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228k
fixed
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int64
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481k
def __mod__(self, args): """ Binds the lazy format with its parameters
def __mod__(self, args): """ Binds the lazy format with its parameters
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sage: def f(x,y): return math.exp(x/5)*math.cos(y)
sage: def f(x,y): return math.exp(x/5)*math.cos(y)
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sage: def f(x,y): return math.exp(x/5)*math.cos(y)
sage: def f(x,y): return math.exp(x/5)*math.cos(y)
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sage: def f(x,y): return math.exp(x/5)*math.cos(y)
sage: def f(x,y): return math.exp(x/5)*math.cos(y)
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sage: def f(x,y): return math.exp(x/5)*math.cos(y)
sage: def f(x,y): return math.exp(x/5)*math.cos(y)
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def __init__(self, indep_var, dep_vars): """ INPUT:
def __init__(self, indep_var, dep_vars): """ INPUT:
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def __init__(self, indep_var, dep_vars): """ INPUT:
def __init__(self, indep_var, dep_vars): """ INPUT:
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def __init__(self, indep_var, dep_vars): """ INPUT:
def __init__(self, indep_var, dep_vars): """ INPUT:
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def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
def to_cartesian(self, func, params=None): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
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def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
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def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
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def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
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def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
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def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
def to_cartesian(self, func, params): """ Returns a 3-tuple of functions, parameterized over ``params``, that represents the cartesian coordinates of the value of ``func``.
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def subs_func(t): return lambda x,y: t.subs({ indep_var_dummy: func(x, y), dep_var_dummies[0]: x, dep_var_dummies[1]: y })
def subs_func(t): return lambda x,y: t.subs({ dep_var_dummy: func(x, y), indep_var_dummies[0]: x, indep_var_dummies[1]: y })
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def subs_func(t): return lambda x,y: t.subs({ indep_var_dummy: func(x, y), dep_var_dummies[0]: x, dep_var_dummies[1]: y })
def subs_func(t): return lambda x,y: t.subs({ indep_var_dummy: func(x, y), dep_var_dummies[0]: x, dep_var_dummies[1]: y })
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def __repr__(self): return '%s (%s in terms of %s)' % \ (self._name, self.indep_var, ', '.join(self.dep_vars))
def __repr__(self): return '%s (%s in terms of %s)' % \ (self._name, self.indep_var, ', '.join(self.dep_vars))
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def __init__(self, custom_trans, fvar): """ INPUT:
def __init__(self, custom_trans, fvar): """ INPUT:
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def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbitraryCoordinates sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
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def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
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def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
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def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
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def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
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def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
def gen_transform(self, f=None, u=None, v=None): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbCoordTrans sage: x, y, z = var('x y z') sage: T = _ArbCoordTrans((x + y, x - y, z), x)
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def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
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def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
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def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
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def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
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def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
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def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
def gen_transform(self, r=None, theta=None, phi=None): """ EXAMPLE:: sage: T = Spherical('r', ['theta', 'phi']) sage: T.gen_transform(r=var('r'), theta=var('theta'), phi=var('phi')) (r*sin(theta)*cos(phi), r*sin(phi)*sin(theta), r*cos(theta)) """ return (r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(th...
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def gen_transform(self, rho=None, phi=None, z=None): """ EXAMPLE::
def gen_transform(self, rho=None, phi=None, z=None): """ EXAMPLE::
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def plot3d(f, urange, vrange, adaptive=False, transformation=None, **kwds): """ INPUT: - ``f`` - a symbolic expression or function of 2 variables - ``urange`` - a 2-tuple (u_min, u_max) or a 3-tuple (u, u_min, u_max) - ``vrange`` - a 2-tuple (v_min, v_max) or a 3-tuple (v, v_min, v_max) - ``adaptive`` - (defau...
def plot3d(f, urange, vrange, adaptive=False, transformation=None, **kwds): """ INPUT: - ``f`` - a symbolic expression or function of 2 variables - ``urange`` - a 2-tuple (u_min, u_max) or a 3-tuple (u, u_min, u_max) - ``vrange`` - a 2-tuple (v_min, v_max) or a 3-tuple (v, v_min, v_max) - ``adaptive`` - (defau...
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def plot3d(f, urange, vrange, adaptive=False, transformation=None, **kwds): """ INPUT: - ``f`` - a symbolic expression or function of 2 variables - ``urange`` - a 2-tuple (u_min, u_max) or a 3-tuple (u, u_min, u_max) - ``vrange`` - a 2-tuple (v_min, v_max) or a 3-tuple (v, v_min, v_max) - ``adaptive`` - (defau...
def plot3d(f, urange, vrange, adaptive=False, transformation=None, **kwds): """ INPUT: - ``f`` - a symbolic expression or function of 2 variables - ``urange`` - a 2-tuple (u_min, u_max) or a 3-tuple (u, u_min, u_max) - ``vrange`` - a 2-tuple (v_min, v_max) or a 3-tuple (v, v_min, v_max) - ``adaptive`` - (defau...
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def plot3d(f, urange, vrange, adaptive=False, transformation=None, **kwds): """ INPUT: - ``f`` - a symbolic expression or function of 2 variables - ``urange`` - a 2-tuple (u_min, u_max) or a 3-tuple (u, u_min, u_max) - ``vrange`` - a 2-tuple (v_min, v_max) or a 3-tuple (v, v_min, v_max) - ``adaptive`` - (defau...
def plot3d(f, urange, vrange, adaptive=False, transformation=None, **kwds): """ INPUT: - ``f`` - a symbolic expression or function of 2 variables - ``urange`` - a 2-tuple (u_min, u_max) or a 3-tuple (u, u_min, u_max) - ``vrange`` - a 2-tuple (v_min, v_max) or a 3-tuple (v, v_min, v_max) - ``adaptive`` - (defau...
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sage: def _(which_plot=[A,B,C,D,E]):
sage: def _(which_plot=[A,B,C,D,E]):
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sage: def _(which_plot=[F, G, H, I, J]):
sage: def _(which_plot=[F, G, H, I, J]):
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sage: def _(which_plot=[F, G, H, I, J]):
sage: def _(which_plot=[F, G, H, I, J]):
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sage: def _(which_plot=[F, G, H, I, J]):
sage: def _(which_plot=[F, G, H, I, J]):
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def spherical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in spherical coordinates in the domain specified by urange and vrange. This function is equivalent to:: sage: var('r,u,u') sage: T = (r*cos(u)*sin(v), r*sin(u)*sin(v), r*cos(v), r) sage: plot3d(f, urange, vrange, transformation=T) INPU...
def spherical_plot3d(f, urange, vrange, **kwds): """ Plots a function in spherical coordinates. This function is equivalent to:: sage: r,u,v=var('r,u,v') sage: f=u*v; urange=(u,0,pi); vrange=(v,0,pi) sage: T = (r*cos(u)*sin(v), r*sin(u)*sin(v), r*cos(v), [u,v]) sage: plot3d(f, urange, vrange, transformation=T) INPUT...
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def spherical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in spherical coordinates in the domain specified by urange and vrange. This function is equivalent to:: sage: var('r,u,u') sage: T = (r*cos(u)*sin(v), r*sin(u)*sin(v), r*cos(v), r) sage: plot3d(f, urange, vrange, transformation=T) INPU...
def spherical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in spherical coordinates in the domain specified by urange and vrange. This function is equivalent to:: sage: var('r,u,u') sage: T = (r*cos(u)*sin(v), r*sin(u)*sin(v), r*cos(v), r) sage: plot3d(f, urange, vrange, transformation=T) INPU...
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def cylindrical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in cylindrical coordinates in the domain specified by urange and vrange. This command is equivalent to:: sage: var('r,u,v') sage: T = (r*cos(u), r*sin(u), v, r) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
def cylindrical_plot3d(f, urange, vrange, **kwds): """ Plots a function in cylindrical coordinates. This function is equivalent to:: sage: r,u,v=var('r,u,v') sage: f=u*v; urange=(u,0,pi); vrange=(v,0,pi) sage: T = (r*cos(u), r*sin(u), v, [u,v]) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
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def cylindrical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in cylindrical coordinates in the domain specified by urange and vrange. This command is equivalent to:: sage: var('r,u,v') sage: T = (r*cos(u), r*sin(u), v, r) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
def cylindrical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in cylindrical coordinates in the domain specified by urange and vrange. This command is equivalent to:: sage: var('r,u,v') sage: T = (r*cos(u), r*sin(u), v, r) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
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def cylindrical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in cylindrical coordinates in the domain specified by urange and vrange. This command is equivalent to:: sage: var('r,u,v') sage: T = (r*cos(u), r*sin(u), v, r) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
def cylindrical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in cylindrical coordinates in the domain specified by urange and vrange. This command is equivalent to:: sage: var('r,u,v') sage: T = (r*cos(u), r*sin(u), v, r) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
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def cylindrical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in cylindrical coordinates in the domain specified by urange and vrange. This command is equivalent to:: sage: var('r,u,v') sage: T = (r*cos(u), r*sin(u), v, r) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
def cylindrical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in cylindrical coordinates in the domain specified by urange and vrange. This command is equivalent to:: sage: var('r,u,v') sage: T = (r*cos(u), r*sin(u), v, r) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
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def cylindrical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in cylindrical coordinates in the domain specified by urange and vrange. This command is equivalent to:: sage: var('r,u,v') sage: T = (r*cos(u), r*sin(u), v, r) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
def cylindrical_plot3d(f, urange, vrange, **kwds): """ Takes a function and plots it in cylindrical coordinates in the domain specified by urange and vrange. This command is equivalent to:: sage: var('r,u,v') sage: T = (r*cos(u), r*sin(u), v, r) sage: plot3d(f, urange, vrange, transformation=T) INPUT: - ``f`` - a sy...
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def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
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def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
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def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
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def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
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def transform(self, **kwds): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbitraryCoordinates sage: x, y, z = var('x y z') sage: T = _ArbitraryCoordinates((x + y, x - y, z), x,[y,z])
def transform(self, **kwds): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbitraryCoordinates sage: x, y, z = var('x y z') sage: T = _ArbitraryCoordinates((x + y, x - y, z), x,[y,z])
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def transform(self, radius=None, azimuth=None, inclination=None): """ A spherical coordinates transform.
def transform(self, radius=None, azimuth=None, inclination=None): """ A spherical coordinates transform.
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def __call__(cls, *args, **options): """ This method implements ``cls(<some arguments>)``.
def __call__(cls, *args, **options): """ This method implements ``cls(<some arguments>)``.
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... def __classcall__(cls):
... def __classcall__(cls):
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... def __init__(self):
... def __init__(self):
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... def __init__(self):
... def __init__(self):
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... def __init__(self):
... def __init__(self):
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def __call__(self, *args): """ Coerces the element into the ring. You may pass a vector in the ambient space, an element of the base_ring, or an argument list of integers (or half-integers for the spin types) which are the components of a vector in the ambient space. INPUT: - ``x`` - a ring element to be coerced; o...
def __call__(self, *args): """ Coerces the element into the ring. You may pass a vector in the ambient space, an element of the base_ring, or an argument list of integers (or half-integers for the spin types) which are the components of a vector in the ambient space. INPUT: - ``x`` - a ring element to be coerced; o...
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def change_weierstrass_model(self, *urst): r""" Return a new Weierstrass model of self under the standard transformation `(u,r,s,,t)` .. math:: (x,y) \mapsto (x',y') = (u^2xr , u^3y + su^2x' + t). EXAMPLES:: sage: E = EllipticCurve('15a') sage: F1 = E.change_weierstrass_model([1/2,0,0,0]); F1 Elliptic Curve define...
def change_weierstrass_model(self, *urst): r""" Return a new Weierstrass model of self under the standard transformation `(u,r,s,t)` .. math:: (x,y) \mapsto (x',y') = (u^2xr , u^3y + su^2x' + t). EXAMPLES:: sage: E = EllipticCurve('15a') sage: F1 = E.change_weierstrass_model([1/2,0,0,0]); F1 Elliptic Curve defined...
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def change_weierstrass_model(self, *urst): r""" Return a new Weierstrass model of self under the standard transformation `(u,r,s,,t)` .. math:: (x,y) \mapsto (x',y') = (u^2xr , u^3y + su^2x' + t). EXAMPLES:: sage: E = EllipticCurve('15a') sage: F1 = E.change_weierstrass_model([1/2,0,0,0]); F1 Elliptic Curve define...
def change_weierstrass_model(self, *urst): r""" Return a new Weierstrass model of self under the standard transformation `(u,r,s,,t)` .. math:: (x,y) \mapsto (x',y') = (u^2x + r , u^3y + su^2x + t). EXAMPLES:: sage: E = EllipticCurve('15a') sage: F1 = E.change_weierstrass_model([1/2,0,0,0]); F1 Elliptic Curve defi...
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def gale_ryser_theorem(p1, p2, algorithm="ryser"): r""" Returns the binary matrix given by the Gale-Ryser theorem. The Gale Ryser theorem asserts that if `p_1,p_2` are two partitions of `n` of respective lengths `k_1,k_2`, then there is a binary `k_1\times k_2` matrix `M` such that `p_1` is the vector of row sums and ...
def gale_ryser_theorem(p1, p2, algorithm="ryser"): r""" Returns the binary matrix given by the Gale-Ryser theorem. The Gale Ryser theorem asserts that if `p_1,p_2` are two partitions of `n` of respective lengths `k_1,k_2`, then there is a binary `k_1\times k_2` matrix `M` such that `p_1` is the vector of row sums and ...
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def gale_ryser_theorem(p1, p2, algorithm="ryser"): r""" Returns the binary matrix given by the Gale-Ryser theorem. The Gale Ryser theorem asserts that if `p_1,p_2` are two partitions of `n` of respective lengths `k_1,k_2`, then there is a binary `k_1\times k_2` matrix `M` such that `p_1` is the vector of row sums and ...
def gale_ryser_theorem(p1, p2, algorithm="ryser"): r""" Returns the binary matrix given by the Gale-Ryser theorem. The Gale Ryser theorem asserts that if `p_1,p_2` are two partitions of `n` of respective lengths `k_1,k_2`, then there is a binary `k_1\times k_2` matrix `M` such that `p_1` is the vector of row sums and ...
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def super_categories(self): """ Returns a list of the immediate super categories of self.
def super_categories(self): """ Returns a list of the immediate super categories of self.
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def one(self): r""" Returns the one of the monoid, that is the unique neutral element for `*`.
def one(self): r""" Returns the one of the monoid, that is the unique neutral element for `*`.
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def one_element(self): r""" Backward compatibility alias for :meth:`self.one()`.
def one_element(self): r""" Backward compatibility alias for :meth:`self.one()`.
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def prod(self, args): r""" n-ary product
def prod(self, args): r""" n-ary product
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def prod(self, args): r""" n-ary product
defprod(self,args):r"""n-aryproduct
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def is_one(self): r""" Returns whether self is the one of the monoid
def is_one(self): r""" Returns whether self is the one of the monoid
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def __pow__(self, n): r""" INPUTS: - n: a non negative integer
def __pow__(self, n): r""" INPUTS: - n: a non negative integer
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def _pow_naive(self, n): r""" A naive implementation of __pow__
def _pow_naive(self, n): r""" A naive implementation of __pow__
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def _pow_naive(self, n): r""" A naive implementation of __pow__
def _pow_naive(self, n): r""" A naive implementation of __pow__
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def _pow_naive(self, n): r""" A naive implementation of __pow__
def _pow_naive(self, n): r""" A naive implementation of __pow__
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def _render_on_subplot(self, subplot): """ TESTS:
def _render_on_subplot(self, subplot): """ TESTS:
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def _render_on_subplot(self, subplot): """ TESTS:
def _render_on_subplot(self, subplot): """ TESTS:
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def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),...
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),...
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def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),...
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),...
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sage: def is_4regular(G):
sage: def is_4regular(G):
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def __init__(self, *args, **kwargs): """ Construct a substitution box (S-box) for a given lookup table `S`.
def __init__(self, *args, **kwargs): """ Construct a substitution box (S-box) for a given lookup table `S`.
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def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun...
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