372 lines
12 KiB
Python
372 lines
12 KiB
Python
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from sympy.core.function import Derivative
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from sympy.core.function import UndefinedFunction, AppliedUndef
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from sympy.core.symbol import Symbol
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from sympy.interactive.printing import init_printing
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from sympy.printing.latex import LatexPrinter
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from sympy.printing.pretty.pretty import PrettyPrinter
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from sympy.printing.pretty.pretty_symbology import center_accent
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from sympy.printing.str import StrPrinter
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from sympy.printing.precedence import PRECEDENCE
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__all__ = ['vprint', 'vsstrrepr', 'vsprint', 'vpprint', 'vlatex',
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'init_vprinting']
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class VectorStrPrinter(StrPrinter):
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"""String Printer for vector expressions. """
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def _print_Derivative(self, e):
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from sympy.physics.vector.functions import dynamicsymbols
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t = dynamicsymbols._t
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if (bool(sum([i == t for i in e.variables])) &
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isinstance(type(e.args[0]), UndefinedFunction)):
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ol = str(e.args[0].func)
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for i, v in enumerate(e.variables):
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ol += dynamicsymbols._str
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return ol
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else:
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return StrPrinter().doprint(e)
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def _print_Function(self, e):
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from sympy.physics.vector.functions import dynamicsymbols
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t = dynamicsymbols._t
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if isinstance(type(e), UndefinedFunction):
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return StrPrinter().doprint(e).replace("(%s)" % t, '')
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return e.func.__name__ + "(%s)" % self.stringify(e.args, ", ")
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class VectorStrReprPrinter(VectorStrPrinter):
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"""String repr printer for vector expressions."""
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def _print_str(self, s):
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return repr(s)
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class VectorLatexPrinter(LatexPrinter):
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"""Latex Printer for vector expressions. """
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def _print_Function(self, expr, exp=None):
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from sympy.physics.vector.functions import dynamicsymbols
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func = expr.func.__name__
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t = dynamicsymbols._t
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if (hasattr(self, '_print_' + func) and not
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isinstance(type(expr), UndefinedFunction)):
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return getattr(self, '_print_' + func)(expr, exp)
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elif isinstance(type(expr), UndefinedFunction) and (expr.args == (t,)):
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# treat this function like a symbol
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expr = Symbol(func)
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if exp is not None:
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# copied from LatexPrinter._helper_print_standard_power, which
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# we can't call because we only have exp as a string.
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base = self.parenthesize(expr, PRECEDENCE['Pow'])
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base = self.parenthesize_super(base)
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return r"%s^{%s}" % (base, exp)
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else:
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return super()._print(expr)
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else:
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return super()._print_Function(expr, exp)
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def _print_Derivative(self, der_expr):
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from sympy.physics.vector.functions import dynamicsymbols
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# make sure it is in the right form
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der_expr = der_expr.doit()
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if not isinstance(der_expr, Derivative):
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return r"\left(%s\right)" % self.doprint(der_expr)
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# check if expr is a dynamicsymbol
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t = dynamicsymbols._t
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expr = der_expr.expr
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red = expr.atoms(AppliedUndef)
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syms = der_expr.variables
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test1 = not all(True for i in red if i.free_symbols == {t})
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test2 = not all(t == i for i in syms)
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if test1 or test2:
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return super()._print_Derivative(der_expr)
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# done checking
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dots = len(syms)
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base = self._print_Function(expr)
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base_split = base.split('_', 1)
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base = base_split[0]
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if dots == 1:
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base = r"\dot{%s}" % base
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elif dots == 2:
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base = r"\ddot{%s}" % base
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elif dots == 3:
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base = r"\dddot{%s}" % base
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elif dots == 4:
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base = r"\ddddot{%s}" % base
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else: # Fallback to standard printing
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return super()._print_Derivative(der_expr)
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if len(base_split) != 1:
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base += '_' + base_split[1]
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return base
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class VectorPrettyPrinter(PrettyPrinter):
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"""Pretty Printer for vectorialexpressions. """
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def _print_Derivative(self, deriv):
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from sympy.physics.vector.functions import dynamicsymbols
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# XXX use U('PARTIAL DIFFERENTIAL') here ?
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t = dynamicsymbols._t
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dot_i = 0
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syms = list(reversed(deriv.variables))
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while len(syms) > 0:
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if syms[-1] == t:
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syms.pop()
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dot_i += 1
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else:
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return super()._print_Derivative(deriv)
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if not (isinstance(type(deriv.expr), UndefinedFunction) and
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(deriv.expr.args == (t,))):
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return super()._print_Derivative(deriv)
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else:
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pform = self._print_Function(deriv.expr)
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# the following condition would happen with some sort of non-standard
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# dynamic symbol I guess, so we'll just print the SymPy way
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if len(pform.picture) > 1:
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return super()._print_Derivative(deriv)
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# There are only special symbols up to fourth-order derivatives
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if dot_i >= 5:
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return super()._print_Derivative(deriv)
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# Deal with special symbols
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dots = {0: "",
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1: "\N{COMBINING DOT ABOVE}",
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2: "\N{COMBINING DIAERESIS}",
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3: "\N{COMBINING THREE DOTS ABOVE}",
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4: "\N{COMBINING FOUR DOTS ABOVE}"}
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d = pform.__dict__
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# if unicode is false then calculate number of apostrophes needed and
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# add to output
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if not self._use_unicode:
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apostrophes = ""
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for i in range(0, dot_i):
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apostrophes += "'"
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d['picture'][0] += apostrophes + "(t)"
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else:
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d['picture'] = [center_accent(d['picture'][0], dots[dot_i])]
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return pform
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def _print_Function(self, e):
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from sympy.physics.vector.functions import dynamicsymbols
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t = dynamicsymbols._t
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# XXX works only for applied functions
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func = e.func
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args = e.args
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func_name = func.__name__
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pform = self._print_Symbol(Symbol(func_name))
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# If this function is an Undefined function of t, it is probably a
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# dynamic symbol, so we'll skip the (t). The rest of the code is
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# identical to the normal PrettyPrinter code
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if not (isinstance(func, UndefinedFunction) and (args == (t,))):
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return super()._print_Function(e)
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return pform
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def vprint(expr, **settings):
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r"""Function for printing of expressions generated in the
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sympy.physics vector package.
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Extends SymPy's StrPrinter, takes the same setting accepted by SymPy's
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:func:`~.sstr`, and is equivalent to ``print(sstr(foo))``.
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Parameters
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==========
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expr : valid SymPy object
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SymPy expression to print.
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settings : args
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Same as the settings accepted by SymPy's sstr().
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Examples
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========
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>>> from sympy.physics.vector import vprint, dynamicsymbols
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>>> u1 = dynamicsymbols('u1')
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>>> print(u1)
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u1(t)
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>>> vprint(u1)
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u1
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"""
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outstr = vsprint(expr, **settings)
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import builtins
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if (outstr != 'None'):
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builtins._ = outstr
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print(outstr)
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def vsstrrepr(expr, **settings):
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"""Function for displaying expression representation's with vector
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printing enabled.
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Parameters
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==========
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expr : valid SymPy object
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SymPy expression to print.
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settings : args
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Same as the settings accepted by SymPy's sstrrepr().
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"""
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p = VectorStrReprPrinter(settings)
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return p.doprint(expr)
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def vsprint(expr, **settings):
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r"""Function for displaying expressions generated in the
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sympy.physics vector package.
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Returns the output of vprint() as a string.
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Parameters
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==========
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expr : valid SymPy object
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SymPy expression to print
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settings : args
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Same as the settings accepted by SymPy's sstr().
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Examples
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========
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>>> from sympy.physics.vector import vsprint, dynamicsymbols
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>>> u1, u2 = dynamicsymbols('u1 u2')
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>>> u2d = dynamicsymbols('u2', level=1)
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>>> print("%s = %s" % (u1, u2 + u2d))
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u1(t) = u2(t) + Derivative(u2(t), t)
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>>> print("%s = %s" % (vsprint(u1), vsprint(u2 + u2d)))
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u1 = u2 + u2'
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"""
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string_printer = VectorStrPrinter(settings)
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return string_printer.doprint(expr)
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def vpprint(expr, **settings):
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r"""Function for pretty printing of expressions generated in the
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sympy.physics vector package.
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Mainly used for expressions not inside a vector; the output of running
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scripts and generating equations of motion. Takes the same options as
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SymPy's :func:`~.pretty_print`; see that function for more information.
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Parameters
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==========
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expr : valid SymPy object
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SymPy expression to pretty print
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settings : args
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Same as those accepted by SymPy's pretty_print.
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"""
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pp = VectorPrettyPrinter(settings)
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# Note that this is copied from sympy.printing.pretty.pretty_print:
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# XXX: this is an ugly hack, but at least it works
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use_unicode = pp._settings['use_unicode']
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from sympy.printing.pretty.pretty_symbology import pretty_use_unicode
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uflag = pretty_use_unicode(use_unicode)
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try:
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return pp.doprint(expr)
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finally:
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pretty_use_unicode(uflag)
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def vlatex(expr, **settings):
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r"""Function for printing latex representation of sympy.physics.vector
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objects.
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For latex representation of Vectors, Dyadics, and dynamicsymbols. Takes the
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same options as SymPy's :func:`~.latex`; see that function for more
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information;
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Parameters
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==========
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expr : valid SymPy object
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SymPy expression to represent in LaTeX form
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settings : args
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Same as latex()
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Examples
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========
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>>> from sympy.physics.vector import vlatex, ReferenceFrame, dynamicsymbols
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>>> N = ReferenceFrame('N')
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>>> q1, q2 = dynamicsymbols('q1 q2')
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>>> q1d, q2d = dynamicsymbols('q1 q2', 1)
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>>> q1dd, q2dd = dynamicsymbols('q1 q2', 2)
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>>> vlatex(N.x + N.y)
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'\\mathbf{\\hat{n}_x} + \\mathbf{\\hat{n}_y}'
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>>> vlatex(q1 + q2)
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'q_{1} + q_{2}'
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>>> vlatex(q1d)
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'\\dot{q}_{1}'
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>>> vlatex(q1 * q2d)
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'q_{1} \\dot{q}_{2}'
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>>> vlatex(q1dd * q1 / q1d)
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'\\frac{q_{1} \\ddot{q}_{1}}{\\dot{q}_{1}}'
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"""
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latex_printer = VectorLatexPrinter(settings)
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return latex_printer.doprint(expr)
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def init_vprinting(**kwargs):
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"""Initializes time derivative printing for all SymPy objects, i.e. any
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functions of time will be displayed in a more compact notation. The main
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benefit of this is for printing of time derivatives; instead of
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displaying as ``Derivative(f(t),t)``, it will display ``f'``. This is
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only actually needed for when derivatives are present and are not in a
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physics.vector.Vector or physics.vector.Dyadic object. This function is a
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light wrapper to :func:`~.init_printing`. Any keyword
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arguments for it are valid here.
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{0}
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Examples
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========
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>>> from sympy import Function, symbols
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>>> t, x = symbols('t, x')
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>>> omega = Function('omega')
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>>> omega(x).diff()
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Derivative(omega(x), x)
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>>> omega(t).diff()
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Derivative(omega(t), t)
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Now use the string printer:
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>>> from sympy.physics.vector import init_vprinting
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>>> init_vprinting(pretty_print=False)
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>>> omega(x).diff()
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Derivative(omega(x), x)
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>>> omega(t).diff()
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omega'
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"""
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kwargs['str_printer'] = vsstrrepr
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kwargs['pretty_printer'] = vpprint
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kwargs['latex_printer'] = vlatex
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init_printing(**kwargs)
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params = init_printing.__doc__.split('Examples\n ========')[0] # type: ignore
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init_vprinting.__doc__ = init_vprinting.__doc__.format(params) # type: ignore
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