Source code for sympy.printing.pretty.pretty

from sympy.core import S, C, Basic, Interval
from sympy.core.function import _coeff_isneg
from sympy.utilities import group
from sympy.utilities.iterables import has_variety
from sympy.core.sympify import SympifyError

from sympy.printing.printer import Printer
from sympy.printing.str import sstr

from .stringpict import prettyForm, stringPict
from .pretty_symbology import xstr, hobj, vobj, xobj, xsym, pretty_symbol,\
        pretty_atom, pretty_use_unicode, pretty_try_use_unicode, greek, U, \
        annotated

from sympy.utilities import default_sort_key

# rename for usage from outside
pprint_use_unicode = pretty_use_unicode
pprint_try_use_unicode = pretty_try_use_unicode

[docs]class PrettyPrinter(Printer): """Printer, which converts an expression into 2D ASCII-art figure.""" printmethod = "_pretty" _default_settings = { "order": None, "full_prec": "auto", "use_unicode": None, "wrap_line": True, "num_columns": None, } def __init__(self, settings=None): Printer.__init__(self, settings) self.emptyPrinter = lambda x: prettyForm(xstr(x)) @property def _use_unicode(self): if self._settings['use_unicode']: return True else: return pretty_use_unicode() def doprint(self, expr): return self._print(expr).render(**self._settings) # empty op so _print(stringPict) returns the same def _print_stringPict(self, e): return e def _print_basestring(self, e): return prettyForm(e) def _print_atan2(self, e): pform = prettyForm(*self._print_seq(e.args).parens()) pform = prettyForm(*pform.left('atan2')) return pform def _print_Symbol(self, e): symb = pretty_symbol(e.name) return prettyForm(symb) def _print_Float(self, e): # we will use StrPrinter's Float printer, but we need to handle the # full_prec ourselves, according to the self._print_level full_prec = self._settings["full_prec"] if full_prec == "auto": full_prec = self._print_level == 1 return prettyForm(sstr(e, full_prec=full_prec)) def _print_Atom(self, e): try: # print atoms like Exp1 or Pi return prettyForm(pretty_atom(e.__class__.__name__)) except KeyError: return self.emptyPrinter(e) # Infinity inherits from Number, so we have to override _print_XXX order _print_Infinity = _print_Atom _print_NegativeInfinity = _print_Atom _print_EmptySet = _print_Atom _print_Naturals = _print_Atom _print_Integers = _print_Atom _print_Reals = _print_Atom def _print_factorial(self, e): x = e.args[0] pform = self._print(x) # Add parentheses if needed if not ((x.is_Integer and x.is_nonnegative) or x.is_Symbol): pform = prettyForm(*pform.parens()) pform = prettyForm(*pform.right('!')) return pform def _print_factorial2(self, e): x = e.args[0] pform = self._print(x) # Add parentheses if needed if not ((x.is_Integer and x.is_nonnegative) or x.is_Symbol): pform = prettyForm(*pform.parens()) pform = prettyForm(*pform.right('!!')) return pform def _print_binomial(self, e): n, k = e.args n_pform = self._print(n) k_pform = self._print(k) bar = ' '*max(n_pform.width(), k_pform.width()) pform = prettyForm(*k_pform.above(bar)) pform = prettyForm(*pform.above(n_pform)) pform = prettyForm(*pform.parens('(', ')')) pform.baseline = (pform.baseline + 1)//2 return pform def _print_Relational(self, e): op = prettyForm(' ' + xsym(e.rel_op) + ' ') l = self._print(e.lhs) r = self._print(e.rhs) pform = prettyForm(*stringPict.next(l, op, r)) return pform def _print_Not(self, e): if self._use_unicode: arg = e.args[0] pform = self._print(arg) if arg.is_Boolean and not arg.is_Not: pform = prettyForm(*pform.parens()) return prettyForm(*pform.left("\u00ac ")) else: return self._print_Function(e) def __print_Boolean(self, e, char, sort=True): args = e.args if sort: args = sorted(e.args, key=default_sort_key) arg = args[0] pform = self._print(arg) if arg.is_Boolean and not arg.is_Not: pform = prettyForm(*pform.parens()) for arg in args[1:]: pform_arg = self._print(arg) if arg.is_Boolean and not arg.is_Not: pform_arg = prettyForm(*pform_arg.parens()) pform = prettyForm(*pform.right(' %s ' % char)) pform = prettyForm(*pform.right(pform_arg)) return pform def _print_And(self, e): if self._use_unicode: return self.__print_Boolean(e, "\u2227") else: return self._print_Function(e, sort=True) def _print_Or(self, e): if self._use_unicode: return self.__print_Boolean(e, "\u2228") else: return self._print_Function(e, sort=True) def _print_Xor(self, e): if self._use_unicode: return self.__print_Boolean(e, "\u22bb") else: return self._print_Function(e, sort=True) def _print_Nand(self, e): if self._use_unicode: return self.__print_Boolean(e, "\u22bc") else: return self._print_Function(e, sort=True) def _print_Nor(self, e): if self._use_unicode: return self.__print_Boolean(e, "\u22bd") else: return self._print_Function(e, sort=True) def _print_Implies(self, e): if self._use_unicode: return self.__print_Boolean(e, "\u2192", sort=False) else: return self._print_Function(e) def _print_Equivalent(self, e): if self._use_unicode: return self.__print_Boolean(e, "\u2261") else: return self._print_Function(e, sort=True) def _print_conjugate(self, e): pform = self._print(e.args[0]) return prettyForm( *pform.above( hobj('_',pform.width())) ) def _print_Abs(self, e): pform = self._print(e.args[0]) pform = prettyForm(*pform.parens('|', '|')) return pform def _print_floor(self, e): if self._use_unicode: pform = self._print(e.args[0]) pform = prettyForm(*pform.parens('lfloor', 'rfloor')) return pform else: return self._print_Function(e) def _print_ceiling(self, e): if self._use_unicode: pform = self._print(e.args[0]) pform = prettyForm(*pform.parens('lceil', 'rceil')) return pform else: return self._print_Function(e) def _print_Derivative(self, deriv): # XXX use U('PARTIAL DIFFERENTIAL') here ? syms = list(reversed(deriv.variables)) x = None for sym, num in group(syms, multiple=False): s = self._print(sym) ds = prettyForm(*s.left('d')) if num > 1: ds = ds**prettyForm(str(num)) if x is None: x = ds else: x = prettyForm(*x.right(' ')) x = prettyForm(*x.right(ds)) f = prettyForm(binding=prettyForm.FUNC, *self._print(deriv.expr).parens()) pform = prettyForm('d') if len(syms) > 1: pform = pform**prettyForm(str(len(syms))) pform = prettyForm(*pform.below(stringPict.LINE, x)) pform.baseline = pform.baseline + 1 pform = prettyForm(*stringPict.next(pform, f)) return pform def _print_Cycle(self, dc): from sympy.combinatorics.permutations import Permutation return self._print_tuple(Permutation(dc.as_list()).cyclic_form) def _print_PDF(self, pdf): lim = self._print(pdf.pdf.args[0]) lim = prettyForm(*lim.right(', ')) lim = prettyForm(*lim.right(self._print(pdf.domain[0]))) lim = prettyForm(*lim.right(', ')) lim = prettyForm(*lim.right(self._print(pdf.domain[1]))) lim = prettyForm(*lim.parens()) f = self._print(pdf.pdf.args[1]) f = prettyForm(*f.right(', ')) f = prettyForm(*f.right(lim)) f = prettyForm(*f.parens()) pform = prettyForm('PDF') pform = prettyForm(*pform.right(f)) return pform def _print_Integral(self, integral): f = integral.function # Add parentheses if arg involves addition of terms and # create a pretty form for the argument prettyF = self._print(f) # XXX generalize parens if f.is_Add: prettyF = prettyForm(*prettyF.parens()) # dx dy dz ... arg = prettyF for x in integral.limits: prettyArg = self._print(x[0]) # XXX qparens (parens if needs-parens) if prettyArg.width() > 1: prettyArg = prettyForm(*prettyArg.parens()) arg = prettyForm(*arg.right(' d', prettyArg)) # \int \int \int ... firstterm = True s = None for lim in integral.limits: x = lim[0] # Create bar based on the height of the argument h = arg.height() H = h+2 # XXX hack! ascii_mode = not self._use_unicode if ascii_mode: H += 2 vint= vobj('int', H) # Construct the pretty form with the integral sign and the argument pform = prettyForm(vint) #pform.baseline = pform.height()//2 # vcenter pform.baseline = arg.baseline + (H-h)//2 # covering the whole argument if len(lim) > 1: # Create pretty forms for endpoints, if definite integral. # Do not print empty endpoints. if len(lim) == 2: prettyA = prettyForm("") prettyB = self._print(lim[1]) if len(lim) == 3: prettyA = self._print(lim[1]) prettyB = self._print(lim[2]) if ascii_mode: # XXX hack # Add spacing so that endpoint can more easily be # identified with the correct integral sign spc = max(1, 3 - prettyB.width()) prettyB = prettyForm(*prettyB.left(' ' * spc)) spc = max(1, 4 - prettyA.width()) prettyA = prettyForm(*prettyA.right(' ' * spc)) pform = prettyForm(*pform.above(prettyB)) pform = prettyForm(*pform.below(prettyA)) #if ascii_mode: # XXX hack # # too much vspace beetween \int and argument # # but I left it as is # pform = prettyForm(*pform.right(' ')) if not ascii_mode: # XXX hack pform = prettyForm(*pform.right(' ')) if firstterm: s = pform # first term firstterm = False else: s = prettyForm(*s.left(pform)) pform = prettyForm(*arg.left(s)) return pform def _print_Product(self, expr): func = expr.term pretty_func = self._print(func) horizontal_chr = xobj('_', 1) corner_chr = xobj('_', 1) vertical_chr = xobj('|', 1) if self._use_unicode: # use unicode corners horizontal_chr = xobj('-', 1) corner_chr = '\u252c' func_height = pretty_func.height() first = True max_upper = 0 sign_height = 0 for lim in expr.limits: width = (func_height + 2) * 5 // 3 - 2 sign_lines = [] sign_lines.append(corner_chr+(horizontal_chr*width)+corner_chr) for i in range(func_height+1): sign_lines.append(vertical_chr+(' '*width)+vertical_chr) pretty_sign = stringPict('') pretty_sign = prettyForm(*pretty_sign.stack(*sign_lines)) pretty_upper = self._print(lim[2]) pretty_lower = self._print(C.Equality(lim[0], lim[1])) max_upper = max(max_upper, pretty_upper.height()) if first: sign_height = pretty_sign.height() pretty_sign = prettyForm(*pretty_sign.above(pretty_upper)) pretty_sign = prettyForm(*pretty_sign.below(pretty_lower)) if first: pretty_func.baseline = 0 first = False height = pretty_sign.height() padding = stringPict('') padding = prettyForm(*padding.stack(*[' ']*(height-1))) pretty_sign = prettyForm(*pretty_sign.right(padding)) pretty_func = prettyForm(*pretty_sign.right(pretty_func)) #pretty_func.baseline = 0 pretty_func.baseline = max_upper + sign_height//2 return pretty_func def _print_Sum(self, expr): ascii_mode = not self._use_unicode def asum(hrequired, lower, upper, use_ascii): def adjust(s, wid=None, how='<^>'): if not wid or len(s)>wid: return s need = wid - len(s) if how == '<^>' or how == "<" or how not in list('<^>'): return s + ' '*need half = need//2 lead = ' '*half if how == ">": return " "*need + s return lead + s + ' '*(need - len(lead)) h = max(hrequired, 2) d = h//2 wrequired = max(lower, upper) w = d + 1 more = hrequired % 2 lines = [] if use_ascii: lines.append("_"*(w) + ' ') lines.append("\%s`" % (' '*(w - 1))) for i in range(1, d): lines.append('%s\\%s' % (' '*i, ' '*(w - i))) if more: lines.append('%s)%s' % (' '*(d), ' '*(w - d))) for i in reversed(list(range(1, d))): lines.append('%s/%s' % (' '*i, ' '*(w - i))) lines.append("/" + "_"*(w - 1) + ',') return d, h + more, lines, 0 else: w = w + more d = d + more vsum = vobj('sum', 4) lines.append("_"*(w)) for i in range(0, d): lines.append('%s%s%s' % (' '*i, vsum[2], ' '*(w - i - 1))) for i in reversed(list(range(0, d))): lines.append('%s%s%s' % (' '*i, vsum[4], ' '*(w - i - 1))) lines.append(vsum[8]*(w)) return d, h + 2*more, lines, more f = expr.function prettyF = self._print(f) if f.is_Add: # add parens prettyF = prettyForm(*prettyF.parens()) H = prettyF.height() + 2 # \sum \sum \sum ... first = True max_upper = 0 sign_height = 0 for lim in expr.limits: if len(lim) == 3: prettyUpper = self._print(lim[2]) prettyLower = self._print(C.Equality(lim[0], lim[1])) elif len(lim) == 2: prettyUpper = self._print("") prettyLower = self._print(C.Equality(lim[0], lim[1])) elif len(lim) == 1: prettyUpper = self._print("") prettyLower = self._print(lim[0]) max_upper = max(max_upper, prettyUpper.height()) # Create sum sign based on the height of the argument d, h, slines, adjustment = asum(H, prettyLower.width(), prettyUpper.width(), ascii_mode) prettySign = stringPict('') prettySign = prettyForm(*prettySign.stack(*slines)) if first: sign_height = prettySign.height() prettySign = prettyForm(*prettySign.above(prettyUpper)) prettySign = prettyForm(*prettySign.below(prettyLower)) if first: # change F baseline so it centers on the sign prettyF.baseline -= d - (prettyF.height()//2 - prettyF.baseline) - adjustment first = False # put padding to the right pad = stringPict('') pad = prettyForm(*pad.stack(*[' ']*h)) prettySign = prettyForm(*prettySign.right(pad)) # put the present prettyF to the right prettyF = prettyForm(*prettySign.right(prettyF)) prettyF.baseline = max_upper + sign_height//2 return prettyF def _print_Limit(self, l): # XXX we do not print dir ... e, z, z0, dir = l.args E = self._print(e) Lim = prettyForm('lim') LimArg = self._print(z) LimArg = prettyForm(*LimArg.right('->')) LimArg = prettyForm(*LimArg.right(self._print(z0))) Lim = prettyForm(*Lim.below(LimArg)) Lim = prettyForm(*Lim.right(E)) return Lim def _print_matrix_contents(self, e): """ This method factors out what is essentially grid printing. """ M = e # matrix Ms = {} # i,j -> pretty(M[i,j]) for i in range(M.rows): for j in range(M.cols): Ms[i,j] = self._print(M[i,j]) # h- and v- spacers hsep = 2 vsep = 1 # max width for columns maxw = [-1] * M.cols for j in range(M.cols): maxw[j] = max([Ms[i,j].width() for i in range(M.rows)] or [0]) # drawing result D = None for i in range(M.rows): D_row = None for j in range(M.cols): s = Ms[i,j] # reshape s to maxw # XXX this should be generalized, and go to stringPict.reshape ? assert s.width() <= maxw[j] # hcenter it, +0.5 to the right 2 # ( it's better to align formula starts for say 0 and r ) # XXX this is not good in all cases -- maybe introduce vbaseline? wdelta = maxw[j] - s.width() wleft = wdelta // 2 wright = wdelta - wleft s = prettyForm(*s.right(' '*wright)) s = prettyForm(*s.left (' '*wleft)) # we don't need vcenter cells -- this is automatically done in # a pretty way because when their baselines are taking into # account in .right() if D_row is None: D_row = s # first box in a row continue D_row = prettyForm(*D_row.right(' '*hsep)) # h-spacer D_row = prettyForm(*D_row.right(s)) if D is None: D = D_row # first row in a picture continue # v-spacer for _ in range(vsep): D = prettyForm(*D.below(' ')) D = prettyForm(*D.below(D_row)) if D is None: D = prettyForm('') # Empty Matrix return D def _print_MatrixBase(self, e): D = self._print_matrix_contents(e) D = prettyForm(*D.parens('[',']')) return D _print_ImmutableMatrix = _print_MatrixBase _print_MutableMatrix = _print_MatrixBase def _print_Transpose(self, T): pform = self._print(T.arg) if (T.arg.is_Add or T.arg.is_Mul or T.arg.is_Pow): pform = prettyForm(*pform.parens()) pform = prettyForm(*pform.right("'")) return pform def _print_Inverse(self, I): pform = self._print(I.arg) if (I.arg.is_Add or I.arg.is_Mul or I.arg.is_Pow): pform = prettyForm(*pform.parens()) pform = prettyForm(*pform.right("^-1")) return pform def _print_BlockMatrix(self, B): if B.mat.shape == (1,1): return self._print(B.mat[0,0]) return self._print(B.mat) def _print_MatMul(self, expr): a = list(expr.args) for i in range(0, len(a)): if a[i].is_Add and len(a) > 1: a[i] = prettyForm(*self._print(a[i]).parens()) else: a[i] = self._print(a[i]) return prettyForm.__mul__(*a) def _print_MatAdd(self, expr): return self._print_seq(expr.args, None, None, ' + ') def _print_FunctionMatrix(self, X): D = self._print(X.lamda.expr) D = prettyForm(*D.parens('[',']')) return D def _print_Piecewise(self, pexpr): P = {} for n, ec in enumerate(pexpr.args): P[n,0] = self._print(ec.expr) if ec.cond == True: P[n,1] = prettyForm('otherwise') else: P[n,1] = prettyForm(*prettyForm('for ').right(self._print(ec.cond))) hsep = 2 vsep = 1 len_args = len(pexpr.args) # max widths maxw = [max([P[i,j].width() for i in range(len_args)]) \ for j in range(2)] # FIXME: Refactor this code and matrix into some tabular environment. # drawing result D = None for i in range(len_args): D_row = None for j in range(2): p = P[i,j] assert p.width() <= maxw[j] wdelta = maxw[j] - p.width() wleft = wdelta // 2 wright = wdelta - wleft p = prettyForm(*p.right(' '*wright)) p = prettyForm(*p.left (' '*wleft)) if D_row is None: D_row = p continue D_row = prettyForm(*D_row.right(' '*hsep)) # h-spacer D_row = prettyForm(*D_row.right(p)) if D is None: D = D_row # first row in a picture continue # v-spacer for _ in range(vsep): D = prettyForm(*D.below(' ')) D = prettyForm(*D.below(D_row)) D = prettyForm(*D.parens('{','')) return D def _hprint_vec(self, v): D = None for a in v: p = a if D is None: D = p else: D = prettyForm(*D.right(', ')) D = prettyForm(*D.right(p)) if D is None: D = stringPict(' ') return D def _hprint_vseparator(self, p1, p2): tmp = prettyForm(*p1.right(p2)) sep = stringPict(vobj('|', tmp.height()), baseline=tmp.baseline) return prettyForm(*p1.right(sep, p2)) def _print_hyper(self, e): # FIXME refactor Matrix, Piecewise, and this into a tabular environment ap = [self._print(a) for a in e.ap] bq = [self._print(b) for b in e.bq] P = self._print(e.argument) P.baseline = P.height()//2 # Drawing result - first create the ap, bq vectors D = None for v in [ap, bq]: D_row = self._hprint_vec(v) if D is None: D = D_row # first row in a picture else: D = prettyForm(*D.below(' ')) D = prettyForm(*D.below(D_row)) # make sure that the argument `z' is centred vertically D.baseline = D.height()//2 # insert horizontal separator P = prettyForm(*P.left(' ')) D = prettyForm(*D.right(' ')) # insert separating `|` D = self._hprint_vseparator(D, P) # add parens D = prettyForm(*D.parens('(', ')')) # create the F symbol above = D.height()//2 - 1 below = D.height() - above - 1 if self._use_unicode: pic = (2, 0, 2, '\u250c\u2500\n\u251c\u2500\n\u2575') else: pic = (3, 0, 3, ' _\n|_\n|\n') sz, t, b, add, img = annotated('F') F = prettyForm('\n' * (above - t) + img + '\n' * (below - b), baseline = above + sz) add = (sz+1)//2 F = prettyForm(*F.left(self._print(len(e.ap)))) F = prettyForm(*F.right(self._print(len(e.bq)))) F.baseline = above + add D = prettyForm(*F.right(' ', D)) return D def _print_meijerg(self, e): # FIXME refactor Matrix, Piecewise, and this into a tabular environment v = {} v[(0, 0)] = [self._print(a) for a in e.an] v[(0, 1)] = [self._print(a) for a in e.aother] v[(1, 0)] = [self._print(b) for b in e.bm] v[(1, 1)] = [self._print(b) for b in e.bother] P = self._print(e.argument) P.baseline = P.height()//2 vp = {} for idx in v: vp[idx] = self._hprint_vec(v[idx]) for i in range(2): maxw = max(vp[(0, i)].width(), vp[(1, i)].width()) for j in range(2): s = vp[(j, i)] left = (maxw - s.width()) // 2 right = maxw - left - s.width() s = prettyForm(*s.left(' ' * left)) s = prettyForm(*s.right(' ' * right)) vp[(j, i)] = s D1 = prettyForm(*vp[(0, 0)].right(' ', vp[(0, 1)])) D1 = prettyForm(*D1.below(' ')) D2 = prettyForm(*vp[(1, 0)].right(' ', vp[(1, 1)])) D = prettyForm(*D1.below(D2)) # make sure that the argument `z' is centred vertically D.baseline = D.height()//2 # insert horizontal separator P = prettyForm(*P.left(' ')) D = prettyForm(*D.right(' ')) # insert separating `|` D = self._hprint_vseparator(D, P) # add parens D = prettyForm(*D.parens('(', ')')) # create the G symbol above = D.height()//2 - 1 below = D.height() - above - 1 sz, t, b, add, img = annotated('G') F = prettyForm('\n' * (above - t) + img + '\n' * (below - b), baseline = above + sz) pp = self._print(len(e.ap)) pq = self._print(len(e.bq)) pm = self._print(len(e.bm)) pn = self._print(len(e.an)) def adjust(p1, p2): diff = p1.width() - p2.width() if diff == 0: return p1, p2 elif diff > 0: return p1, prettyForm(*p2.left(' '*diff)) else: return prettyForm(*p1.left(' '*-diff)), p2 pp, pm = adjust(pp, pm) pq, pn = adjust(pq, pn) pu = prettyForm(*pm.right(', ', pn)) pl = prettyForm(*pp.right(', ', pq)) ht = F.baseline - above - 2 if ht > 0: pu = prettyForm(*pu.below('\n'*ht)) p = prettyForm(*pu.below(pl)) F.baseline = above F = prettyForm(*F.right(p)) F.baseline = above + add D = prettyForm(*F.right(' ', D)) return D def _print_ExpBase(self, e): # TODO should exp_polar be printed differently? # what about exp_polar(0), exp_polar(1)? base = prettyForm(pretty_atom('Exp1', 'e')) return base ** self._print(e.args[0]) def _print_Function(self, e, sort=False): # XXX works only for applied functions func = e.func args = e.args if sort: args = sorted(args, key=default_sort_key) n = len(args) func_name = func.__name__ prettyFunc = self._print(C.Symbol(func_name)) prettyArgs = prettyForm(*self._print_seq(args).parens()) pform = prettyForm(binding=prettyForm.FUNC, *stringPict.next(prettyFunc, prettyArgs)) # store pform parts so it can be reassembled e.g. when powered pform.prettyFunc = prettyFunc pform.prettyArgs = prettyArgs return pform def _print_GeometryEntity(self, expr): # GeometryEntity is based on Tuple but should not print like a Tuple return self.emptyPrinter(expr) def _print_Lambda(self, e): symbols, expr = e.args if len(symbols) == 1: symbols = self._print(symbols[0]) else: symbols = self._print(tuple(symbols)) args = (symbols, self._print(expr)) prettyFunc = self._print(C.Symbol("Lambda")) prettyArgs = prettyForm(*self._print_seq(args).parens()) pform = prettyForm(binding=prettyForm.FUNC, *stringPict.next(prettyFunc, prettyArgs)) # store pform parts so it can be reassembled e.g. when powered pform.prettyFunc = prettyFunc pform.prettyArgs = prettyArgs return pform def _print_Order(self, e): pform = self._print(e.expr) pform = prettyForm(*pform.parens()) pform = prettyForm(*pform.left('O')) return pform def _print_gamma(self, e): if self._use_unicode: pform = self._print(e.args[0]) pform = prettyForm(*pform.parens()) pform = prettyForm(*pform.left(greek['gamma'][1])) return pform else: return self._print_Function(e) def _print_uppergamma(self, e): if self._use_unicode: pform = self._print(e.args[0]) pform = prettyForm(*pform.right(', ', self._print(e.args[1]))) pform = prettyForm(*pform.parens()) pform = prettyForm(*pform.left(greek['gamma'][1])) return pform else: return self._print_Function(e) def _print_lowergamma(self, e): if self._use_unicode: pform = self._print(e.args[0]) pform = prettyForm(*pform.right(', ', self._print(e.args[1]))) pform = prettyForm(*pform.parens()) pform = prettyForm(*pform.left(greek['gamma'][0])) return pform else: return self._print_Function(e) def _print_expint(self, e): from sympy import Function if e.args[0].is_Integer and self._use_unicode: return self._print_Function(Function('E_%s' % e.args[0])(e.args[1])) return self._print_Function(e) def _print_Chi(self, e): # This needs a special case since otherwise it comes out as greek # letter chi... prettyFunc = prettyForm("Chi") prettyArgs = prettyForm(*self._print_seq(e.args).parens()) pform = prettyForm(binding=prettyForm.FUNC, *stringPict.next(prettyFunc, prettyArgs)) # store pform parts so it can be reassembled e.g. when powered pform.prettyFunc = prettyFunc pform.prettyArgs = prettyArgs return pform def _print_Add(self, expr, order=None): if self.order == 'none': terms = list(expr.args) else: terms = self._as_ordered_terms(expr, order=order) pforms, indices = [], [] def pretty_negative(pform, index): """Prepend a minus sign to a pretty form. """ if index == 0: if pform.height() > 1: pform_neg = '- ' else: pform_neg = '-' else: pform_neg = ' - ' pform = stringPict.next(pform_neg, pform) return prettyForm(binding=prettyForm.NEG, *pform) for i, term in enumerate(terms): if term.is_Mul and _coeff_isneg(term): pform = self._print(-term) pforms.append(pretty_negative(pform, i)) elif term.is_Rational and term.q > 1: pforms.append(None) indices.append(i) elif term.is_Number and term < 0: pform = self._print(-term) pforms.append(pretty_negative(pform, i)) else: pforms.append(self._print(term)) if indices: large = True for pform in pforms: if pform is not None and pform.height() > 1: break else: large = False for i in indices: term, negative = terms[i], False if term < 0: term, negative = -term, True if large: pform = prettyForm(str(term.p))/prettyForm(str(term.q)) else: pform = self._print(term) if negative: pform = pretty_negative(pform, i) pforms[i] = pform return prettyForm.__add__(*pforms) def _print_Mul(self, product): a = [] # items in the numerator b = [] # items that are in the denominator (if any) if self.order not in ('old', 'none'): args = product.as_ordered_factors() else: args = product.args # Gather terms for numerator/denominator for item in args: if item.is_commutative and item.is_Pow and item.exp.is_Rational and item.exp.is_negative: b.append(C.Pow(item.base, -item.exp)) elif item.is_Rational and item is not S.Infinity: if item.p != 1: a.append( C.Rational(item.p) ) if item.q != 1: b.append( C.Rational(item.q) ) else: a.append(item) # Convert to pretty forms. Add parens to Add instances if there # is more than one term in the numer/denom for i in range(0, len(a)): if a[i].is_Add and len(a) > 1: a[i] = prettyForm(*self._print(a[i]).parens()) else: a[i] = self._print(a[i]) for i in range(0, len(b)): if b[i].is_Add and len(b) > 1: b[i] = prettyForm(*self._print(b[i]).parens()) else: b[i] = self._print(b[i]) # Construct a pretty form if len(b) == 0: return prettyForm.__mul__(*a) else: if len(a) == 0: a.append( self._print(S.One) ) return prettyForm.__mul__(*a)/prettyForm.__mul__(*b) # A helper function for _print_Pow to print x**(1/n) def _print_nth_root (self, base, expt): bpretty = self._print(base) # Construct root sign, start with the \/ shape _zZ = xobj('/',1) rootsign = xobj('\\',1) + _zZ # Make exponent number to put above it if isinstance(expt, C.Rational): exp = str(expt.q) if exp == '2': exp = '' else: exp = str(expt.args[0]) exp = exp.ljust(2) if len(exp) > 2: rootsign = ' '*(len(exp) - 2) + rootsign # Stack the exponent rootsign = stringPict(exp + '\n' + rootsign) rootsign.baseline = 0 # Diagonal: length is one less than height of base linelength = bpretty.height() - 1 diagonal = stringPict('\n'.join( ' '*(linelength - i - 1) + _zZ + ' '*i for i in range(linelength) )) # Put baseline just below lowest line: next to exp diagonal.baseline = linelength - 1 # Make the root symbol rootsign = prettyForm(*rootsign.right(diagonal)) # Det the baseline to match contents to fix the height # but if the height of bpretty is one, the rootsign must be one higher rootsign.baseline = max(1, bpretty.baseline) #build result s = prettyForm(hobj('_', 2 + bpretty.width())) s = prettyForm(*bpretty.above(s)) s = prettyForm(*s.left(rootsign)) return s def _print_Pow(self, power): from sympy import fraction b, e = power.as_base_exp() if power.is_commutative: if e is S.NegativeOne: return prettyForm("1")/self._print(b) n, d = fraction(e) if n is S.One and d.is_Atom and not e.is_Integer: return self._print_nth_root(b, e) if e.is_Rational and e < 0: return prettyForm("1")/self._print(b)**self._print(-e) # None of the above special forms, do a standard power return self._print(b)**self._print(e) def __print_numer_denom(self, p, q): if q == 1: if p < 0: return prettyForm(str(p),binding=prettyForm.NEG) else: return prettyForm(str(p)) elif abs(p) >= 10 and abs(q) >= 10: # If more than one digit in numer and denom, print larger fraction if p < 0: pform = prettyForm(str(-p))/prettyForm(str(q)) return prettyForm(binding=prettyForm.NEG, *pform.left('- ')) else: return prettyForm(str(p))/prettyForm(str(q)) else: return None def _print_Rational(self, expr): result = self.__print_numer_denom(expr.p, expr.q) if result is not None: return result else: return self.emptyPrinter(expr) def _print_Fraction(self, expr): result = self.__print_numer_denom(expr.numerator, expr.denominator) if result is not None: return result else: return self.emptyPrinter(expr) def _print_ProductSet(self, p): if len(p.sets) > 1 and not has_variety(p.sets): from sympy import Pow return self._print(Pow(p.sets[0], len(p.sets), evaluate=False)) else: prod_char = '\xd7' return self._print_seq(p.sets, None, None, ' %s '%prod_char, parenthesize = lambda set:set.is_Union or set.is_Intersection) def _print_FiniteSet(self, s): items = sorted(s.args, key=default_sort_key) return self._print_seq(items, '{', '}', ', ' ) def _print_Range(self, s): if self._use_unicode: dots = "\u2026" else: dots = '...' if len(s) > 4: it = iter(s) printset = next(it), next(it), dots, s._last_element else: printset = tuple(s) return self._print_seq(printset, '{', '}', ', ' ) def _print_Interval(self, i): if i.start == i.end: return self._print_seq(i.args[:1], '{', '}') else: if i.left_open: left = '(' else: left = '[' if i.right_open: right = ')' else: right = ']' return self._print_seq(i.args[:2], left, right) def _print_Intersection(self, u): delimiter = ' %s ' % pretty_atom('Intersection') return self._print_seq(u.args, None, None, delimiter, parenthesize = lambda set:set.is_ProductSet or set.is_Union) def _print_Union(self, u): union_delimiter = ' %s ' % pretty_atom('Union') return self._print_seq(u.args, None, None, union_delimiter, parenthesize = lambda set:set.is_ProductSet or set.is_Intersection) def _print_TransformationSet(self, ts): if self._use_unicode: inn = "\u220a" else: inn = 'in' variables = self._print_seq(ts.lamda.variables) expr = self._print(ts.lamda.expr) bar = self._print("|") base = self._print(ts.base_set) return self._print_seq((expr, bar, variables, inn, base), "{", "}", ' ') def _print_seq(self, seq, left=None, right=None, delimiter=', ', parenthesize=lambda x: False): s = None for item in seq: pform = self._print(item) if parenthesize(item): pform = prettyForm(*pform.parens()) if s is None: # first element s = pform else: s = prettyForm(*stringPict.next(s, delimiter)) s = prettyForm(*stringPict.next(s, pform)) if s is None: s = stringPict('') s = prettyForm(*s.parens(left, right, ifascii_nougly=True)) return s def join(self, delimiter, args): pform = None for arg in args: if pform is None: pform = arg else: pform = prettyForm(*pform.right(delimiter)) pform = prettyForm(*pform.right(arg)) if pform is None: return prettyForm("") else: return pform def _print_list(self, l): return self._print_seq(l, '[', ']') def _print_tuple(self, t): if len(t) == 1: ptuple = prettyForm(*stringPict.next(self._print(t[0]), ',')) return prettyForm(*ptuple.parens('(', ')', ifascii_nougly=True)) else: return self._print_seq(t, '(', ')') def _print_Tuple(self, expr): return self._print_tuple(expr) def _print_dict(self, d): keys = sorted(list(d.keys()), key=default_sort_key) items = [] for k in keys: K = self._print(k) V = self._print(d[k]) s = prettyForm(*stringPict.next(K, ': ', V)) items.append(s) return self._print_seq(items, '{', '}') def _print_Dict(self, d): return self._print_dict(d) def _print_set(self, s): items = sorted(s, key=default_sort_key) pretty = self._print_seq(items, '[', ']') pretty = prettyForm(*pretty.parens('(', ')', ifascii_nougly=True)) pretty = prettyForm(*stringPict.next(type(s).__name__, pretty)) return pretty _print_frozenset = _print_set def _print_AlgebraicNumber(self, expr): if expr.is_aliased: return self._print(expr.as_poly().as_expr()) else: return self._print(expr.as_expr()) def _print_RootOf(self, expr): args = [self._print_Add(expr.expr, order='lex'), expr.index] pform = prettyForm(*self._print_seq(args).parens()) pform = prettyForm(*pform.left('RootOf')) return pform def _print_RootSum(self, expr): args = [self._print_Add(expr.expr, order='lex')] if expr.fun is not S.IdentityFunction: args.append(self._print(expr.fun)) pform = prettyForm(*self._print_seq(args).parens()) pform = prettyForm(*pform.left('RootSum')) return pform def _print_FiniteField(self, expr): if self._use_unicode: form = '\u2124_%d' else: form = 'GF(%d)' return prettyForm(pretty_symbol(form % expr.mod)) def _print_IntegerRing(self, expr): if self._use_unicode: return prettyForm('\u2124') else: return prettyForm('ZZ') def _print_RationalField(self, expr): if self._use_unicode: return prettyForm('\u211A') else: return prettyForm('QQ') def _print_RealDomain(self, expr): if self._use_unicode: return prettyForm('\u211D') else: return prettyForm('RR') def _print_ComplexDomain(self, expr): if self._use_unicode: return prettyForm('\u2102') else: return prettyForm('CC') def _print_PolynomialRingBase(self, expr): g = expr.gens if str(expr.order) != str(expr.default_order): g = g + ("order=" + str(expr.order),) pform = self._print_seq(g, '[', ']') pform = prettyForm(*pform.left(self._print(expr.dom))) return pform def _print_FractionField(self, expr): pform = self._print_seq(expr.gens, '(', ')') pform = prettyForm(*pform.left(self._print(expr.dom))) return pform def _print_GroebnerBasis(self, basis): cls = basis.__class__.__name__ exprs = [ self._print_Add(arg, order=basis.order) for arg in basis.exprs ] exprs = prettyForm(*self.join(", ", exprs).parens(left="[", right="]")) gens = [ self._print(gen) for gen in basis.gens ] domain = prettyForm(*prettyForm("domain=").right(self._print(basis.domain))) order = prettyForm(*prettyForm("order=").right(self._print(basis.order))) pform = self.join(", ", [exprs] + gens + [domain, order]) pform = prettyForm(*pform.parens()) pform = prettyForm(*pform.left(basis.__class__.__name__)) return pform def _print_Subs(self, e): pform = self._print(e.expr) pform = prettyForm(*pform.parens()) h = pform.height() if pform.height() > 1 else 2 rvert = stringPict(vobj('|', h), baseline=pform.baseline) pform = prettyForm(*pform.right(rvert)) b = pform.baseline pform.baseline = pform.height() - 1 pform = prettyForm(*pform.right(self._print_seq([ self._print_seq((self._print(v[0]), xsym('=='), self._print(v[1])), delimiter='') for v in zip(e.variables, e.point) ]))) pform.baseline = b return pform def _print_euler(self, e): pform = prettyForm("E") arg = self._print(e.args[0]) pform_arg = prettyForm(" "*arg.width()) pform_arg = prettyForm(*pform_arg.below(arg)) pform = prettyForm(*pform.right(pform_arg)) return pform def _print_catalan(self, e): pform = prettyForm("C") arg = self._print(e.args[0]) pform_arg = prettyForm(" "*arg.width()) pform_arg = prettyForm(*pform_arg.below(arg)) pform = prettyForm(*pform.right(pform_arg)) return pform def _print_KroneckerDelta(self, e): pform = self._print(e.args[0]) pform = prettyForm(*pform.right((prettyForm(',')))) pform = prettyForm(*pform.right((self._print(e.args[1])))) if self._use_unicode: a = stringPict(pretty_symbol('delta')) else: a = stringPict('d') b = pform top = stringPict(*b.left(' '*a.width())) bot = stringPict(*a.right(' '*b.width())) return prettyForm(binding=prettyForm.POW, *bot.below(top)) def _print_atan2(self, e): pform = prettyForm(*self._print_seq(e.args).parens()) pform = prettyForm(*pform.left('atan2')) return pform def _print_RandomDomain(self, d): try: pform = self._print('Domain: ') pform = prettyForm(*pform.right(self._print(d.as_boolean()))) return pform except: try: pform = self._print('Domain: ') pform = prettyForm(*pform.right(self._print(d.symbols))) pform = prettyForm(*pform.right(self._print(' in '))) pform = prettyForm(*pform.right(self._print(d.set))) return pform except: return self._print(None) def _print_DMP(self, p): try: if p.ring is not None: # TODO incorporate order return self._print(p.ring.to_sympy(p)) except SympifyError: pass return self._print(repr(p)) def _print_DMF(self, p): return self._print_DMP(p) def _print_Object(self, object): return self._print(pretty_symbol(object.name)) def _print_Morphism(self, morphism): arrow = xsym("-->") domain = self._print(morphism.domain) codomain = self._print(morphism.codomain) tail = domain.right(arrow, codomain)[0] return prettyForm(tail) def _print_NamedMorphism(self, morphism): pretty_name = self._print(pretty_symbol(morphism.name)) pretty_morphism = self._print_Morphism(morphism) return prettyForm(pretty_name.right(":", pretty_morphism)[0]) def _print_IdentityMorphism(self, morphism): from sympy.categories import NamedMorphism return self._print_NamedMorphism( NamedMorphism(morphism.domain, morphism.codomain, "id")) def _print_CompositeMorphism(self, morphism): from sympy.categories import NamedMorphism circle = xsym(".") # All components of the morphism have names and it is thus # possible to build the name of the composite. component_names_list = [pretty_symbol(component.name) for \ component in morphism.components] component_names_list.reverse() component_names = circle.join(component_names_list) + ":" pretty_name = self._print(component_names) pretty_morphism = self._print_Morphism(morphism) return prettyForm(pretty_name.right(pretty_morphism)[0]) def _print_Category(self, category): return self._print(pretty_symbol(category.name)) def _print_Diagram(self, diagram): if not diagram.premises: # This is an empty diagram. return self._print(S.EmptySet) pretty_result = self._print(diagram.premises) if diagram.conclusions: results_arrow = " %s " % xsym("==>") pretty_conclusions = self._print(diagram.conclusions)[0] pretty_result = pretty_result.right(results_arrow, pretty_conclusions) return prettyForm(pretty_result[0]) def _print_DiagramGrid(self, grid): from sympy.matrices import Matrix from sympy import Symbol matrix = Matrix([[grid[i, j] if grid[i, j] else Symbol(" ") for j in range(grid.width)] for i in range(grid.height)]) return self._print_matrix_contents(matrix) def _print_FreeModuleElement(self, m): # Print as row vector for convenience, for now. return self._print_seq(m, '[', ']') def _print_SubModule(self, M): return self._print_seq(M.gens, '<', '>') def _print_FreeModule(self, M): return self._print(M.ring)**self._print(M.rank) def _print_ModuleImplementedIdeal(self, M): return self._print_seq([x for [x] in M._module.gens], '<', '>') def _print_QuotientRing(self, R): return self._print(R.ring) / self._print(R.base_ideal) def _print_QuotientRingElement(self, R): return self._print(R.data) + self._print(R.ring.base_ideal) def _print_QuotientModuleElement(self, m): return self._print(m.data) + self._print(m.module.killed_module) def _print_QuotientModule(self, M): return self._print(M.base) / self._print(M.killed_module) def _print_MatrixHomomorphism(self, h): matrix = self._print(h._sympy_matrix()) matrix.baseline = matrix.height() // 2 pform = prettyForm(*matrix.right(' : ', self._print(h.domain), ' %s> ' % hobj('-', 2), self._print(h.codomain))) return pform def _print_BaseScalarField(self, field): string = field._coord_sys._names[field._index] return self._print(pretty_symbol(string)) def _print_BaseVectorField(self, field): s = U('PARTIAL DIFFERENTIAL')+'_'+field._coord_sys._names[field._index] return self._print(pretty_symbol(s)) def _print_Differential(self, diff): field = diff._form_field if hasattr(field, '_coord_sys'): string = field._coord_sys._names[field._index] return self._print('\u2146 '+pretty_symbol(string)) else: pform = self._print(field) pform = prettyForm(*pform.parens()) return prettyForm(*pform.left("\u2146")) def _print_Tr(self, p): #TODO: Handle indices pform = self._print(p.args[0]) pform = prettyForm(*pform.left('%s(' % (p.__class__.__name__))) pform = prettyForm(*pform.right(')')) return pform
[docs]def pretty(expr, **settings): """Returns a string containing the prettified form of expr. For information on keyword arguments see pretty_print function. """ pp = PrettyPrinter(settings) # XXX: this is an ugly hack, but at least it works use_unicode = pp._settings['use_unicode'] uflag = pretty_use_unicode(use_unicode) try: return pp.doprint(expr) finally: pretty_use_unicode(uflag)
[docs]def pretty_print(expr, **settings): """Prints expr in pretty form. pprint is just a shortcut for this function. Parameters ========== expr : expression the expression to print wrap_line : bool, optional line wrapping enabled/disabled, defaults to True num_columns : bool, optional number of columns before line breaking (default to None which reads the terminal width), useful when using SymPy without terminal. use_unicode : bool or None, optional use unicode characters, such as the Greek letter pi instead of the string pi. full_prec : bool or string, optional use full precision. Default to "auto" order : bool or string, optional set to 'none' for long expressions if slow; default is None """ print(pretty(expr, **settings))
pprint = pretty_print def pager_print(expr, **settings): """Prints expr using the pager, in pretty form. This invokes a pager command using pydoc. Lines are not wrapped automatically. This routine is meant to be used with a pager that allows sideways scrolling, like ``less -S``. Parameters are the same as for ``pretty_print``. If you wish to wrap lines, pass ``num_columns=None`` to auto-detect the width of the terminal. """ from pydoc import pager from locale import getpreferredencoding if 'num_columns' not in settings: settings['num_columns'] = 500000 # disable line wrap pager(pretty(expr, **settings).encode(getpreferredencoding()))