bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ Load and *execute* the content of ``filename`` in Macaulay2. :param filename: the name of the file to be loaded and executed. :type filename: string :returns: Macaulay2 command loading and executing commands in ``filename``, that is, ``'load "filename"'``. :rtype: string ... | 460,900 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("sage_test = 7;") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sa... | 460,901 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional sage: macaulay2.e... | 460,902 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | 460,903 |
def univariate_polynomial(self, R=None): """ Returns a univariate polynomial associated to this multivariate polynomial. INPUT: - ``R`` - (default: None) PolynomialRing If this polynomial is not in at most one variable, then a ValueError exception is raised. This is checked using the is_univariate() method. The n... | def univariate_polynomial(self, R=None): TESTS:: sage: P = PolynomialRing(QQ, 0, '') sage: P(5).univariate_polynomial() 5 """ if self.parent().ngens() == 0: if R is None: return self.base_ring()(self) else: return R(self) Returns a univariate polynomial associated to this multivariate polynomial. INPUT: - ``R`` ... | 460,904 |
def factor(self, proof=True): r""" Compute the irreducible factorization of this polynomial. INPUT: - ``proof'' - insist on provably correct results (ignored, always ``True``) ALGORITHM: Use univariate factorization code. If a polynomial is univariate, the appropriate univariate factorization code is called. :: s... | def if self == 0: raise ArithmeticError, "Prime factorization of 0 not defined." if R.ngens() == 0: base_ring = self.base_ring() if base_ring.is_field(): return Factorization([],unit=self.base_ring()(self)) else: F = base_ring(self).factor() return Factorization([(R(f),m) for f,m in F], unit=F.unit()) factor(self, ... | 460,905 |
... def variance(self, bias = False): | ... def variance(self, bias = False): | 460,906 |
def spherical_bessel_J(n, var, algorithm="maxima"): r""" Returns the spherical Bessel function of the first kind for integers n -1. Reference: AS 10.1.8 page 437 and AS 10.1.15 page 439. EXAMPLES:: sage: spherical_bessel_J(2,x) ((3/x^2 - 1)*sin(x) - 3*cos(x)/x)/x """ if algorithm=="scipy": import scipy.special ans =... | def spherical_bessel_J(n, var, algorithm="maxima"): r""" Returns the spherical Bessel function of the first kind for integers n >= 1. Reference: AS 10.1.8 page 437 and AS 10.1.15 page 439. EXAMPLES:: sage: spherical_bessel_J(2,x) ((3/x^2 - 1)*sin(x) - 3*cos(x)/x)/x """ if algorithm=="scipy": import scipy.special ans... | 460,907 |
def spherical_bessel_J(n, var, algorithm="maxima"): r""" Returns the spherical Bessel function of the first kind for integers n -1. Reference: AS 10.1.8 page 437 and AS 10.1.15 page 439. EXAMPLES:: sage: spherical_bessel_J(2,x) ((3/x^2 - 1)*sin(x) - 3*cos(x)/x)/x """ if algorithm=="scipy": import scipy.special ans =... | def spherical_bessel_J(n, var, algorithm="maxima"): r""" Returns the spherical Bessel function of the first kind for integers n -1. Reference: AS 10.1.8 page 437 and AS 10.1.15 page 439. EXAMPLES:: sage: spherical_bessel_J(2,x) ((3/x^2 - 1)*sin(x) - 3*cos(x)/x)/x """ if algorithm=="scipy": from scipy.special.specfun... | 460,908 |
'def identity_matrix' | 'def identity_matrix' | 460,909 |
def upgrade(): """ Download and build the latest version of Sage. You must have an internet connection. Also, you will have to restart Sage for the changes to take affect. This upgrades to the latest version of core packages (optional packages are not automatically upgraded). This will not work on systems that don't... | def upgrade(): """ Download and build the latest version of Sage. You must have an internet connection. Also, you will have to restart Sage for the changes to take affect. This upgrades to the latest version of core packages (optional packages are not automatically upgraded). This will not work on systems that don't... | 460,910 |
def global_integral_model(self): r""" Return a model of self which is integral at all primes. EXAMPLES:: | def global_integral_model(self): r""" Return a model of self which is integral at all primes. EXAMPLES:: | 460,911 |
def __init__(self, point, r, angle, options): """ Initializes base class Disk. | def __init__(self, point, r, angle, options): """ Initializes base class Disk. | 460,912 |
def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | 460,913 |
def _allowed_options(self): """ Return the allowed options for the Disk class. | def _allowed_options(self): """ Return the allowed options for the Disk class. | 460,914 |
def _repr_(self): """ String representation of Disk primitive. | def _repr_(self): """ String representation of Disk primitive. | 460,915 |
def plot3d(self, z=0, **kwds): """ Plots a 2D disk (actually a 52-gon) in 3D, with default height zero. | def plot3d(self, z=0, **kwds): """ Plots a 2D disk (actually a 52-gon) in 3D, with default height zero. | 460,916 |
def _add_(self, right): """ Add quotient ring element ``self`` to another quotient ring element, ``right``. If the quotient is `R/I`, the addition is carried out in `R` and then reduced to `R/I`. | def _add_(self, right): """ Add quotient ring element ``self`` to another quotient ring element, ``right``. If the quotient is `R/I`, the addition is carried out in `R` and then reduced to `R/I`. | 460,917 |
def _sub_(self, right): """ Subtract quotient ring element ``right`` from quotient ring element ``self``. If the quotient is `R/I`, the subtraction is carried out in `R` and then reduced to `R/I`. | def _sub_(self, right): """ Subtract quotient ring element ``right`` from quotient ring element ``self``. If the quotient is `R/I`, the subtraction is carried out in `R` and then reduced to `R/I`. | 460,918 |
def _mul_(self, right): """ Multiply quotient ring element ``self`` by another quotient ring element, ``right``. If the quotient is `R/I`, the multiplication is carried out in `R` and then reduced to `R/I`. | def _mul_(self, right): """ Multiply quotient ring element ``self`` by another quotient ring element, ``right``. If the quotient is `R/I`, the multiplication is carried out in `R` and then reduced to `R/I`. | 460,919 |
def __neg__(self): """ EXAMPLES:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class 'sage.rings.quotient_ring_element.QuotientRingElement'> sage: -a # indirect doctest -a sage: -(a+b) -a - b """ return QuotientRingElement(self.parent(), -self.__rep) | def __neg__(self): """ EXAMPLES:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class 'sage.rings.quotient_ring_element.QuotientRingElement'> sage: -a # indirect doctest -a sage: -(a+b) -a - b """ return self.parent()(-self.__rep) | 460,920 |
def __invert__(self): """ EXAMPLES:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class 'sage.rings.quotient_ring_element.QuotientRingElement'> sage: ~S(2/3) 3/2 | def __invert__(self): """ EXAMPLES:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class 'sage.rings.quotient_ring_element.QuotientRingElement'> sage: ~S(2/3) 3/2 | 460,921 |
def lt(self): """ Return the leading term of this quotient ring element. EXAMPLE:: sage: R.<x,y,z>=PolynomialRing(GF(7),3,order='lex') sage: I = sage.rings.ideal.FieldIdeal(R) sage: Q = R.quo( I ) sage: f = Q( z*y + 2*x ) sage: f.lt() 2*xbar | def lt(self): """ Return the leading term of this quotient ring element. EXAMPLE:: sage: R.<x,y,z>=PolynomialRing(GF(7),3,order='lex') sage: I = sage.rings.ideal.FieldIdeal(R) sage: Q = R.quo( I ) sage: f = Q( z*y + 2*x ) sage: f.lt() 2*xbar | 460,922 |
def lm(self): """ Return the leading monomial of this quotient ring element. EXAMPLE:: sage: R.<x,y,z>=PolynomialRing(GF(7),3,order='lex') sage: I = sage.rings.ideal.FieldIdeal(R) sage: Q = R.quo( I ) sage: f = Q( z*y + 2*x ) sage: f.lm() xbar TESTS:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class... | def lm(self): """ Return the leading monomial of this quotient ring element. EXAMPLE:: sage: R.<x,y,z>=PolynomialRing(GF(7),3,order='lex') sage: I = sage.rings.ideal.FieldIdeal(R) sage: Q = R.quo( I ) sage: f = Q( z*y + 2*x ) sage: f.lm() xbar TESTS:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class... | 460,923 |
def variables(self): """ EXAMPLES:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class 'sage.rings.quotient_ring_element.QuotientRingElement'> sage: a.variables() (a,) sage: b.variables() (b,) sage: s = a^2 + b^2 + 1; s 1 sage: s.variables() () sage: (a+b).variables() (a, b) """ return tuple([QuotientRin... | def variables(self): """ EXAMPLES:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class 'sage.rings.quotient_ring_element.QuotientRingElement'> sage: a.variables() (a,) sage: b.variables() (b,) sage: s = a^2 + b^2 + 1; s 1 sage: s.variables() () sage: (a+b).variables() (a, b) """ return tuple([QuotientRin... | 460,924 |
def monomials(self): """ EXAMPLES:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class 'sage.rings.quotient_ring_element.QuotientRingElement'> sage: a.monomials() [a] sage: (a+a*b).monomials() [a*b, a] """ return [QuotientRingElement(self.parent(),m) for m in self.__rep.monomials()] | def monomials(self): """ EXAMPLES:: sage: R.<x,y> = QQ[]; S.<a,b> = R.quo(x^2 + y^2); type(a) <class 'sage.rings.quotient_ring_element.QuotientRingElement'> sage: a.monomials() [a] sage: (a+a*b).monomials() [a*b, a] """ return [QuotientRingElement(self.parent(),m) for m in self.__rep.monomials()] | 460,925 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ Load and *execute* the content of ``filename`` in Macaulay2. :param filename: the name of the file to be loaded and executed. :type filename: string :returns: Macaulay2 command loading and executing commands in ``filename``, that is, ``'load "filename"'``. :rtype: string ... | 460,926 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("sage_test = 7;") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sa... | 460,927 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional sage: macaulay2.e... | 460,928 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | 460,929 |
def install_package(package=None, force=False): """ Install a package or return a list of all packages that have been installed into this Sage install. You must have an internet connection. Also, you will have to restart Sage for the changes to take affect. It is not needed to provide the version number. INPUT: - ... | def install_package(package=None, force=False): """ Install a package or return a list of all packages that have been installed into this Sage install. You must have an internet connection. Also, you will have to restart Sage for the changes to take affect. It is not needed to provide the version number. INPUT: - ... | 460,930 |
def install_package(package=None, force=False): """ Install a package or return a list of all packages that have been installed into this Sage install. You must have an internet connection. Also, you will have to restart Sage for the changes to take affect. It is not needed to provide the version number. INPUT: - ... | def install_package(package=None, force=False): """ Install a package or a list of all packages that have been installed into this Sage install. You must have an internet connection. Also, you will have to restart Sage for the changes to take affect. It is not needed to provide the version number. INPUT: - ``pac... | 460,931 |
def upgrade(): """ Download and build the latest version of Sage. You must have an internet connection. Also, you will have to restart Sage for the changes to take affect. This upgrades to the latest version of core packages (optional packages are not automatically upgraded). This will not work on systems that don't... | def upgrade(): """ Download and build the latest version of Sage. You must have an internet connection. Also, you will have to restart Sage for the changes to take affect. This upgrades to the latest version of core packages (optional packages are not automatically upgraded). This will not work on systems that don't... | 460,932 |
def _repr_(self): """ The printing representation of self. EXAMPLES:: sage: V = VectorSpace(QQ,5) sage: U = V.submodule([ V.gen(i) - V.gen(0) for i in range(1,5) ]) sage: print U # indirect doctest Vector space of degree 5 and dimension 4 over Rational Field Basis matrix: [ 1 0 0 0 -1] [ 0 1 0 0 -1] [ 0 0 1 ... | def _repr_(self): """ The printing representation of self. EXAMPLES:: sage: V = VectorSpace(QQ,5) sage: U = V.submodule([ V.gen(i) - V.gen(0) for i in range(1,5) ]) sage: print U # indirect doctest Vector space of degree 5 and dimension 4 over Rational Field Basis matrix: [ 1 0 0 0 -1] [ 0 1 0 0 -1] [ 0 0 1 ... | 460,933 |
def _repr_(self): """ The default printing representation of self. EXAMPLES:: sage: V = VectorSpace(QQ,5) sage: U = V.submodule([ V.gen(i) - V.gen(0) for i in range(1,5) ]) sage: print U # indirect doctest Vector space of degree 5 and dimension 4 over Rational Field Basis matrix: [ 1 0 0 0 -1] [ 0 1 0 0 -1] [ 0... | def _repr_(self): """ The default printing representation of self. EXAMPLES:: sage: V = VectorSpace(QQ,5) sage: U = V.submodule([ V.gen(i) - V.gen(0) for i in range(1,5) ]) sage: print U # indirect doctest Vector space of degree 5 and dimension 4 over Rational Field Basis matrix: [ 1 0 0 0 -1] [ 0 1 0 0 -1] [ 0... | 460,934 |
def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=None): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in t... | 460,935 |
def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | 460,936 |
def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | 460,937 |
def _limit_latex_(*args): r""" Return latex expression for limit of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _limit_latex_ sage: var('x,a') (x, a) sage: f(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hossain (20... | def _limit_latex_(self, f, x, a): r""" Return latex expression for limit of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _limit_latex_ sage: var('x,a') (x, a) sage: f(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hos... | 460,938 |
def _limit_latex_(*args): r""" Return latex expression for limit of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _limit_latex_ sage: var('x,a') (x, a) sage: f(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hossain (20... | def _limit_latex_(*args): r""" Return latex expression for limit of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _limit_latex_ sage: var('x,a') (x, a) sage: f = function('f',x) sage: _limit_latex_(0, f, x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hossain (2009-... | 460,939 |
def _limit_latex_(*args): r""" Return latex expression for limit of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _limit_latex_ sage: var('x,a') (x, a) sage: f(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hossain (20... | def _limit_latex_(*args): r""" Return latex expression for limit of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _limit_latex_ sage: var('x,a') (x, a) sage: f(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hossain (20... | 460,940 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(self, f, x, *args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integr... | 460,941 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f = function('f',x) sage: _integrate_latex_(0,f,x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f(x),... | 460,942 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(0... | 460,943 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | 460,944 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | 460,945 |
def _laplace_latex_(*args): r""" Return LaTeX expression for Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _laplace_latex_ sage: var('s,t') (s, t) sage: f(t) = function('f',t) sage: _laplace_latex_(f(t),t,s) '\\mathcal{L}\\left(f\\left(t\\right), t, s\\right)' AUTHORS:... | def _laplace_latex_(self, *args): r""" Return LaTeX expression for Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _laplace_latex_ sage: var('s,t') (s, t) sage: f(t) = function('f',t) sage: _laplace_latex_(f(t),t,s) '\\mathcal{L}\\left(f\\left(t\\right), t, s\\right)' AU... | 460,946 |
def _laplace_latex_(*args): r""" Return LaTeX expression for Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _laplace_latex_ sage: var('s,t') (s, t) sage: f(t) = function('f',t) sage: _laplace_latex_(f(t),t,s) '\\mathcal{L}\\left(f\\left(t\\right), t, s\\right)' AUTHORS:... | def _laplace_latex_(*args): r""" Return LaTeX expression for Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _laplace_latex_ sage: var('s,t') (s, t) sage: f = function('f',t) sage: _laplace_latex_(0,f,t,s) '\\mathcal{L}\\left(f\\left(t\\right), t, s\\right)' AUTHORS: - ... | 460,947 |
def _inverse_laplace_latex_(*args): r""" Return LaTeX expression for inverse Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _inverse_laplace_latex_ sage: var('s,t') (s, t) sage: F(s) = function('F',s) sage: _inverse_laplace_latex_(F(s),s,t) '\\mathcal{L}^{-1}\\left(F\\le... | def _inverse_laplace_latex_(self, *args): r""" Return LaTeX expression for inverse Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _inverse_laplace_latex_ sage: var('s,t') (s, t) sage: F(s) = function('F',s) sage: _inverse_laplace_latex_(F(s),s,t) '\\mathcal{L}^{-1}\\left... | 460,948 |
def _inverse_laplace_latex_(*args): r""" Return LaTeX expression for inverse Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _inverse_laplace_latex_ sage: var('s,t') (s, t) sage: F(s) = function('F',s) sage: _inverse_laplace_latex_(F(s),s,t) '\\mathcal{L}^{-1}\\left(F\\le... | def _inverse_laplace_latex_(*args): r""" Return LaTeX expression for inverse Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _inverse_laplace_latex_ sage: var('s,t') (s, t) sage: F = function('F',s) sage: _inverse_laplace_latex_(0,F,s,t) '\\mathcal{L}^{-1}\\left(F\\left(s... | 460,949 |
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 ... | 460,950 |
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 ... | 460,951 |
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 ... | 460,952 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,953 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,954 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,955 |
def integral(self, x=None, a=None, b=None, definite=False): r""" By default, returns the indefinite integral of the function. If definite=True is given, returns the definite integral. | def integral(self, x=None, a=None, b=None, definite=False): r""" By default, returns the indefinite integral of the function. If definite=True is given, returns the definite integral. | 460,956 |
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o... | def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o... | 460,957 |
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o... | def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o... | 460,958 |
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o... | def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o... | 460,959 |
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o... | def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o... | 460,960 |
def trial_division(n, bound=None): """ Return the smallest prime divisor <= bound of the positive integer n, or n if there is no such prime. If the optional argument bound is omitted, then bound <= n. INPUT: - ``n`` - a positive integer - ``bound`` - (optional) a positive integer OUTPUT: - ``int`` - a prime p=bo... | def trial_division(n, bound=None): """ Return the smallest prime divisor <= bound of the positive integer n, or n if there is no such prime. If the optional argument bound is omitted, then bound <= n. INPUT: - ``n`` - a positive integer - ``bound`` - (optional) a positive integer OUTPUT: - ``int`` - a prime p=bo... | 460,961 |
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 if n < 10000000000000: return factorization.Factorization(__factor_using_trial_division(n), unit) factor(n, if n < 10000000000000: return factorization.Factorization(__factor_using_trial_division(n), unit) proof=None, if n < 10000000000000: return factorization.Factorization(__factor_using_trial_division(n), unit... | 460,962 |
def is_divisible_by(self, m): """ Return True if there exists a point `Q` defined over the same field as self such that `mQ` == self. | def is_divisible_by(self, m): """ Return True if there exists a point `Q` defined over the same field as self such that `mQ` == self. | 460,963 |
cdef RealNumber result = domain(fn(*py_args)) | cdef RealNumber result = domain(fn(*py_args)) | 460,964 |
def write_interpreter(self, write): r""" Generate the code for the C interpreter. | def write_interpreter(self, write): r""" Generate the code for the C interpreter. | 460,965 |
def write_interpreter(self, write): r""" Generate the code for the C interpreter. | def write_interpreter(self, write): r""" Generate the code for the C interpreter. | 460,966 |
def write_wrapper(self, write): r""" Generate the code for the Cython wrapper. This function calls its write parameter successively with strings; when these strings are concatenated, the result is the code for the wrapper. | def write_wrapper(self, write): r""" Generate the code for the Cython wrapper. This function calls its write parameter successively with strings; when these strings are concatenated, the result is the code for the wrapper. | 460,967 |
def write_wrapper(self, write): r""" Generate the code for the Cython wrapper. This function calls its write parameter successively with strings; when these strings are concatenated, the result is the code for the wrapper. | def write_wrapper(self, write): r""" Generate the code for the Cython wrapper. This function calls its write parameter successively with strings; when these strings are concatenated, the result is the code for the wrapper. | 460,968 |
def write_pxd(self, write): r""" Generate the pxd file for the Cython wrapper. This function calls its write parameter successively with strings; when these strings are concatenated, the result is the code for the pxd file. | def write_pxd(self, write): r""" Generate the pxd file for the Cython wrapper. This function calls its write parameter successively with strings; when these strings are concatenated, the result is the code for the pxd file. | 460,969 |
def write_pxd(self, write): r""" Generate the pxd file for the Cython wrapper. This function calls its write parameter successively with strings; when these strings are concatenated, the result is the code for the pxd file. | def write_pxd(self, write): r""" Generate the pxd file for the Cython wrapper. This function calls its write parameter successively with strings; when these strings are concatenated, the result is the code for the pxd file. | 460,970 |
def get_interpreter(self): r""" Returns the code for the C interpreter. | def get_interpreter(self): r""" Returns the code for the C interpreter. | 460,971 |
def get_wrapper(self): r""" Returns the code for the Cython wrapper. | def get_wrapper(self): r""" Returns the code for the Cython wrapper. | 460,972 |
def get_pxd(self): r""" Returns the code for the Cython .pxd file. | def get_pxd(self): r""" Returns the code for the Cython .pxd file. | 460,973 |
def get_pxd(self): r""" Returns the code for the Cython .pxd file. | def get_pxd(self): r""" Returns the code for the Cython .pxd file. | 460,974 |
def build_interp(interp_spec, dir): r""" Given an InterpreterSpec, writes the C interpreter and the Cython wrapper (generates a pyx and a pxd file). EXAMPLES: sage: from sage.ext.gen_interpreters import * sage: testdir = tmp_filename() sage: os.mkdir(testdir) sage: rdf_interp = RDFInterpreter() sage: build_interp(rdf_... | def build_interp(interp_spec, dir): r""" Given an InterpreterSpec, writes the C interpreter and the Cython wrapper (generates a pyx and a pxd file). EXAMPLES: sage: from sage.ext.gen_interpreters import * sage: testdir = tmp_filename() sage: os.mkdir(testdir) sage: rdf_interp = RDFInterpreter() sage: build_interp(rdf_... | 460,975 |
def rebuild(dir): r""" Check whether the interpreter and wrapper sources have been written since the last time this module was changed. If not, write them. EXAMPLES: sage: from sage.ext.gen_interpreters import * sage: testdir = tmp_filename() sage: os.mkdir(testdir) sage: rebuild(testdir) Building interpreters for fa... | def rebuild(dir): r""" Check whether the interpreter and wrapper sources have been written since the last time this module was changed. If not, write them. EXAMPLES: sage: from sage.ext.gen_interpreters import * sage: testdir = tmp_filename() sage: os.mkdir(testdir) sage: rebuild(testdir) Building interpreters for fa... | 460,976 |
def contradicts(self, soln): """ Returns ``True`` if this assumption is violated by the given variable assignment(s). EXAMPLES:: sage: from sage.symbolic.assumptions import GenericDeclaration sage: GenericDeclaration(x, 'integer').contradicts(x==4) False sage: GenericDeclaration(x, 'integer').contradicts(x==4.0) Fals... | def contradicts(self, soln): """ Returns ``True`` if this assumption is violated by the given variable assignment(s). EXAMPLES:: sage: from sage.symbolic.assumptions import GenericDeclaration sage: GenericDeclaration(x, 'integer').contradicts(x==4) False sage: GenericDeclaration(x, 'integer').contradicts(x==4.0) Fals... | 460,977 |
def simon_two_descent(self, verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Computes lower and upper bounds on the rank of the Mordell-Weil group, and a list of independent points. INPUT: | def simon_two_descent(self, verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Computes lower and upper bounds on the rank of the Mordell-Weil group, and a list of independent points. Used internally by the :meth:`~rank`, :meth:`~rank_bounds` and :meth:`~gens` methods. INPUT: | 460,978 |
def simon_two_descent(self, verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Computes lower and upper bounds on the rank of the Mordell-Weil group, and a list of independent points. INPUT: | def simon_two_descent(self, verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Computes lower and upper bounds on the rank of the Mordell-Weil group, and a list of independent points. INPUT: | 460,979 |
def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | 460,980 |
def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | 460,981 |
def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | 460,982 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,983 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,984 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,985 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,986 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,987 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,988 |
def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | 460,989 |
def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | 460,990 |
def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | 460,991 |
def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | 460,992 |
def trial_division(n, bound=None): """ Return the smallest prime divisor <= bound of the positive integer n, or n if there is no such prime. If the optional argument bound is omitted, then bound <= n. INPUT: - ``n`` - a positive integer - ``bound`` - (optional) a positive integer OUTPUT: - ``int`` - a prime p=bo... | def trial_division(n, bound=None): """ Return the smallest prime divisor <= bound of the positive integer n, or n if there is no such prime. If the optional argument bound is omitted, then bound <= n. INPUT: - ``n`` - a positive integer - ``bound`` - (optional) a positive integer OUTPUT: - ``int`` - a prime p=bo... | 460,993 |
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 if n < 10000000000000: return factorization.Factorization(__factor_using_trial_division(n), unit) factor(n, if n < 10000000000000: return factorization.Factorization(__factor_using_trial_division(n), unit) proof=None, if n < 10000000000000: return factorization.Factorization(__factor_using_trial_division(n), unit... | 460,994 |
def ModularForms(group = 1, weight = 2, base_ring = None, use_cache = True, prec = defaults.DEFAULT_PRECISION): r""" Create an ambient space of modular forms. INPUT: - ``group`` - A congruence subgroup or a Dirichlet character eps. - ``weight`` - int, the weight, which must be an integer = 1. - ``base_ring`` -... | def ModularForms(group = 1, weight = 2, base_ring = None, use_cache = True, prec = defaults.DEFAULT_PRECISION): r""" Create an ambient space of modular forms. INPUT: - ``group`` - A congruence subgroup or a Dirichlet character eps. - ``weight`` - int, the weight, which must be an integer = 1. - ``base_ring`` -... | 460,995 |
def __cmp__(self, right): r""" Compare ``self`` and ``right``. INPUT: - ``right`` -- anything. OUTPUT: - 0 if ``right`` is of the same type as ``self`` and their rays are the same and listed in the same order. 1 or -1 otherwise. TESTS:: sage: c1 = Cone([(1,0), (0,1)]) sage: c2 = Cone([(0,1), (1,0)]) sage: c3 = Co... | def __cmp__(self, right): r""" Compare ``self`` and ``right``. INPUT: - ``right`` -- anything. OUTPUT: - 0 if ``right`` is of the same type as ``self`` and their rays are the same and listed in the same order. 1 or -1 otherwise. TESTS:: sage: c1 = Cone([(1,0), (0,1)]) sage: c2 = Cone([(0,1), (1,0)]) sage: c3 = Co... | 460,996 |
def canonical_label(self, partition=None, certify=False, verbosity=0, edge_labels=False): """ Returns the canonical label with respect to the partition. If no partition is given, uses the unit partition. INPUT: - ``partition`` - if given, the canonical label with respect to this partition will be computed. The defa... | def canonical_label(self, partition=None, certify=False, verbosity=0, edge_labels=False): """ Returns the unique graph on \{0,1,...,n-1\} ( n = self.order() ) which - is isomorphic to self, - has canonical vertex labels, - allows only permutations of vertices respecting the input set partition (if given). Canonical he... | 460,997 |
def canonical_label(self, partition=None, certify=False, verbosity=0, edge_labels=False): """ Returns the canonical label with respect to the partition. If no partition is given, uses the unit partition. INPUT: - ``partition`` - if given, the canonical label with respect to this partition will be computed. The defa... | defcanonical_label(self,partition=None,certify=False,verbosity=0,edge_labels=False):"""Returnsthecanonicallabelwithrespecttothepartition.Ifnopartitionisgiven,usestheunitpartition.INPUT:-``partition``-ifgiven,thecanonicallabelwithrespecttothispartitionwillbecomputed.Thedefaultistheunitpartition.-``certify``-ifTrue,adict... | 460,998 |
def canonical_label(self, partition=None, certify=False, verbosity=0, edge_labels=False): """ Returns the canonical label with respect to the partition. If no partition is given, uses the unit partition. INPUT: - ``partition`` - if given, the canonical label with respect to this partition will be computed. The defa... | def canonical_label(self, partition=None, certify=False, verbosity=0, edge_labels=False): """ Returns the canonical label with respect to the partition. If no partition is given, uses the unit partition. INPUT: - ``partition`` - if given, the canonical label with respect to this set partition will be computed. The ... | 460,999 |
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