rem stringlengths 1 322k | add stringlengths 0 2.05M | context stringlengths 4 228k | meta stringlengths 156 215 |
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sage: rho, phi, z = var('rho phi z') sage: T.gen_transform(rho=rho, phi=phi, z=z) (rho*cos(phi), rho*sin(phi), z) Use with plot3d on a made-up function:: sage: plot3d(phi * z, (phi, 0, 1), (z, 0, 1), transformation=T) To graph a function ``z`` in terms of ``phi`` and ``rho`` you would use:: sage: Cylindrical('z', [... | sage: r, theta, z = var('r theta z') sage: T.transform(radius=r, azimuth=theta, height=z) (r*cos(theta), r*sin(theta), z) We can plot with this transform. Remember that the independent variable is the height, and the dependent variables are the radius and the azimuth (in that order):: sage: plot3d(9-r^2, (r, 0, 3), ... | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
_name = 'Cylindrical coordinate system' all_vars = ['rho', 'phi', 'z'] def gen_transform(self, rho=None, phi=None, z=None): """ | def transform(self, radius=None, azimuth=None, height=None): """ A cylindrical coordinates transform. | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
sage: T = Cylindrical('z', ['phi', 'rho']) sage: T.gen_transform(rho=var('rho'), phi=var('phi'), z=var('z')) (rho*cos(phi), rho*sin(phi), z) """ return (rho * cos(phi), rho * sin(phi), z) | sage: T = Cylindrical('height', ['azimuth', 'radius']) sage: T.transform(radius=var('r'), azimuth=var('theta'), height=var('z')) (r*cos(theta), r*sin(theta), z) """ return (radius * cos(azimuth), radius * sin(azimuth), height) | def gen_transform(self, rho=None, phi=None, z=None): """ EXAMPLE:: | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
- ``transformation`` - (default: None) a transformation to apply. May be a 4-tuple (x_func, y_func, z_func, fvar) where the first 3 items indicate a transformation to cartesian coordinates (from your coordinate system) in terms of u, v, and the function variable fvar (for which the value of f will be substituted). May ... | - ``transformation`` - (default: None) a transformation to apply. May be a 3 or 4-tuple (x_func, y_func, z_func, independent_vars) where the first 3 items indicate a transformation to cartesian coordinates (from your coordinate system) in terms of u, v, and the function variable fvar (for which the value of f will be s... | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
sage: trans=(r*cos(phi),r*sin(phi),z,z) | sage: trans=(r*cos(phi),r*sin(phi),z) | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
sage: rectangular=(u,v,w,w) sage: spherical=(w*cos(u)*sin(v),w*sin(u)*sin(v),w*cos(v),w) sage: cylindric_radial=(w*cos(u),w*sin(u),v,w) sage: cylindric_axial=(v*cos(u),v*sin(u),w,w) sage: parabolic_cylindrical=(w*v,(v^2-w^2)/2,u,w) | sage: rectangular=(u,v,w) sage: spherical=(w*cos(u)*sin(v),w*sin(u)*sin(v),w*cos(v)) sage: cylindric_radial=(w*cos(u),w*sin(u),v) sage: cylindric_axial=(v*cos(u),v*sin(u),w) sage: parabolic_cylindrical=(w*v,(v^2-w^2)/2,u) | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
sage: def _(which_plot=[A,B,C,D,E]): | ... def _(which_plot=[A,B,C,D,E]): | sage: def _(which_plot=[A,B,C,D,E]): | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
sage: def _(which_plot=[F, G, H, I, J]): | ... def _(which_plot=[F, G, H, I, J]): | sage: def _(which_plot=[F, G, H, I, J]): | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
else: raise ValueError, 'expected 3-tuple for urange and vrange' | sage: def _(which_plot=[F, G, H, I, J]): | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py | |
transformation = _ArbCoordTrans(transformation[0:3], transformation[3]) if isinstance(transformation, _CoordTrans): | if len(transformation)==3: if params is None: raise ValueError, "must specify independent variable names in the ranges when using generic transformation" indep_vars = params elif len(transformation)==4: indep_vars = transformation[3] transformation = transformation[0:3] else: raise ValueError, "unknown transformation t... | sage: def _(which_plot=[F, G, H, I, J]): | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
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) | 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]) | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
return plot3d(f, urange, vrange, transformation=Spherical('r', ['phi', 'theta']), **kwds) | return plot3d(f, urange, vrange, transformation=Spherical('radius', ['azimuth', 'inclination']), **kwds) | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
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) | 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]) | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
- ``f`` - a symbolic expression or function of two variables. - ``urange`` - a 3-tuple (u, u_min, u_max), the domain of the azimuth variable. - ``vrange`` - a 3-tuple (v, v_min, v_max), the domain of the elevation (z) variable. | - ``f`` - a symbolic expression or function of two variables, representing the radius from the `z`-axis. - ``urange`` - a 3-tuple (u, u_min, u_max), the domain of the azimuth variable. - ``vrange`` - a 3-tuple (v, v_min, v_max), the domain of the elevation (`z`) variable. | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
sage: var('fi,z') sage: cylindrical_plot3d(2,(fi,0,3*pi/2),(z,-2,2)) | sage: theta,z=var('theta,z') sage: cylindrical_plot3d(2,(theta,0,3*pi/2),(z,-2,2)) | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
sage: cylindrical_plot3d(cosh(z),(fi,0,2*pi),(z,-2,2)) | sage: cylindrical_plot3d(cosh(z),(theta,0,2*pi),(z,-2,2)) | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
sage: cylindrical_plot3d(e^(-z^2)*(cos(4*fi)+2)+1,(fi,0,2*pi),(z,-2,2),plot_points=[80,80]).show(aspect_ratio=(1,1,1)) """ return plot3d(f, urange, vrange, transformation=Cylindrical('rho', ['phi', 'z']), **kwds) | sage: cylindrical_plot3d(e^(-z^2)*(cos(4*theta)+2)+1,(theta,0,2*pi),(z,-2,2),plot_points=[80,80]).show(aspect_ratio=(1,1,1)) """ return plot3d(f, urange, vrange, transformation=Cylindrical('radius', ['azimuth', 'height']), **kwds) | 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... | 6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/6a6b82f7e5f5e44ecfe79fc9e370831de7c2ec87/plot3d.py |
assert z.denominator() == 1, "bug in global_integral_model: %s" % ai | assert z.is_integral(), "bug in global_integral_model: %s" % list(ai) | def global_integral_model(self): r""" Return a model of self which is integral at all primes. EXAMPLES:: | 1e1b84dfb562091e50358476d5081739bd059460 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/1e1b84dfb562091e50358476d5081739bd059460/ell_number_field.py |
SL(n); you also some information about representations of E6 | SL(n); you also lose some information about representations of E6 | def WeylCharacterRing(ct, base_ring=ZZ, prefix=None, cache=False, style="lattice"): r""" A class for rings of Weyl characters. The Weyl character is a character of a semisimple (or reductive) Lie group or algebra. They form a ring, in which the addition and multiplication correspond to direct sum and tensor product of ... | b52994188bcd78a4f611d59c6a1849a3a6aff83e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/b52994188bcd78a4f611d59c6a1849a3a6aff83e/weyl_characters.py |
"automorphic", "symmetric", "extended", "triality" or "miscellaneous". The use of these rules will be explained next. After the examples we will explain how to write your own branching rules for cases that we have omitted. | "automorphic", "symmetric", "extended", "orthogonal_sum", "tensor", "triality" or "miscellaneous". The use of these rules will be explained next. After the examples we will explain how to write your own branching rules for cases that we have omitted. | def branch_weyl_character(chi, R, S, rule="default"): r""" A Branching rule describes the restriction of representations from a Lie group or algebra G to a smaller one. See for example, R. C. King, Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A 8 (1975), 429-449, Howe, Tan and Will... | b52994188bcd78a4f611d59c6a1849a3a6aff83e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/b52994188bcd78a4f611d59c6a1849a3a6aff83e/weyl_characters.py |
SYMMETRIC TYPE. Related to the automorphic type, when either the Dynkin diagram or the extended diagram has a symmetry there is a branching rule to the subalgebra (or subgroup) of invariants under the automorphism. Use rule="symmetric". | SYMMETRIC TYPE. Related to the automorphic type, when G admits an outer automorphism (usually of degree 2) we may consider the branching rule to the isotropy subgroup H. In many cases the Dynkin diagram of H can be obtained by folding the Dynkin diagram of G. For such isotropy subgroups use rule="symmetric". | def branch_weyl_character(chi, R, S, rule="default"): r""" A Branching rule describes the restriction of representations from a Lie group or algebra G to a smaller one. See for example, R. C. King, Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A 8 (1975), 429-449, Howe, Tan and Will... | b52994188bcd78a4f611d59c6a1849a3a6aff83e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/b52994188bcd78a4f611d59c6a1849a3a6aff83e/weyl_characters.py |
Using rule="extended" you can get any branching rule SO(n) => SO(a) x SO(b) x SO(c) x ... where n = a+b+c+ ... Sp(2n) => Sp(2a) x Sp(2b) x Sp(2c) x ... where n = a+b+c+ ... where O(a) = ['D',r] (a=2r) or ['B',r] (a=2r+1) and Sp(2r)=['C',r]. | def branch_weyl_character(chi, R, S, rule="default"): r""" A Branching rule describes the restriction of representations from a Lie group or algebra G to a smaller one. See for example, R. C. King, Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A 8 (1975), 429-449, Howe, Tan and Will... | b52994188bcd78a4f611d59c6a1849a3a6aff83e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/b52994188bcd78a4f611d59c6a1849a3a6aff83e/weyl_characters.py | |
elif rule == "extended": if not s == r: | elif rule == "extended" or rule == "orthogonal_sum": if rule == "extended" and not s == r: | def rule(x) : x[len(x)-1] = -x[len(x)-1]; return x | b52994188bcd78a4f611d59c6a1849a3a6aff83e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/b52994188bcd78a4f611d59c6a1849a3a6aff83e/weyl_characters.py |
if x == 0: | if x == 0 and not x in self._space: | def __call__(self, *args): """ Coerces the element into the ring. INPUT: - ``x`` - a ring element EXAMPLES:: sage: a2 = WeightRing(WeylCharacterRing(['A',2])) sage: a2(-1) -a2(0,0,0) """ if len(args) == 1: x = args[0] else: x = args if x == 0: return WeightRingElement(self, {}) if x in ZZ: mdict = {self._origin:... | b52994188bcd78a4f611d59c6a1849a3a6aff83e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/b52994188bcd78a4f611d59c6a1849a3a6aff83e/weyl_characters.py |
sage: G = matrix(GF(2),[[1,0,0],[1,1,0]]) sage: C = LinearCode(G) sage: C.dimension() 2 | sage: G = matrix(GF(2),[[1,0,0],[1,1,0]]) sage: C = LinearCode(G) sage: C.dimension() 2 | def dimension(self): r""" Returns the dimension of this code. EXAMPLES:: sage: G = matrix(GF(2),[[1,0,0],[1,1,0]]) sage: C = LinearCode(G) sage: C.dimension() 2 """ return self.__dim | f1481b520156da7cdd4d6adefe31299a038fab0a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/f1481b520156da7cdd4d6adefe31299a038fab0a/linear_code.py |
Returns the Duursama data `v` and `m` of this formally s.d. code `C` | Returns the Duursma data `v` and `m` of this formally s.d. code `C` | def sd_duursma_data(C, i): r""" Returns the Duursama data `v` and `m` of this formally s.d. code `C` and the type number `i` in (1,2,3,4). Does *not* check if this code is actually sd. INPUT: - ``i`` - Type number OUTPUT: - Pair ``(v, m)`` as in Duursama [D]_ REFERENCES: - [D] - I. Duursma, "Extremal weight enum... | f1481b520156da7cdd4d6adefe31299a038fab0a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/f1481b520156da7cdd4d6adefe31299a038fab0a/linear_code.py |
- Pair ``(v, m)`` as in Duursama [D]_ | - Pair ``(v, m)`` as in Duursma [D]_ | def sd_duursma_data(C, i): r""" Returns the Duursama data `v` and `m` of this formally s.d. code `C` and the type number `i` in (1,2,3,4). Does *not* check if this code is actually sd. INPUT: - ``i`` - Type number OUTPUT: - Pair ``(v, m)`` as in Duursama [D]_ REFERENCES: - [D] - I. Duursma, "Extremal weight enum... | f1481b520156da7cdd4d6adefe31299a038fab0a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/f1481b520156da7cdd4d6adefe31299a038fab0a/linear_code.py |
- [D] - I. Duursma, "Extremal weight enumerators and ultraspherical polynomials" | .. [D] I. Duursma, "Extremal weight enumerators and ultraspherical polynomials" | def sd_duursma_data(C, i): r""" Returns the Duursama data `v` and `m` of this formally s.d. code `C` and the type number `i` in (1,2,3,4). Does *not* check if this code is actually sd. INPUT: - ``i`` - Type number OUTPUT: - Pair ``(v, m)`` as in Duursama [D]_ REFERENCES: - [D] - I. Duursma, "Extremal weight enum... | f1481b520156da7cdd4d6adefe31299a038fab0a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/f1481b520156da7cdd4d6adefe31299a038fab0a/linear_code.py |
- Coefficients `q_0, q_1, ...` of `q(T)` as in Duursama [D]_ | - Coefficients `q_0, q_1, ...` of `q(T)` as in Duursma [D]_ | def sd_duursma_q(C,i,d0): r""" INPUT: - ``C`` - sd code; does *not* check if `C` is actually an sd code - ``i`` - Type number, one of 1,2,3,4 - ``d0`` - Divisor, the smallest integer such that each `A_i > 0` iff `i` is divisible by `d0` OUTPUT: - Coefficients `q_0, q_1, ...` of `q(T)` as in Duursama [D]_ REFEREN... | f1481b520156da7cdd4d6adefe31299a038fab0a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/f1481b520156da7cdd4d6adefe31299a038fab0a/linear_code.py |
'How big the point is.' | 'How big the point is (i.e., area in points^2=(1/72 inch)^2).' | def _allowed_options(self): """ Return the allowed options for the Point class. | 8f9c28d814253042e193c64fe9c63ee15b32aacb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8f9c28d814253042e193c64fe9c63ee15b32aacb/point.py |
'size': 'How big the point is.', | 'size': 'How big the point is (i.e., area in points^2=(1/72 inch)^2).', | def _allowed_options(self): """ Return the allowed options for the Point class. | 8f9c28d814253042e193c64fe9c63ee15b32aacb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8f9c28d814253042e193c64fe9c63ee15b32aacb/point.py |
def point(points, **kwds): """ Returns either a 2-dimensional or 3-dimensional point or sum of points. INPUT: - ``points`` - either a single point (as a tuple) or a list of points. For information regarding additional arguments, see either point2d? or point3d?. EXAMPLES:: sage: point((1,2)) sage: point((1,2,3)) s... | 8f9c28d814253042e193c64fe9c63ee15b32aacb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8f9c28d814253042e193c64fe9c63ee15b32aacb/point.py | ||
img = self(letter) | img = self.image(letter) | def is_identity(self): r""" Returns ``True`` if ``self`` is the identity morphism. EXAMPLES:: | 1680aa30535c96273945f9221b43e9446ab94d05 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/1680aa30535c96273945f9221b43e9446ab94d05/morphism.py |
sage: K.<a> = NumberField(polygen(QQ)) sage: K._S_class_group_and_units( (K.ideal(5),) ) ([5, -1], []) | def _S_class_group_and_units(self, S, proof=True): """ Compute S class group and units. INPUT: - ``S`` - a tuple of primes of the base field - ``proof`` - if False, assume Pari's GRH++ in computing the class group OUTPUT: - ``units, clgp_gens``, where: - ``units`` - A list of generators of the unit group. - ``cl... | 833988df1fc989b4d40636261251b29552777642 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/833988df1fc989b4d40636261251b29552777642/number_field.py | |
""" | r""" | def selmer_group(self, S, m, proof=True): """ Compute the Selmer group `K(S,m)`, which is defined to be the subgroup of `K^\times/(K^\times)^m` consisting of elements `a` such that `K(\sqrt[m]{a})/K` is unramified at all primes of `K` lying above a place outside of `S`. INPUT: - ``S`` - A set of primes of self. - ``... | 833988df1fc989b4d40636261251b29552777642 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/833988df1fc989b4d40636261251b29552777642/number_field.py |
raise ValueError, "n must be greater than lbound: %s"%(lbound) | raise ValueError, "n must be at least lbound: %s"%(lbound) | def random_prime(n, proof=None, lbound=2): """ Returns a random prime p between `lbound` and n (i.e. `lbound <= p <= n`). The returned prime is chosen uniformly at random from the set of prime numbers less than or equal to n. INPUT: - ``n`` - an integer >= 2. - ``proof`` - bool or None (default: None) If False, th... | f8af711701bc089bc1b8de230c2f1e8220eef67e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/f8af711701bc089bc1b8de230c2f1e8220eef67e/arith.py |
return ZZ(n) | return n lbound = max(2, lbound) if lbound > 2: if lbound == 3 or n <= 2*lbound - 2: if lbound < 25 or n <= 6*lbound/5: if lbound < 2010760 or n <= 16598*lbound/16597: if proof: smallest_prime = ZZ(lbound-1).next_prime() else: smallest_prime = ZZ(lbound-1).next_probable_prime() if smallest_prime > n: raise ValueErro... | def random_prime(n, proof=None, lbound=2): """ Returns a random prime p between `lbound` and n (i.e. `lbound <= p <= n`). The returned prime is chosen uniformly at random from the set of prime numbers less than or equal to n. INPUT: - ``n`` - an integer >= 2. - ``proof`` - bool or None (default: None) If False, th... | f8af711701bc089bc1b8de230c2f1e8220eef67e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/f8af711701bc089bc1b8de230c2f1e8220eef67e/arith.py |
if not proof: prime_test = is_pseudoprime else: prime_test = is_prime randint = current_randstate().python_random().randint while(1): p = randint(lbound,n) if prime_test(p): return ZZ(p) | prime_test = is_pseudoprime randint = current_randstate().python_random().randint while True: p = randint(lbound, n) if prime_test(p): return ZZ(p) | def random_prime(n, proof=None, lbound=2): """ Returns a random prime p between `lbound` and n (i.e. `lbound <= p <= n`). The returned prime is chosen uniformly at random from the set of prime numbers less than or equal to n. INPUT: - ``n`` - an integer >= 2. - ``proof`` - bool or None (default: None) If False, th... | f8af711701bc089bc1b8de230c2f1e8220eef67e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/f8af711701bc089bc1b8de230c2f1e8220eef67e/arith.py |
""" | r""" | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. | INPUT: - ``extend`` -- boolean (default: True) decides if base field extensions should be considered or not. | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
We compute the eigenvalues of an endomorphism of QQ^3:: | We compute the eigenvalues of an endomorphism of `\QQ^3`:: | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
Note the effect of the extend option:: | Note the effect of the ``extend`` option:: | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py | ||
- extend (True) decides if base field extensions should be considered or not. | - ``extend`` -- boolean (default: True) decides if base field extensions should be considered or not. | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors, and the algebraic multiplicity of the eigenvalue. | A sequence of tuples. Each tuple contains an eigenvalue, a sequence with a basis of the corresponding subspace of eigenvectors, and the algebraic multiplicity of the eigenvalue. | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
[(3, [(0, 0, 1, -6/7)], 1), (-1*I, [(1, 1*I, 0, -0.571428571428572? + 2.428571428571429?*I)], 1), (1*I, [(1, -1*I, 0, -0.571428571428572? - 2.428571428571429?*I)], 1)] | [(3, [ (0, 0, 1, -6/7) ], 1), (-1*I, [ (1, 1*I, 0, -0.571428571428572? + 2.428571428571429?*I) ], 1), (1*I, [ (1, -1*I, 0, -0.571428571428572? - 2.428571428571429?*I) ], 1)] | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
[(3, [(0, 0, 1, -6/7)], 1)] | [(3, [ (0, 0, 1, -6/7) ], 1)] | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
[(3, [(0, 0, 1, -6/7)], 1), (2, [(0, 1, 0, 17/7)], 2)] | [(3, [ (0, 0, 1, -6/7) ], 1), (2, [ (0, 1, 0, 17/7) ], 2)] | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
[(3, [(0, 0, 1, -6/7)], 1), (2, [(0, 1, 0, 17/7)], 2)] | [(3, [ (0, 0, 1, -6/7) ], 1), (2, [ (0, 1, 0, 17/7) ], 2)] | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
svectors=map(lambda j: V(j * V.basis_matrix()),i[1]) resu.append(tuple([i[0],svectors,i[2]])) | svectors=Sequence(map(lambda j: V(j * V.basis_matrix()),i[1]), cr=True) resu.append((i[0],svectors,i[2])) | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
- ``var`` - string (default: 'x') a variable | - ``var`` - string (default: 'x') a variable name | def minpoly(self,var='x'): """ Computes the minimal polynomial. INPUT: - ``var`` - string (default: 'x') a variable OUTPUT: polynomial in var - the minimal polynomial of the endomorphism. EXAMPLES: Compute the minimal polynomial, and check it :: sage: V=GF(7)^3 sage: H=V.Hom(V)([[0,1,2],[-1,0,3],[2,4,1]]) sage:... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
raise TypeError, "not an endomorphism" | raise TypeError, "not an endomorphism" | def minpoly(self,var='x'): """ Computes the minimal polynomial. INPUT: - ``var`` - string (default: 'x') a variable OUTPUT: polynomial in var - the minimal polynomial of the endomorphism. EXAMPLES: Compute the minimal polynomial, and check it :: sage: V=GF(7)^3 sage: H=V.Hom(V)([[0,1,2],[-1,0,3],[2,4,1]]) sage:... | 9bb09580aa7e219d556bbf2e0ec6c8440ac569f7 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/9bb09580aa7e219d556bbf2e0ec6c8440ac569f7/free_module_morphism.py |
def CharacteristicSturmianWord(self, cf, alphabet=(0, 1), bits=None): r""" Returns the characteristic Sturmian word of the given slope ``cf``. The `n`-th term of the characteristic Sturmian word of an irrational slope `\alpha` is `\lfloor\alpha(n+1)\rfloor - \lfloor\alpha n\rfloor + \lfloor\alpha\rfloor`. [1] | def CharacteristicSturmianWord(self, slope, alphabet=(0, 1), bits=None): r""" Returns the characteristic Sturmian word (also called standard Sturmian word) of given slope. Over a binary alphabet `\{a,b\}`, the characteristic Sturmian word `c_\alpha` of slope `\alpha` is the infinite word satisfying `s_{\alpha,0} = ac_... | def CharacteristicSturmianWord(self, cf, alphabet=(0, 1), bits=None): r""" Returns the characteristic Sturmian word of the given slope ``cf``. | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
- ``cf`` - the slope of the word. It can be one of the following : | - ``slope`` - the slope of the word. It can be one of the following : | def CharacteristicSturmianWord(self, cf, alphabet=(0, 1), bits=None): r""" Returns the characteristic Sturmian word of the given slope ``cf``. | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
- ``bits`` - integer (optional and considered only if ``cf`` is a real number) the number of bits to consider when computing the | - ``bits`` - integer (optional and considered only if ``slope`` is a real number) the number of bits to consider when computing the | def CharacteristicSturmianWord(self, cf, alphabet=(0, 1), bits=None): r""" Returns the characteristic Sturmian word of the given slope ``cf``. | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
slope `\alpha` is the limit of the sequence: `s_0 = 1`, `s_1 = 0` | slope `\alpha` is the limit of the sequence: `s_0 = b`, `s_1 = a` | def CharacteristicSturmianWord(self, cf, alphabet=(0, 1), bits=None): r""" Returns the characteristic Sturmian word of the given slope ``cf``. | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
The characteristic sturmian word of slope `(\sqrt(3)-1)/2`:: | The characteristic sturmian word of slope `(\sqrt{3}-1)/2`:: | sage: def cf(): | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
`(\sqrt(3)-1)/2`:: | `(\sqrt{3}-1)/2`:: | sage: def cf(): | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
sturmian word of slope `(\sqrt(3)-1)/2`:: | sturmian word of slope `(\sqrt{3}-1)/2`:: | sage: def cf(): | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
NotImplementedError: The argument cf (=5/4) must be in ]0,1[. | ValueError: The argument slope (=5/4) must be in ]0,1[. | sage: def cf(): | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
if cf in RR: if not 0 < cf < 1: msg = "The argument cf (=%s) must be in ]0,1[."%cf raise NotImplementedError, msg | if slope in RR: if not 0 < slope < 1: msg = "The argument slope (=%s) must be in ]0,1[."%slope raise ValueError, msg | sage: def cf(): | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
cf = iter(CFF(cf, bits=bits)) | cf = iter(CFF(slope, bits=bits)) | sage: def cf(): | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
elif hasattr(cf, '__iter__'): cf = iter(cf) | elif hasattr(slope, '__iter__'): cf = iter(slope) | sage: def cf(): | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
raise TypeError("cf (=%s) must be a real number"%cf + | raise TypeError("slope (=%s) must be a real number"%slope + | sage: def cf(): | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
Returns the lower mechanical word. The word `s_{\alpha,\rho}` is the *lower mechanical word* with slope `\alpha` and intercept `\rho` defined by | Returns the lower mechanical word with slope `\alpha` and intercept `\rho` The lower mechanical word `s_{\alpha,\rho}` with slope `\alpha` and intercept `\rho` is defined by | def LowerMechanicalWord(self, alpha, rho=0, alphabet=None): r""" Returns the lower mechanical word. | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
\lfloor\alpha n + \rho\rfloor`. [1] | \lfloor\alpha n + \rho\rfloor` [1]. | def LowerMechanicalWord(self, alpha, rho=0, alphabet=None): r""" Returns the lower mechanical word. | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
raise NotImplementedError, msg | raise ValueError, msg | def LowerMechanicalWord(self, alpha, rho=0, alphabet=None): r""" Returns the lower mechanical word. | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
Returns the upper mechanical word. The word `s'_{\alpha,\rho}` is the *upper mechanical word* with slope `\alpha` and intercept `\rho` defined by | Returns the upper mechanical word with slope `\alpha` and intercept `\rho` The upper mechanical word `s'_{\alpha,\rho}` with slope `\alpha` and intercept `\rho` is defined by | def UpperMechanicalWord(self, alpha, rho=0, alphabet=None): r""" Returns the upper mechanical word. | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
raise NotImplementedError, msg | raise ValueError, msg | def UpperMechanicalWord(self, alpha, rho=0, alphabet=None): r""" Returns the upper mechanical word. | a5b928a04b88cb182372bb9a126740cba8c57ec9 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/a5b928a04b88cb182372bb9a126740cba8c57ec9/word_generators.py |
occured. Please put there the version of sageq at the time of deprecation. | occurred. Please put there the version of sage at the time of deprecation. | def deprecation(message, version=None): r""" Issue a deprecation warning. INPUT: - ``message`` - an explanation why things are deprecated and by what it should be replaced. - ``version`` - (optional) on which version and when the deprecation occured. Please put there the version of sageq at the time of deprecation. ... | b71f787ebeb60368a6fd10dd72fd720b8414ea3c /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/b71f787ebeb60368a6fd10dd72fd720b8414ea3c/misc.py |
A wrapper around methods or functions wich automatically print the correct | A wrapper around methods or functions which automatically print the correct | sage: def bar(): | b71f787ebeb60368a6fd10dd72fd720b8414ea3c /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/b71f787ebeb60368a6fd10dd72fd720b8414ea3c/misc.py |
sage: def is_4regular(G): ... D = G.degree_sequence() ... return all(d == 4 for d in D) sage: is_4regular(G) | sage: G.is_regular(4) | sage: def is_4regular(G): | d0b299777a1d933e2d50ac19e0a3ed2fea5c664c /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d0b299777a1d933e2d50ac19e0a3ed2fea5c664c/graph_generators.py |
xy_data_arrays = map(lambda g: [[g(x, y) for x in xsrange(*ranges[0], include_endpoint=True)] for y in xsrange(*ranges[1], include_endpoint=True)], g) xy_data_array = map(lambda *rows: map(lambda *vals: mangle_neg(vals), *rows), *xy_data_arrays) | xy_data_arrays = numpy.asarray([[[func(x, y) for x in xsrange(*ranges[0], include_endpoint=True)] for y in xsrange(*ranges[1], include_endpoint=True)] for func in g],dtype=float) xy_data_array=numpy.abs(xy_data_arrays.prod(axis=0)) neg_indices = (xy_data_arrays<0).all(axis=0) xy_data_array[neg_indices]=-xy_data_array... | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth): 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), (ymin, ym... | 98d332aa4388605d75a37f824a43a7ac50c110c0 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/98d332aa4388605d75a37f824a43a7ac50c110c0/contour_plot.py |
def mangle_neg(vals): """ Returns the product of all values in vals, with the result nonnegative if any of the values is nonnegative. EXAMPLES:: sage: from sage.plot.contour_plot import mangle_neg sage: mangle_neg([-1.2, -0.74, -2.56, -1.01]) -2.29601280000000 sage: mangle_neg([-1.2, 0.0, -2.56]) 0.000000000000000 s... | def equify(f): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x^2 - 2 sage: equify(x^2 > 2) -x^2 + 2 sage: equify(x*y > 1) -x*y + 1 sage: equify(... | 98d332aa4388605d75a37f824a43a7ac50c110c0 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/98d332aa4388605d75a37f824a43a7ac50c110c0/contour_plot.py | |
if P.eval("%s %s %s"%(self.name(), P._equality_symbol(), other.name())) == P._true_symbol(): return 0 elif P.eval("%s %s %s"%(self.name(), P._lessthan_symbol(), other.name())) == P._true_symbol(): return -1 elif P.eval("%s %s %s"%(self.name(), P._greaterthan_symbol(), other.name())) == P._true_symbol(): return 1 | try: if P.eval("%s %s %s"%(self.name(), P._equality_symbol(), other.name())) == P._true_symbol(): return 0 except RuntimeError: pass try: if P.eval("%s %s %s"%(self.name(), P._lessthan_symbol(), other.name())) == P._true_symbol(): return -1 except RuntimeError: pass try: if P.eval("%s %s %s"%(self.name(), P._greatertha... | def __cmp__(self, other): P = self.parent() if P.eval("%s %s %s"%(self.name(), P._equality_symbol(), other.name())) == P._true_symbol(): return 0 elif P.eval("%s %s %s"%(self.name(), P._lessthan_symbol(), other.name())) == P._true_symbol(): return -1 elif P.eval("%s %s %s"%(self.name(), P._greaterthan_symbol(), other.n... | f6bba5b7c5e29901f4bdb654837918cf9694bc98 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/f6bba5b7c5e29901f4bdb654837918cf9694bc98/expect.py |
sage: P4 = simplicial_complexes.RealProjectiveSpace(4) sage: P4.f_vector() | sage: P4 = simplicial_complexes.RealProjectiveSpace(4) sage: P4.f_vector() | def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | 48bcc4068d651cff86f439b3ba106c1b2aa53157 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/48bcc4068d651cff86f439b3ba106c1b2aa53157/examples.py |
sage: P4.homology() | sage: P4.homology() | def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | 48bcc4068d651cff86f439b3ba106c1b2aa53157 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/48bcc4068d651cff86f439b3ba106c1b2aa53157/examples.py |
sage: P5.homology() | The following computation can take a long time -- over half an hour -- with Sage's default computation of homology groups, but if you have CHomP installed, Sage will use that and the computation should only take a second or two. (You can download CHomP from http://chomp.rutgers.edu/, or you can install it as a Sage p... | def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | 48bcc4068d651cff86f439b3ba106c1b2aa53157 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/48bcc4068d651cff86f439b3ba106c1b2aa53157/examples.py |
sage: P4.dimension() | sage: P4.dimension() | def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | 48bcc4068d651cff86f439b3ba106c1b2aa53157 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/48bcc4068d651cff86f439b3ba106c1b2aa53157/examples.py |
self._error_re = re.compile('(Principal Value|debugmode|Incorrect syntax|Maxima encountered a Lisp error)') | self._error_re = re.compile('(Principal Value|debugmode|incorrect syntax|Maxima encountered a Lisp error)') | def __init__(self, script_subdirectory=None, logfile=None, server=None, init_code = None): """ Create an instance of the Maxima interpreter. | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py |
sage: maxima.eval('sage0: x == x;') | sage: maxima._eval_line('sage0: x == x;') | def _eval_line(self, line, allow_use_file=False, wait_for_prompt=True, reformat=True, error_check=True): """ EXAMPLES: We check that errors are correctly checked:: sage: maxima._eval_line('1+1;') '2' sage: maxima.eval('sage0: x == x;') Traceback (most recent call last): ... TypeError: error evaluating "sage0: x == x;... | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py |
TypeError: error evaluating "sage0: x == x;":... | TypeError: Error executing code in Maxima... | def _eval_line(self, line, allow_use_file=False, wait_for_prompt=True, reformat=True, error_check=True): """ EXAMPLES: We check that errors are correctly checked:: sage: maxima._eval_line('1+1;') '2' sage: maxima.eval('sage0: x == x;') Traceback (most recent call last): ... TypeError: error evaluating "sage0: x == x;... | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py |
self._expect_expr(self._display_prompt) pre_out = self._before() self._expect_expr() out = self._before() | assert line_echo.strip() == line.strip() self._expect_expr(self._display_prompt) out = self._before() | def _eval_line(self, line, allow_use_file=False, wait_for_prompt=True, reformat=True, error_check=True): """ EXAMPLES: We check that errors are correctly checked:: sage: maxima._eval_line('1+1;') '2' sage: maxima.eval('sage0: x == x;') Traceback (most recent call last): ... TypeError: error evaluating "sage0: x == x;... | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py |
self._error_check(line, pre_out) | def _eval_line(self, line, allow_use_file=False, wait_for_prompt=True, reformat=True, error_check=True): """ EXAMPLES: We check that errors are correctly checked:: sage: maxima._eval_line('1+1;') '2' sage: maxima.eval('sage0: x == x;') Traceback (most recent call last): ... TypeError: error evaluating "sage0: x == x;... | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py | |
def _eval_line(self, line, allow_use_file=False, wait_for_prompt=True, reformat=True, error_check=True): """ EXAMPLES: We check that errors are correctly checked:: sage: maxima._eval_line('1+1;') '2' sage: maxima.eval('sage0: x == x;') Traceback (most recent call last): ... TypeError: error evaluating "sage0: x == x;... | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py | ||
self._expect_expr() assert len(self._before())==0, 'Maxima expect interface is confused!' | def _eval_line(self, line, allow_use_file=False, wait_for_prompt=True, reformat=True, error_check=True): """ EXAMPLES: We check that errors are correctly checked:: sage: maxima._eval_line('1+1;') '2' sage: maxima.eval('sage0: x == x;') Traceback (most recent call last): ... TypeError: error evaluating "sage0: x == x;... | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py | |
i = o.rfind('(%o') return o[:i] | def _eval_line(self, line, allow_use_file=False, wait_for_prompt=True, reformat=True, error_check=True): """ EXAMPLES: We check that errors are correctly checked:: sage: maxima._eval_line('1+1;') '2' sage: maxima.eval('sage0: x == x;') Traceback (most recent call last): ... TypeError: error evaluating "sage0: x == x;... | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py | |
def _command_runner(self, command, s, redirect=True): """ Run ``command`` in a new Maxima session and return its output as an ``AsciiArtString``. If redirect is set to False, then the output of the command is not returned as a string. Instead, it behaves like os.system. This is used for interactive things like Maxima'... | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py | ||
for _ in range(3): | for _ in range(5): | def _command_runner(self, command, s, redirect=True): """ Run ``command`` in a new Maxima session and return its output as an ``AsciiArtString``. If redirect is set to False, then the output of the command is not returned as a string. Instead, it behaves like os.system. This is used for interactive things like Maxima'... | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py |
'5.20.1' | '5.22.1' | def version(self): """ Return the version of Maxima that Sage includes. EXAMPLES:: sage: maxima.version() '5.20.1' """ return maxima_version() | 18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/18bea2c8fdd74c7656bf4d7e11ecb828a4ecfd18/maxima.py |
def parse_deps(self, filename, verify=True): | def parse_deps(self, filename, ext_module, verify=True): | def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []... | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): | if not is_cython_file(filename): | def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []... | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
for idir in CYTHON_INCLUDE_DIRS: new_path = os.path.normpath(idir + base_dependency_name) | for idir in ext_module.include_dirs + CYTHON_INCLUDE_DIRS + include_dirs + extra_include_dirs: new_path = os.path.normpath(idir + '/' + base_dependency_name) | def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []... | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
if path[-2:] != '.h': raise IOError, "could not find dependency %s included in %s."%(path, filename) | msg = 'could not find dependency %s included in %s.'%(path, filename) if is_cython_file(filename): raise IOError, msg else: warnings.warn(msg+' I will assume it is a system C/C++ header.') | def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []... | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
def immediate_deps(self, filename): | def immediate_deps(self, filename, ext_module): | def immediate_deps(self, filename): """ Returns a list of files directly referenced by this file. """ if (filename not in self._deps or self.timestamp(filename) < self._last_parse[filename]): self._deps[filename] = self.parse_deps(filename) self._last_parse[filename] = self.timestamp(filename) return self._deps[filenam... | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
self._deps[filename] = self.parse_deps(filename) | self._deps[filename] = self.parse_deps(filename, ext_module) | def immediate_deps(self, filename): """ Returns a list of files directly referenced by this file. """ if (filename not in self._deps or self.timestamp(filename) < self._last_parse[filename]): self._deps[filename] = self.parse_deps(filename) self._last_parse[filename] = self.timestamp(filename) return self._deps[filenam... | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
def all_deps(self, filename, path=None): | def all_deps(self, filename, ext_module, path=None): | def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file. A recursive algorithm is used here to maximize caching, but it is still robust for circular cimports (via the path parameter). """ if filename not in self._deps_all: circular = False deps = set([filename]) if... | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
for f in self.immediate_deps(filename): | for f in self.immediate_deps(filename, ext_module): | def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file. A recursive algorithm is used here to maximize caching, but it is still robust for circular cimports (via the path parameter). """ if filename not in self._deps_all: circular = False deps = set([filename]) if... | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
deps.update(self.all_deps(f, path)) | deps.update(self.all_deps(f, ext_module, path)) | def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file. A recursive algorithm is used here to maximize caching, but it is still robust for circular cimports (via the path parameter). """ if filename not in self._deps_all: circular = False deps = set([filename]) if... | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
def newest_dep(self, filename): | def newest_dep(self, filename, ext_module): | def newest_dep(self, filename): """ Returns the most recently modified file that filename depends on, along with its timestamp. """ nfile = filename ntime = self.timestamp(filename) for f in self.all_deps(filename): if self.timestamp(f) > ntime: nfile = f ntime = self.timestamp(f) return nfile, ntime | 578b3dc4ae6572d8955745050879ff3bb3e0334a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/578b3dc4ae6572d8955745050879ff3bb3e0334a/setup.py |
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