d.size()
3
sage: d = Diagram([(0,0),(1,0),(2,0),(3,0),(0,1),(2,1)])
sage: d.size()
6
"""
return Integer(len(self._cells))
def cells(self):
"""
Gives the list of the matrix coordinates of the cells of the diagram.
OUTPUT: The list of the diagram's cells.
EXAMPLES ::
sage: d = Diagram([(0,0),(3,0),(6,0)])
sage: d.cells()
[(0, 0), (0, 3), (0, 6)]
sage: d = Diagram([(0,0),(1,0),(2,0),(3,0),(0,1),(2,1)])
sage: d.cells()
[(0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 2)]
"""
return self._cells
def nb_cols(self):
"""
Gives the number of columns of the diagram including the empty ones
that lie between unempty ones.
The number of columns thus corresponds to the greatest $a_i$.
OUTPUT: The number of columns of the diagram.
EXAMPLES ::
sage: d = Diagram([(0,0),(3,0),(6,0)])
sage: d.nb_cols()
6
sage: d = Diagram([(0,0),(1,0),(2,0),(3,0),(0,1),(2,1)])
sage: d.nb_cols()
3
"""
return max([c[1] for c in self.cells()])
def draw(self):
"""
Print the diagram.
EXAMPLES ::
sage: Diagram([(0,0),(1,1),(2,2)]).draw()
_
_|_|
_|_|
|_|
sage: Diagram([(0,0), (1,0), (2,0), (0,1), (2,1)]).draw()
_ _
|_|_|_|
|_|_|_|
sage: Diagram([(0,2),(1,1),(2,0)]).draw()
_
|_|_
|_|_
|_|
sage: Diagram([(0,0),(1,1)]).draw()
_
_|_|
|_|
sage: Diagram([(0,1),(1,0),(1,1)]).draw()
_ _
|_|_|
|_|
sage: Diagram([(0,1),(2,2)]).draw()
_
_ |_|
|_|
sage: Diagram([(0,1),(2,3)]).draw()
_
|_|
_
|_|
sage: Diagram([(0,1),(3,2),(3,3)]).draw()
_
|_|
_ |_|
|_|
sage: Diagram([(0,1),(3,2),(2,3)]).draw()
_
|_|_
_ |_|
|_|
"""
cells = self.cells()
max_a = max(a for a,b in cells)
max_b = max(b for a,b in cells)
diag_string = []
k = 0
for a in range(max_a, -2, -1):
string = ''
for b in range(max_b+1):
if a==-1 and ((0,b) in cells):
if (0,b+1) in cells :
string += '|_'
else:
string += '|_|'
elif a==max_a:
if ((a,b) in cells):
string += ' _'
else:
string += ' '
elif ((a,b) in cells):
if b==0 or (a+1,b-1) not in cells:
if (a+1,b) in cells:
if (a+1, b+1) in cells:
string += '|_'
else:
string += '|_|'
else:
string += ' _'
else:
if (a+1,b) in cells:
string += '|_|'
elif (a+1,b+1) in cells:
string += '_'
else :
string += '_ '
else:
if b==0 or (a+1,b-1) not in cells:
if (a+1,b) in cells:
if (a+1, b+1) not in cells:
string += '|_|'
else:
string += '|_'
else:
string += ' '
else:
if (a+1,b) in cells:
string += '|_|'
else:
string += ' '
print(string)