def simplify_expr(expr):
"""
Return a simplified version of the expression.
"""
tree = AST.strip_parse(expr)
simplify_ast = _simplify_ast(tree)
return AST.ast2str(simplify_ast)
def extract_comps(expr):
"""
Extract all comparisons from the expression.
"""
comps_found = []
_extract_comps_ast(AST.strip_parse(expr), comps_found)
comps_found = [AST.ast2str(ast) for ast in comps_found]
return set(comps_found)
def extract_funcs(expr):
"""
Return a Set of the functions used in an expression.
The elements of the Set are ('function_name', #arguments).
"""
funcs_found = []
_extract_funcs_ast(AST.strip_parse(expr), funcs_found)
return set(funcs_found)
def expr2TeX(expr, name_dict={}):
"""
Return a TeX version of a python math expression.
name_dict: A dictionary mapping variable names used in the expression to
preferred TeX expressions.
"""
ast = AST.strip_parse(expr)
return _ast2TeX(ast, name_dict=name_dict)
def extract_vars(expr):
"""
Return a Set of the variables used in an expression.
"""
try:
return extract_vars_cache[expr]
except KeyError:
vars_found = []
_extract_vars_ast(AST.strip_parse(expr), vars_found)
vars_found = [AST.ast2str(ast) for ast in vars_found]
result = set(vars_found)
extract_vars_cache[expr] = result
return result
def diff_expr(expr, wrt):
"""
Return the derivative of the expression with respect to a given variable.
"""
logger.debug('Taking derivative of %s wrt %s' % (expr, wrt))
key = '%s__derivWRT__%s' % (expr, wrt)
if key in __deriv_saved:
deriv = __deriv_saved[key]
logger.debug('Found saved result %s.' % deriv)
return deriv
ast = AST.strip_parse(expr)
deriv = _diff_ast(ast, wrt)
deriv = Simplify._simplify_ast(deriv)
deriv = AST.ast2str(deriv)
__deriv_saved[key] = deriv
logger.debug('Computed result %s.' % deriv)
return deriv
def dict2TeX(d, name_dict, lhs_form='%s', split_terms=False, simpleTeX=False):
lines = []
for lhs, rhs in list(d.items()):
if split_terms:
ast = AST.strip_parse(rhs)
pos, neg = [], []
AST._collect_pos_neg(ast, pos, neg)
try:
lhsTeX = lhs_form % expr2TeX(lhs, name_dict=name_dict)
except TypeError:
lhsTeX = lhs_form
rhsTeX = _ast2TeX(pos[0], name_dict=name_dict)
lines.append(r'$ %s $ &=& $ %s $\\' % (lhsTeX, rhsTeX))
for term in pos[1:]:
TeXed = _ast2TeX(term, name_dict=name_dict)
lines.append(r' & & $ + \, %s $\\' % TeXed)
for term in neg:
TeXed = _ast2TeX(term, name_dict=name_dict)
lines.append(r' & & $ - \, %s $\\' % TeXed)
else:
lhsTeX = lhs_form % expr2TeX(lhs, name_dict=name_dict)
rhsTeX = expr2TeX(rhs, name_dict=name_dict)
lines.append(r'$ %s $ & = & $ %s $\\' % (lhsTeX, rhsTeX))
if not simpleTeX:
# Force a space between TeX'd entries
lines[-1] = '%s[5mm]' % lines[-1]
all = os.linesep.join(lines)
if not simpleTeX:
all = all.replace(r'\frac{', r'\tabfrac{')
# This makes the fractions look much nicer in the tabular output. See
# http://www.texnik.de/table/table.phtml#fractions
lines = [
r'\providecommand{\tabfrac}[2]{%',
r' \setlength{\fboxrule}{0pt}%', r' \fbox{$\frac{#1}{#2}$}}',
r'\begin{longtable}{lll}'
] + [all] + [r'\end{longtable}']
all = os.linesep.join(lines)
return all
