def _eval_(self, x):
"""
EXAMPLES::
sage: arg(3+i)
arctan(1/3)
sage: arg(-1+i)
3/4*pi
sage: arg(2+2*i)
1/4*pi
sage: arg(2+x)
arg(x + 2)
sage: arg(2.0+i+x)
arg(x + 2.00000000000000 + 1.00000000000000*I)
sage: arg(-3)
pi
sage: arg(3)
0
sage: arg(0)
0
sage: arg(sqrt(2)+i)
arg(sqrt(2) + I)
"""
if not isinstance(x,Expression):
# x contains no variables
if is_inexact(x):
# inexact complex numbers, e.g. 2.0+i
return self._evalf_(x, parent(x))
else:
# exact complex numbers, e.g. 2+i
return arctan2(imag_part(x),real_part(x))
else:
# x contains variables, e.g. 2+i+y or 2.0+i+y
# or x involves an expression such as sqrt(2)
return None
def _eval_(self, x):
"""
EXAMPLES::
sage: arg(3+i)
arctan(1/3)
sage: arg(-1+i)
3/4*pi
sage: arg(2+2*i)
1/4*pi
sage: arg(2+x)
arg(x + 2)
sage: arg(2.0+i+x)
arg(x + 2.00000000000000 + 1.00000000000000*I)
sage: arg(-3)
pi
sage: arg(3)
0
sage: arg(0)
0
sage: arg(sqrt(2)+i)
arg(sqrt(2) + I)
"""
if not isinstance(x, Expression):
# x contains no variables
if is_inexact(x):
# inexact complex numbers, e.g. 2.0+i
return self._evalf_(x, parent(x))
else:
# exact complex numbers, e.g. 2+i
return arctan2(imag_part(x), real_part(x))
else:
# x contains variables, e.g. 2+i+y or 2.0+i+y
# or x involves an expression such as sqrt(2)
return None
def _latex_(self):
r"""
Return a TikZ representation of the hypergraph.
EXAMPLES::
sage: H = Hypergraph([{1,2,3},{2,3,4},{3,4,5},{4,5,6}]); H
Hypergraph on 6 vertices containing 4 sets
sage: view(H) # not tested
With sets of size 4::
sage: g = graphs.Grid2dGraph(5,5)
sage: C4 = graphs.CycleGraph(4)
sage: sets = Set(map(Set,list(g.subgraph_search_iterator(C4))))
sage: H = Hypergraph(sets)
sage: view(H) # not tested
"""
from sage.rings.integer import Integer
from sage.functions.trig import arctan2
from sage.misc.misc import warn
warn("\nThe hypergraph is drawn as a set of closed curves. The curve "
"representing a set S go **THROUGH** the vertices contained "
"in S.\n A vertex which is encircled by a curve but is not located "
"on its boundary is **NOT** included in the corresponding set.\n"
"\n"
"The colors are picked for readability and have no other meaning.")
latex.add_package_to_preamble_if_available("tikz")
if not latex.has_file("tikz.sty"):
raise RuntimeError("You must have TikZ installed in order "
"to draw a hypergraph.")
domain = self.domain()
pos = self._spring_layout()
tex = "\\begin{tikzpicture}[scale=3]\n"
colors = ["black", "red", "green", "blue", "cyan", "magenta", "yellow","pink","brown"]
colored_sets = [(s,i) for i,S in enumerate(self.edge_coloring()) for s in S]
# Prints each set with its color
for s,i in colored_sets:
current_color = colors[i%len(colors)]
if len(s) == 2:
s = list(s)
tex += ("\\draw[color="+str(current_color)+","+
"line width=.1cm,opacity = .6] "+
str(pos[s[0]])+" -- "+str(pos[s[1]])+";\n")
continue
tex += ("\\draw[color="+str(current_color)+","
"line width=.1cm,opacity = .6,"
"line cap=round,"
"line join=round]"
"plot [smooth cycle,tension=1] coordinates {")
# Reorders the vertices of s according to their angle with the
# "center", i.e. the vertex representing the set s
cx,cy = pos[s]
s = map(lambda x:pos[x],s)
s = sorted(s, key = lambda (x,y) : arctan2(x-cx,y-cy))
for x in s:
tex += str(x)+" "
tex += "};\n"
# Prints each vertex
for v in domain:
tex += "\\draw node[fill,circle,scale=.5,label={90:$"+latex(v)+"$}] at "+str(pos[v])+" {};\n"
tex += "\\end{tikzpicture}"
return tex
def _latex_(self):
r"""
Return a TikZ representation of the hypergraph.
EXAMPLES::
sage: H = Hypergraph([{1,2,3},{2,3,4},{3,4,5},{4,5,6}]); H
Hypergraph on 6 vertices containing 4 sets
sage: view(H) # not tested
With sets of size 4::
sage: g = graphs.Grid2dGraph(5,5)
sage: C4 = graphs.CycleGraph(4)
sage: sets = Set(map(Set,list(g.subgraph_search_iterator(C4))))
sage: H = Hypergraph(sets)
sage: view(H) # not tested
"""
from sage.rings.integer import Integer
from sage.functions.trig import arctan2
from sage.misc.misc import warn
warn(
"\nThe hypergraph is drawn as a set of closed curves. The curve "
"representing a set S go **THROUGH** the vertices contained "
"in S.\n A vertex which is encircled by a curve but is not located "
"on its boundary is **NOT** included in the corresponding set.\n"
"\n"
"The colors are picked for readability and have no other meaning.")
latex.add_package_to_preamble_if_available("tikz")
if not latex.has_file("tikz.sty"):
raise RuntimeError("You must have TikZ installed in order "
"to draw a hypergraph.")
domain = self.domain()
pos = self._spring_layout()
tex = "\\begin{tikzpicture}[scale=3]\n"
colors = [
"black", "red", "green", "blue", "cyan", "magenta", "yellow",
"pink", "brown"
]
colored_sets = [(s, i) for i, S in enumerate(self.edge_coloring())
for s in S]
# Prints each set with its color
for s, i in colored_sets:
current_color = colors[i % len(colors)]
if len(s) == 2:
s = list(s)
tex += ("\\draw[color=" + str(current_color) + "," +
"line width=.1cm,opacity = .6] " + str(pos[s[0]]) +
" -- " + str(pos[s[1]]) + ";\n")
continue
tex += ("\\draw[color=" + str(current_color) + ","
"line width=.1cm,opacity = .6,"
"line cap=round,"
"line join=round]"
"plot [smooth cycle,tension=1] coordinates {")
# Reorders the vertices of s according to their angle with the
# "center", i.e. the vertex representing the set s
cx, cy = pos[s]
s = map(lambda x: pos[x], s)
s = sorted(s, key=lambda (x, y): arctan2(x - cx, y - cy))
for x in s:
tex += str(x) + " "
tex += "};\n"
# Prints each vertex
for v in domain:
tex += "\\draw node[fill,circle,scale=.5,label={90:$" + latex(
v) + "$}] at " + str(pos[v]) + " {};\n"
tex += "\\end{tikzpicture}"
return tex
