bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def _discrete_log(self,x): # EVEN DUMBER IMPLEMENTATION! u = [y for y in self.list() if y.element() == x] if len(u) == 0: raise TypeError, "Not in group" if len(u) > 1: raise NotImplementedError return u[0] | def _discrete_log(self,x): # EVEN DUMBER IMPLEMENTATION! u = [y for y in self.list() if y.element() == x] if len(u) == 0: raise TypeError, "Not in group" if len(u) > 1: raise NotImplementedError return u[0] | 459,700 |
def cardinality(self): """ Returns the cardinality of this disjoint union. | def cardinality(self): """ Returns the cardinality of this disjoint union. | 459,701 |
def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. :: sage: magma(MatrixSpace(QQ,3)) # optional - magma Full Matrix Algebra of degree 3 over Rational Field :: sage: magma(MatrixSpace(Integers(8),2,3)) # optional - magma Full RMatrixSpace of 2 by 3 matrices ... | def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. :: sage: magma(MatrixSpace(QQ,3)) # optional - magma Full Matrix Algebra of degree 3 over Rational Field :: sage: magma(MatrixSpace(Integers(8),2,3)) # optional - magma Full RMatrixSpace of 2 by 3 matrices ... | 459,702 |
def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. :: sage: magma(MatrixSpace(QQ,3)) # optional - magma Full Matrix Algebra of degree 3 over Rational Field :: sage: magma(MatrixSpace(Integers(8),2,3)) # optional - magma Full RMatrixSpace of 2 by 3 matrices ... | def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. :: sage: magma(MatrixSpace(QQ,3)) # optional - magma Full Matrix Algebra of degree 3 over Rational Field :: sage: magma(MatrixSpace(Integers(8),2,3)) # optional - magma Full RMatrixSpace of 2 by 3 matrices ... | 459,703 |
def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. :: sage: magma(MatrixSpace(QQ,3)) # optional - magma Full Matrix Algebra of degree 3 over Rational Field :: sage: magma(MatrixSpace(Integers(8),2,3)) # optional - magma Full RMatrixSpace of 2 by 3 matrices ... | def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. :: sage: magma(MatrixSpace(QQ,3)) # optional - magma Full Matrix Algebra of degree 3 over Rational Field :: sage: magma(MatrixSpace(Integers(8),2,3)) # optional - magma Full RMatrixSpace of 2 by 3 matrices ... | 459,704 |
def _subdivide_palp(self, new_rays, verbose): r""" Subdivide ``self`` adding ``new_rays`` one by one. | def _subdivide_palp(self, new_rays, verbose): r""" Subdivide ``self`` adding ``new_rays`` one by one. | 459,705 |
def _subdivide_palp(self, new_rays, verbose): r""" Subdivide ``self`` adding ``new_rays`` one by one. | def _subdivide_palp(self, new_rays, verbose): r""" Subdivide ``self`` adding ``new_rays`` one by one. | 459,706 |
def is_Gamma0_equivalent(self, other, N, Transformation=False): r""" Checks if cusps ``self`` and ``other`` are `\Gamma_0(N)`- equivalent. | def is_Gamma0_equivalent(self, other, N, Transformation=False): r""" Checks if cusps ``self`` and ``other`` are `\Gamma_0(N)`- equivalent. | 459,707 |
def NumberField(polynomial, name=None, check=True, names=None, cache=True, embedding=None, latex_name=None): r""" Return *the* number field defined by the given irreducible polynomial and with variable with the given name. If check is True (the default), also verify that the defining polynomial is irreducible and over ... | def NumberField(polynomial, name=None, check=True, names=None, cache=True, embedding=None, latex_name=None): r""" Return *the* number field defined by the given irreducible polynomial and with variable with the given name. If check is True (the default), also verify that the defining polynomial is irreducible and over ... | 459,708 |
def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | def QuadraticField(D, names, check=True, embedding=True, latex_name='sqrt'): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ... | 459,709 |
def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | 459,710 |
def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | 459,711 |
def rim(self): r""" Returns the rim of ``self`` | def rim(self): r""" Returns the rim of ``self`` | 459,712 |
def rim(self): r""" Returns the rim of ``self`` | def rim(self): r""" Returns the rim of ``self`` | 459,713 |
def outer_rim(self): """ Returns the outer rim of ``self`` | def outer_rim(self): """ Returns the outer rim of ``self`` | 459,714 |
def outer_rim(self): """ Returns the outer rim of ``self`` | def outer_rim(self): """ Returns the outer rim of ``self`` | 459,715 |
def desolve(de, dvar, ics=None, ivar=None, show_method=False, contrib_ode=False): """ Solves a 1st or 2nd order linear ODE via maxima. Including IVP and BVP. *Use* ``desolve? <tab>`` *if the output in truncated in notebook.* INPUT: - ``de`` - an expression or equation representing the ODE - ``dvar`` - the dependent... | def desolve(de, dvar, ics=None, ivar=None, show_method=False, contrib_ode=False): """ Solves a 1st or 2nd order linear ODE via maxima. Including IVP and BVP. *Use* ``desolve? <tab>`` *if the output in truncated in notebook.* INPUT: - ``de`` - an expression or equation representing the ODE - ``dvar`` - the dependent... | 459,716 |
def desolve(de, dvar, ics=None, ivar=None, show_method=False, contrib_ode=False): """ Solves a 1st or 2nd order linear ODE via maxima. Including IVP and BVP. *Use* ``desolve? <tab>`` *if the output in truncated in notebook.* INPUT: - ``de`` - an expression or equation representing the ODE - ``dvar`` - the dependent... | def desolve(de, dvar, ics=None, ivar=None, show_method=False, contrib_ode=False): """ Solves a 1st or 2nd order linear ODE via maxima. Including IVP and BVP. *Use* ``desolve? <tab>`` *if the output in truncated in notebook.* INPUT: - ``de`` - an expression or equation representing the ODE - ``dvar`` - the dependent... | 459,717 |
def desolve_system_strings(des,vars,ics=None): """ Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: de -- a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") vars -- a list of strings representing the variables (eg, vars = [... | def desolve_system_strings(des,vars,ics=None): r""" Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: de -- a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") vars -- a list of strings representing the variables (eg, vars = ... | 459,718 |
def desolve_system_strings(des,vars,ics=None): """ Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: de -- a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") vars -- a list of strings representing the variables (eg, vars = [... | def desolve_system_strings(des,vars,ics=None): """ Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: - ``de`` - a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") - ``vars`` - a list of strings representing the variables (eg, ... | 459,719 |
def desolve_system_strings(des,vars,ics=None): """ Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: de -- a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") vars -- a list of strings representing the variables (eg, vars = [... | def desolve_system_strings(des,vars,ics=None): """ Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: de -- a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") vars -- a list of strings representing the variables (eg, vars = [... | 459,720 |
def desolve_system_strings(des,vars,ics=None): """ Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: de -- a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") vars -- a list of strings representing the variables (eg, vars = [... | def desolve_system_strings(des,vars,ics=None): """ Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: de -- a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") vars -- a list of strings representing the variables (eg, vars = [... | 459,721 |
def desolve_system_strings(des,vars,ics=None): """ Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: de -- a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") vars -- a list of strings representing the variables (eg, vars = [... | def desolve_system_strings(des,vars,ics=None): """ Solves any size system of 1st order ODE's. Initials conditions are optional. INPUT: de -- a list of strings representing the ODEs in maxima notation (eg, de = "diff(f(x),x,2)=diff(f(x),x)+sin(x)") vars -- a list of strings representing the variables (eg, vars = [... | 459,722 |
def eulers_method(f,x0,y0,h,x1,method="table"): """ This implements Euler's method for finding numerically the solution of the 1st order ODE ``y' = f(x,y)``, ``y(a)=c``. The "x" column of the table increments from ``x0`` to ``x1`` by ``h`` (so ``(x1-x0)/h`` must be an integer). In the "y" column, the new y-value equals... | def eulers_method(f,x0,y0,h,x1,method="table"): r""" This implements Euler's method for finding numerically the solution of the 1st order ODE ``y' = f(x,y)``, ``y(a)=c``. The "x" column of the table increments from ``x0`` to ``x1`` by ``h`` (so ``(x1-x0)/h`` must be an integer). In the "y" column, the new y-value equal... | 459,723 |
def eulers_method_2x2(f,g, t0, x0, y0, h, t1,method="table"): """ This implements Euler's method for finding numerically the solution of the 1st order system of two ODEs ``x' = f(t, x, y), x(t0)=x0.`` ``y' = g(t, x, y), y(t0)=y0.`` The "t" column of the table increments from `t_0` to `t_1` by `h` (so `\\frac{t_1-t_0... | def eulers_method_2x2(f,g, t0, x0, y0, h, t1,method="table"): r""" This implements Euler's method for finding numerically the solution of the 1st order system of two ODEs ``x' = f(t, x, y), x(t0)=x0.`` ``y' = g(t, x, y), y(t0)=y0.`` The "t" column of the table increments from `t_0` to `t_1` by `h` (so `\\frac{t_1-t_... | 459,724 |
def eulers_method_2x2_plot(f,g, t0, x0, y0, h, t1): """ This plots the soln in the rectangle ``(xrange[0],xrange[1]) x (yrange[0],yrange[1])`` and plots using Euler's method the numerical solution of the 1st order ODEs `x' = f(t,x,y)`, `x(a)=x_0`, `y' = g(t,x,y)`, `y(a) = y_0`. *For pedagogical purposes only.* EXAMPL... | def eulers_method_2x2_plot(f,g, t0, x0, y0, h, t1): r""" Plots solution of ODE This plots the soln in the rectangle ``(xrange[0],xrange[1]) x (yrange[0],yrange[1])`` and plots using Euler's method the numerical solution of the 1st order ODEs `x' = f(t,x,y)`, `x(a)=x_0`, `y' = g(t,x,y)`, `y(a) = y_0`. *For pedagogical... | 459,725 |
def eulers_method_2x2_plot(f,g, t0, x0, y0, h, t1): """ This plots the soln in the rectangle ``(xrange[0],xrange[1]) x (yrange[0],yrange[1])`` and plots using Euler's method the numerical solution of the 1st order ODEs `x' = f(t,x,y)`, `x(a)=x_0`, `y' = g(t,x,y)`, `y(a) = y_0`. *For pedagogical purposes only.* EXAMPL... | def eulers_method_2x2_plot(f,g, t0, x0, y0, h, t1): """ This plots the soln in the rectangle ``(xrange[0],xrange[1]) x (yrange[0],yrange[1])`` and plots using Euler's method the numerical solution of the 1st order ODEs `x' = f(t,x,y)`, `x(a)=x_0`, `y' = g(t,x,y)`, `y(a) = y_0`. *For pedagogical purposes only.* EXAMPL... | 459,726 |
def eulers_method_2x2_plot(f,g, t0, x0, y0, h, t1): """ This plots the soln in the rectangle ``(xrange[0],xrange[1]) x (yrange[0],yrange[1])`` and plots using Euler's method the numerical solution of the 1st order ODEs `x' = f(t,x,y)`, `x(a)=x_0`, `y' = g(t,x,y)`, `y(a) = y_0`. *For pedagogical purposes only.* EXAMPL... | def eulers_method_2x2_plot(f,g, t0, x0, y0, h, t1): """ This plots the soln in the rectangle ``(xrange[0],xrange[1]) x (yrange[0],yrange[1])`` and plots using Euler's method the numerical solution of the 1st order ODEs `x' = f(t,x,y)`, `x(a)=x_0`, `y' = g(t,x,y)`, `y(a) = y_0`. *For pedagogical purposes only.* EXAMPL... | 459,727 |
def install_packages(self, package_name): """ Install an R package into Sage's R installation. | def install_packages(self, package_name): """ Install an R package into Sage's R installation. | 459,728 |
def install_packages(self, package_name): """ Install an R package into Sage's R installation. | def install_packages(self, package_name): """ Install an R package into Sage's R installation. | 459,729 |
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... | 459,730 |
def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using the Tachyon ray tracer. | def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using the Tachyon ray tracer. | 459,731 |
def obj_repr(self, render_params): """ Returns complete representation of the point as a sphere. | def obj_repr(self, render_params): """ Returns complete representation of the point as a sphere. | 459,732 |
def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using the Tachyon ray tracer. | def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using the Tachyon ray tracer. | 459,733 |
def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix with nonnegative real entries such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose ... | 459,734 |
def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | 459,735 |
def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | 459,736 |
def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | 459,737 |
def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | 459,738 |
def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | 459,739 |
def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | 459,740 |
def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | 459,741 |
def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | 459,742 |
def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | 459,743 |
def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | 459,744 |
def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | 459,745 |
def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False): """ Returns a polynomial of degree at most `degree` which is approximately satisfied by the number `z`. Note that the returned polynomial need not be irreducible, and indeed usually won't be if `z`... | 459,746 |
def is_pseudoprime_small_power(n, bound=1024, get_data=False): r""" Return True if `n` is a small power of a pseudoprime, and False otherwise. The result is *NOT* proven correct - *this IS a pseudo-primality test!*. If `get_data` is set to true and `n = p^d`, for a pseudoprime `p` and power `d`, return [(p, d)]. IN... | def is_pseudoprime_small_power(n, bound=1024, get_data=False): r""" Return True if `n` is a small power of a pseudoprime, and False otherwise. The result is *NOT* proven correct - *this IS a pseudo-primality test!*. If `get_data` is set to true and `n = p^d`, for a pseudoprime `p` and power `d`, return [(p, d)]. IN... | 459,747 |
def factor(n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds): """ Returns the factorization of n. The result depends on the type of n. If n is an integer, factor returns the factorization of the integer n as an object of type Factorization. If n is not an integer, ``n.factor(proof=proof, **kwds)`` gets ... | def factor(n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds): """ Returns the factorization of n. The result depends on the type of n. If n is an integer, factor returns the factorization of the integer n as an object of type Factorization. If n is not an integer, ``n.factor(proof=proof, **kwds)`` gets ... | 459,748 |
def rim(self): r""" Returns the rim of ``self`` | def rim(self): r""" Returns the rim of ``self`` | 459,749 |
def rim(self): r""" Returns the rim of ``self`` | def rim(self): r""" Returns the rim of ``self`` | 459,750 |
def outer_rim(self): """ Returns the outer rim of ``self`` | def outer_rim(self): """ Returns the outer rim of ``self`` | 459,751 |
def outer_rim(self): """ Returns the outer rim of ``self`` | def outer_rim(self): """ Returns the outer rim of ``self`` | 459,752 |
def module_morphism(self, on_basis = None, diagonal = None, triangular = None, **keywords): r""" Constructs morphisms by linearity | def module_morphism(self, on_basis = None, diagonal = None, triangular = None, **keywords): r""" Constructs morphisms by linearity | 459,753 |
def leading_item(self, cmp=None): r""" Returns the pair ``(k, c)`` where ``c`` * (the basis elt. indexed by ``k``) is the leading term of ``self``. | def leading_item(self, cmp=None): r""" Returns the pair ``(k, c)`` where ``c`` * (the basis elt. indexed by ``k``) is the leading term of ``self``. | 459,754 |
def leading_monomial(self, cmp=None): r""" Returns the leading monomial of ``self``. | def leading_monomial(self, cmp=None): r""" Returns the leading monomial of ``self``. | 459,755 |
def leading_coefficient(self, cmp=None): r""" Returns the leading coefficient of ``self``. | def leading_coefficient(self, cmp=None): r""" Returns the leading coefficient of ``self``. | 459,756 |
def leading_term(self, cmp=None): r""" Returns the leading term of ``self``. | def leading_term(self, cmp=None): r""" Returns the leading term of ``self``. | 459,757 |
def trailing_item(self, cmp=None): r""" Returns the pair ``(c, k)`` where ``c*self.parent().monomial(k)`` is the trailing term of ``self``. | def trailing_item(self, cmp=None): r""" Returns the pair ``(c, k)`` where ``c*self.parent().monomial(k)`` is the trailing term of ``self``. | 459,758 |
def trailing_monomial(self, cmp=None): r""" Returns the trailing monomial of ``self``. | def trailing_monomial(self, cmp=None): r""" Returns the trailing monomial of ``self``. | 459,759 |
def trailing_coefficient(self, cmp=None): r""" Returns the trailing coefficient of ``self``. | def trailing_coefficient(self, cmp=None): r""" Returns the trailing coefficient of ``self``. | 459,760 |
def trailing_term(self, cmp=None): r""" Returns the trailing term of ``self``. | def trailing_term(self, cmp=None): r""" Returns the trailing term of ``self``. | 459,761 |
def extra_super_categories(self): """ EXAMPLES:: | def extra_super_categories(self): """ EXAMPLES:: | 459,762 |
sage: def phi_on_basis(i): return Y.monomial(abs(i)) | sage: def phi_on_basis(i): return Y.monomial(abs(i)) | 459,763 |
sage: def phi_on_basis(i): return Y.monomial(abs(i)) | sage: def phi_on_basis(i): return Y.monomial(abs(i)) | 459,764 |
sage: def phi_on_basis(i): return Y.monomial(abs(i)) | sage: def phi_on_basis(i): return Y.monomial(abs(i)) | 459,765 |
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | 459,766 |
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | 459,767 |
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | 459,768 |
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | 459,769 |
def _compute_dim(self, compute_vertices): r""" Compute the dimension of this polytope and its vertices, if necessary. If ``compute_vertices`` is ``True``, then ``self._vertices`` should contain points whose convex hull will be computed and placed back into ``self._vertices``. If the dimension of this polytope is not ... | def _compute_dim(self, compute_vertices): r""" Compute the dimension of this polytope and its vertices, if necessary. If ``compute_vertices`` is ``True``, then ``self._vertices`` should contain points whose convex hull will be computed and placed back into ``self._vertices``. If ... | 459,770 |
def _compute_dim(self, compute_vertices): r""" Compute the dimension of this polytope and its vertices, if necessary. If ``compute_vertices`` is ``True``, then ``self._vertices`` should contain points whose convex hull will be computed and placed back into ``self._vertices``. If the dimension of this polytope is not ... | def _compute_dim(self, compute_vertices): r""" Compute the dimension of this polytope and its vertices, if necessary. If ``compute_vertices`` is ``True``, then ``self._vertices`` should contain points whose convex hull will be computed and placed back into ``self._vertices``. If the dimension of this polytope is not ... | 459,771 |
def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | 459,772 |
def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | 459,773 |
def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | 459,774 |
def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | 459,775 |
def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be orthogonal to the integer kernel of the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- th... | 459,776 |
def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | 459,777 |
def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | 459,778 |
def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | 459,779 |
def from_polynomial_exp(self, p): r""" Conversion from polynomial in exponential notation | def from_polynomial_exp(self, p): r""" Conversion from polynomial in exponential notation | 459,780 |
def __cmp__(self, right): r""" Compare ``self`` and ``right``. | def __cmp__(self, right): r""" Compare ``self`` and ``right``. | 459,781 |
sage: def maple_leaf(t): | sage: def maple_leaf(t): | 459,782 |
sage: def maple_leaf(t): | sage: def maple_leaf(t): | 459,783 |
sage: def maple_leaf(t): | sage: def maple_leaf(t): | 459,784 |
sage: def maple_leaf(t): | sage: def maple_leaf(t): | 459,785 |
def has_good_reduction(self, P=None): r""" Returns True iff this point has good reduction modulo a prime. | def has_good_reduction(self, P=None): r""" Returns True iff this point has good reduction modulo a prime. | 459,786 |
def has_good_reduction(self, P=None): r""" Returns True iff this point has good reduction modulo a prime. | def has_good_reduction(self, P=None): r""" Returns True iff this point has good reduction modulo a prime. | 459,787 |
def Set(X): r""" Create the underlying set of $X$. If $X$ is a list, tuple, Python set, or ``X.is_finite()`` is true, this returns a wrapper around Python's enumerated immutable frozenset type with extra functionality. Otherwise it returns a more formal wrapper. If you need the functionality of mutable sets, use Pyt... | def Set(X): r""" Create the underlying set of $X$. If $X$ is a list, tuple, Python set, or ``X.is_finite()`` is true, this returns a wrapper around Python's enumerated immutable frozenset type with extra functionality. Otherwise it returns a more formal wrapper. If you need the functionality of mutable sets, use Pyt... | 459,788 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | @rename_keyword(deprecated='Sage version 4.6.1', l='arg') def iter_morphisms(self, arg=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,789 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,790 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,791 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,792 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,793 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,794 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,795 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,796 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,797 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,798 |
def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, l=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 459,799 |
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