bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | 462,400 |
def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | 462,401 |
def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | 462,402 |
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, - is invariant in the isomorphism class. In other words, given two graphs ``G`` and ``H`` which are isomorphic, suppose ``G_c`` a... | 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, - is invariant in the isomorphism class. In other words, given two graphs ``G`` and ``H`` which are isomorphic, suppose ``G_c``... | 462,403 |
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, - is invariant in the isomorphism class. In other words, given two graphs ``G`` and ``H`` which are isomorphic, suppose ``G_c`` a... | 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, - is invariant in the isomorphism class. In other words, given two graphs ``G`` and ``H`` which are isomorphic, suppose ``G_c`` a... | 462,404 |
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | def enum_projective_rational_field(X,B): r""" Enumerates projective, rational points on scheme ``X`` of height up to bound ``B``. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, s... | 462,405 |
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme; - ``B`` - a positive integer bound. OUTPUT: - a list containing the projective points of X of height up to B, sorted. ... | 462,406 |
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of ``X`` of height up to ``B``, so... | 462,407 |
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | 462,408 |
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | 462,409 |
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | 462,410 |
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | 462,411 |
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E... | 462,412 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme ``X`` (defined over `\QQ`) up to bound ``B``. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorte... | 462,413 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme; - ``B`` - a positive integer bound. OUTPUT: - a list containing the affine points of X of height up to B, sorted. EX... | 462,414 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of ``X`` of height up to ``B``, sorte... | 462,415 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | 462,416 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | defenum_affine_rational_field(X,B):"""EnumeratesaffinerationalpointsonschemeX(definedover`\QQ`)uptoboundB.INPUT:-``X``-aschemeorsetofabstractrationalpointsofascheme-``B``-apositiveintegerboundOUTPUT:-alistcontainingtheaffinepointsofXofheightuptoB,sorted.EXAMPLES::sage:A.<x,y,z>=AffineSpace(3,QQ)sage:fromsage.schemes.ge... | 462,417 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | 462,418 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | 462,419 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | 462,420 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | 462,421 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | 462,422 |
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM... | 462,423 |
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s... | def enum_projective_finite_field(X): """ Enumerates projective points on scheme ``X`` defined over a finite field. INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES... | 462,424 |
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s... | def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or a set of abstract rational points of such a scheme. OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES::... | 462,425 |
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s... | def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of ``X`` over the finite field, sorted. EXAMPLES... | 462,426 |
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s... | def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s... | 462,427 |
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s... | def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s... | 462,428 |
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s... | def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s... | 462,429 |
def __call__(self, im_gens, check=True): """ Return the homomorphism defined by images of generators. | def __call__(self, im_gens, check=True): """ Return the homomorphism defined by images of generators. | 462,430 |
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`. | 462,431 |
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`. | 462,432 |
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`. | 462,433 |
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) | 462,434 |
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 | 462,435 |
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 | 462,436 |
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... | 462,437 |
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... | 462,438 |
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()] | 462,439 |
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... | 462,440 |
def bin_to_ascii(B): r""" Return the ASCII representation of the binary string ``B``. INPUT: - ``B`` -- a non-empty binary string or a non-empty list of bits. The number of bits in ``B`` must be a multiple of 8. OUTPUT: - The ASCII string corresponding to ``B``. ALGORITHM: Consider a block of bits `B = b_0 b_1 \c... | def bin_to_ascii(B): r""" Return the ASCII representation of the binary string ``B``. INPUT: - ``B`` -- a non-empty binary string or a non-empty list of bits. The number of bits in ``B`` must be a multiple of 8. OUTPUT: - The ASCII string corresponding to ``B``. ALGORITHM: Consider a block of bits `B = b_0 b_1 \c... | 462,441 |
sage: def my_carmichael(n): | sage: def my_carmichael(n): | 462,442 |
sage: def my_carmichael(n): | sage: def my_carmichael(n): | 462,443 |
sage: def my_carmichael(n): | sage: def my_carmichael(n): | 462,444 |
sage: def my_carmichael(n): | sage: def my_carmichael(n): | 462,445 |
sage: def my_carmichael(n): | sage: def my_carmichael(n): | 462,446 |
sage: def my_carmichael(n): | sage: def my_carmichael(n): | 462,447 |
def least_significant_bits(n, k): r""" Return the ``k`` least significant bits of ``n``. INPUT: - ``n`` -- an integer. - ``k`` -- a positive integer. OUTPUT: - The ``k`` least significant bits of the integer ``n``. If ``k=1``, then return the parity bit of the integer ``n``. Let `b` be the binary representation of... | def least_significant_bits(n, k): r""" Return the ``k`` least significant bits of ``n``. INPUT: - ``n`` -- an integer. - ``k`` -- a positive integer. OUTPUT: - The ``k`` least significant bits of the integer ``n``. If ``k=1``, then return the parity bit of the integer ``n``. Let `b` be the binary representation of... | 462,448 |
def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | def is_integral_domain(self, proof=True): r""" With ``proof`` equal to ``True`` (the default), this function may raise a ``NotImplementedError``. When ``proof`` is ``False``, if ``True`` is returned, then self is definitely an integral domain. If the function returns ``False``, then either self is not an integral do... | 462,449 |
def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | 462,450 |
def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | 462,451 |
def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | 462,452 |
def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | 462,453 |
def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | 462,454 |
def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | 462,455 |
def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0): r""" Returns a longest path of ``self``. | 462,456 |
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... | 462,457 |
def get_fake_div(self, ex): """ EXAMPLES:: | def get_fake_div(self, ex): """ EXAMPLES:: | 462,458 |
def get_fake_div(self, ex): """ EXAMPLES:: | def get_fake_div(self, ex): """ EXAMPLES:: | 462,459 |
def arithmetic(self, ex, operator): r""" EXAMPLES:: | def arithmetic(self, ex, operator): r""" EXAMPLES:: | 462,460 |
def update(self): """ Updates some properties from ``curve``. | def update(self): """ Updates some properties from ``curve``. | 462,461 |
sage: def foo(use_database): | sage: def foo(use_database): | 462,462 |
def iterated_right_palindromic_closure(self, f=None, algorithm='recursive'): r""" Returns the iterated (`f`-)palindromic closure of self. INPUT: | def iterated_right_palindromic_closure(self, f=None, algorithm='recursive'): r""" Returns the iterated (`f`-)palindromic closure of self. INPUT: | 462,463 |
def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | 462,464 |
def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | 462,465 |
def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | 462,466 |
def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | 462,467 |
def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | 462,468 |
def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | 462,469 |
def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | 462,470 |
def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure. INPUT: | 462,471 |
def __init__(self, bb=False, delimiters=["(", ")"]): """ Define an object that holds LaTeX global preferences. """ self._option = {} self._option["blackboard_bold"] = bb self._option["matrix_delimiters"] = list(delimiters) self._option["vector_delimiters"] = list(delimiters) self._option["macros"] = "" self._option["pr... | def __init__(self, bb=False, delimiters=["(", ")"]): """ Define an object that holds LaTeX global preferences. """ self._option = {} self._option["blackboard_bold"] = bb self._option["matrix_delimiters"] = list(delimiters) self._option["vector_delimiters"] = list(delimiters) self._option["macros"] = "" self._option["pr... | 462,472 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, engine=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't convert... | 462,473 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if engine is either ``pdflatex`` or ``xelatex'') and if ``png`` is True, "filename.png". If ``png`` is True an... | 462,474 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,475 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,476 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,477 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,478 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,479 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,480 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,481 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,482 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,483 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,484 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,485 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,486 |
def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 462,487 |
def __init__(self, debug=False, slide=False, density=150, pdflatex=None): self.__debug = debug self.__slide = slide self.__pdflatex = pdflatex self.__density = density | def __init__(self, debug=False, slide=False, density=150, pdflatex=None, engine=None): self.__debug = debug self.__slide = slide self.__pdflatex = pdflatex self.__density = density | 462,488 |
def _relation_symbols(self): """ Returns a dictionary whose keys are attributes of the :mod:`operator` module and whose values are the corresponding LaTeX expressions. EXAMPLES:: | def_relation_symbols(self):"""Returnsadictionarywhosekeysareattributesofthe:mod:`operator`moduleandwhosevaluesarethecorrespondingLaTeXexpressions.EXAMPLES:: | 462,489 |
def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, engine=None, locals={}): """ INPUT: | 462,490 |
def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 462,491 |
def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 462,492 |
def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 462,493 |
def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 462,494 |
def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 462,495 |
def pdflatex(self, t = None): """ Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. INPUT: - ``t`` -- boolean or None | def pdflatex(self, t = None): """ This is deprecated. Use engine("pdflatex") instead. Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. INPUT: - ``t`` -- boolean or None | 462,496 |
def pdflatex(self, t = None): """ Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. INPUT: - ``t`` -- boolean or None | def pdflatex(self, t = None): """ Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. INPUT: - ``t`` -- boolean or None | 462,497 |
def pdflatex(self, t = None): """ Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. INPUT: - ``t`` -- boolean or None | def pdflatex(self, t = None): """ Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. INPUT: - ``t`` -- boolean or None | 462,498 |
def pdflatex(self, t = None): """ Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. INPUT: - ``t`` -- boolean or None | def pdflatex(self, t = None): """ Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. INPUT: - ``t`` -- boolean or None | 462,499 |
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