def brackets_to_table(L):
r"""
Return a html table enumerating all Lie brackets.
INPUT:
- ``L`` -- a Lie algebra
"""
# if the base ring is QQbar, display coefficients as radicals
disp = QQbar.options('display_format')
QQbar.options(display_format="radical")
rows = []
for X, Y in combinations(L.basis(), 2):
Z = X.bracket(Y)
if Z:
rows.append((X, Y, Z))
if not rows:
return ""
htmlstr = '<table class="brackets">\n'
for (X, Y, Z) in rows:
htmlstr += '<tr>'
htmlstr += '<td class="brkt">[%s, %s]</td>' % (X, Y)
htmlstr += '<td class="eq">=</td>'
htmlstr += '<td class="res">%s</td>' % Z
htmlstr += '</tr>\n'
htmlstr += '</table>'
return htmlstr
def brackets_to_txt(L):
r"""
Return a text string enumerating all Lie brackets.
INPUT:
- ``L`` -- a Lie algebra
"""
# if the base ring is QQbar, display coefficients as radicals
disp = QQbar.options('display_format')
QQbar.options(display_format="radical")
bracketstr = ""
for X, Y in combinations(L.basis(), 2):
Z = X.bracket(Y)
if Z:
bracketstr += " [%s, %s] = %s\n" % (X, Y, Z)
QQbar.options(display_format=disp)
return bracketstr
def isom_class_to_html_tablerow(label, ic, mathjax):
r"""
Return a html table row describing a labelled isomorphism class of gradings.
INPUT:
- ``label`` -- a string identifier
- ``ic`` -- a :class:`GradingIsomorphismClass`
- ``mathjax`` -- a boolean; whether to output the table as mathjax or not
"""
# if the base ring is QQbar, display coefficients as radicals
disp = QQbar.options('display_format')
QQbar.options(display_format="radical")
indent = " " * 4
classname = "grading"
# test if stratification or positivisable
L = ic.representative().lie_algebra()
try:
st = stratification(L)
strat = True
except ValueError:
strat = False
if strat and st in ic:
classname += " stratification positive"
else:
if ic.representative().has_positive_realization():
classname += " positive"
else:
classname += " nonpositive"
tablerow = '<tr class="%s">\n' % classname
tablerow += indent + '<td class="label">%s</td>\n' % label
if mathjax:
icstr = "\\(%s\\)" % grading_to_array(ic.representative(), amp="&")
else:
icstr = grading_to_html_table(ic.representative())
tablerow += indent + '<td>%s</td>\n' % icstr
tablerow += "</tr>"
QQbar.options(display_format=disp)
return tablerow
def brackets_to_align(L, amp="&"):
r"""
Return a latex align* environment enumerating all Lie brackets.
INPUT:
- ``L`` -- a Lie algebra
- ``amp`` -- a string to use as the ampersand symbol in the output
"""
rows = []
for X, Y in combinations(L.basis(), 2):
Z = X.bracket(Y)
if Z:
row = "[%s, %s] %s = %s" % (latex(X), latex(Y), amp, latex(Z))
rows.append(row)
if not rows:
return ""
latexstr = "\\begin{align*}\n"
latexstr += "\\\\\n".join(rows)
latexstr += "\\end{align*}"
QQbar.options(display_format=disp)
return latexstr
