rem stringlengths 0 322k | add stringlengths 0 2.05M | context stringlengths 8 228k |
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sage: W = Words('012') sage: W('012012012').is_cube() True sage: W('01010101').is_cube() False sage: W().is_cube() True sage: W('012012').is_cube() | sage: Word('012012012').is_cube() True sage: Word('01010101').is_cube() False sage: Word().is_cube() True sage: Word('012012').is_cube() | def is_cube(self): r""" Returns True if self is a cube, and False otherwise. EXAMPLES:: sage: W = Words('012') sage: W('012012012').is_cube() True sage: W('01010101').is_cube() False sage: W().is_cube() True sage: W('012012').is_cube() False """ if self.length() % 3 != 0: return False l = self.length() / 3 return sel... |
sage: W = Words('123') sage: W('12312').is_cube_free() True sage: W('32221').is_cube_free() False sage: W().is_cube_free() True """ l = self.length() if l < 3: | sage: Word('12312').is_cube_free() True sage: Word('32221').is_cube_free() False sage: Word().is_cube_free() True TESTS: We make sure that sage: Word('111').is_cube_free() False sage: Word('2111').is_cube_free() False sage: Word('32111').is_cube_free() False """ L = self.length() if L < 3: | def is_cube_free(self): r""" Returns True if self does not contain cubes, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_cube_free() True sage: W('32221').is_cube_free() False sage: W().is_cube_free() True """ l = self.length() if l < 3: return True suff = self for i in xrange(0, l - 3): f... |
suff = self for i in xrange(0, l - 3): for ll in xrange(3, l-i+1, 3): if suff[:ll].is_cube(): | for start in xrange(0, L - 2): for end in xrange(start+3, L+1, 3): if self[start:end].is_cube(): | def is_cube_free(self): r""" Returns True if self does not contain cubes, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_cube_free() True sage: W('32221').is_cube_free() False sage: W().is_cube_free() True """ l = self.length() if l < 3: return True suff = self for i in xrange(0, l - 3): f... |
suff = suff[1:] | def is_cube_free(self): r""" Returns True if self does not contain cubes, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_cube_free() True sage: W('32221').is_cube_free() False sage: W().is_cube_free() True """ l = self.length() if l < 3: return True suff = self for i in xrange(0, l - 3): f... | |
return CRT_list(vec,mod) | return tuple(CRT_vectors(vec,mod)) | def basiclemmavec(self,M): """ Finds a vector where the value of the quadratic form is coprime to M. EXAMPLES: sage: Q = QuadraticForm(ZZ, 2, [2, 1, 5]) sage: Q.basiclemmavec(10) (6, 5) sage: Q(_) 227 """ V=FreeModule(self.base_ring(),self.dim()) mat = self.matrix() vec = [] mod = [] M0 = abs(M) if M0 == 1: return V(... |
p.add_constraint(v[x] + b[x][y] - v[y], min=0, max=0) | p.add_constraint(v[x] + b[x][y] - v[y], min=0) | def edge_cut(self, s, t, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns a minimum edge cut between vertices `s` and `t` represented by a list of edges. |
- ``catch` - a boolean (default: True) | - ``catch`` - a boolean (default: True) | def run(self, category = None, skip = [], catch = True, raise_on_failure = False, **options): """ Run all the tests from this test suite: |
sage: ZZ._tester() Testing utilities for Integer Ring | sage: QQ._tester() Testing utilities for Rational Field | def instance_tester(instance, tester = None, **options): """ Returns a gadget attached to ``instance`` providing testing utilities. EXAMPLES:: sage: from sage.misc.sage_unittest import instance_tester sage: tester = instance_tester(ZZ) sage: tester.assert_(1 == 1) sage: tester.assert_(1 == 0) Traceback (most recent ... |
sage: ZZ._tester() Testing utilities for Integer Ring | sage: QQ._tester() Testing utilities for Rational Field | def __init__(self, instance, elements = None, verbose = False, prefix = "", **options): """ A gadget attached to an instance providing it with testing utilities. |
sage: for lset in polytopes.cross_polytope(2).face_lattice().level_sets(): print lset[0] (None, (0, 1, 2, 3)) ((1,), (2, 3)) ((1, 2), (3,)) ((0, 1, 2, 3), None) | sage: level_sets = polytopes.cross_polytope(2).face_lattice().level_sets() sage: print level_sets[0], level_sets[-1] [(None, (0, 1, 2, 3))] [((0, 1, 2, 3), None)] | def face_lattice(self): """ Computes the face-lattice poset. Elements are tuples of (vertices, facets) - i.e. this keeps track of both the vertices in each face, and all the facets containing them. |
""" Enumerates projective, rational points on scheme X of height up to bound B. | r""" Enumerates projective, rational points on scheme ``X`` of height up to bound ``B``. | 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... |
- ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound | - ``X`` - a scheme or set of abstract rational points of a scheme; - ``B`` - a positive integer bound. | 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... |
- a list containing the projective points of X of height up to B, sorted. | - a list containing the projective points of ``X`` of height up to ``B``, sorted. | 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... |
of projective space to see if they lie on X. | of projective space to see if they lie on ``X``. | 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... |
John Cremona and Charlie Turner (06-2010) | - John Cremona and Charlie Turner (06-2010) | 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... |
n = X.codomain().ambient_space().ngens()-1 zero=tuple([0 for _ in range(n+1)]) pts =[] for c in cartesian_product_iterator([srange(-B,B+1) for _ in range(n+1)]): if gcd(c)==1 and c>zero: | n = X.codomain().ambient_space().ngens() zero = (0,) * n pts = [] for c in cartesian_product_iterator([srange(-B,B+1) for _ in range(n)]): if gcd(c) == 1 and c > zero: | 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... |
except: | except TypeError: | 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... |
Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. | Enumerates affine rational points on scheme ``X`` (defined over `\QQ`) up to bound ``B``. | 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... |
- ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound | - ``X`` - a scheme or set of abstract rational points of a scheme; - ``B`` - a positive integer bound. | 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... |
- a list containing the affine points of X of height up to B, sorted. | - a list containing the affine points of ``X`` of height up to ``B``, sorted. | 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... |
AUTHOR: David R. Kohel <kohel@maths.usyd.edu.au> (small adjustments by Charlie Turner 06-2010) | AUTHORS: - David R. Kohel <kohel@maths.usyd.edu.au>: original version. - Charlie Turner (06-2010): small adjustments. | 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... |
Q = [ k+1 for k in range(B) ] R = [ 0 ] + [ s*k for k in range(1,B+1) for s in [1,-1] ] | Q = range(1, B + 1) R = [ 0 ] + [ s*k for k in range(1, B+1) for s in [1, -1] ] | 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... |
P = [ 0 for _ in range(n) ] | P = [0] * n | 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... |
except: | except TypeError: | 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... |
[ iters[j].next() for j in range(n) ] | for it in iters: it.next() | 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... |
m = m.gcd(a) P[i] = a for b in Q: if m.gcd(b) == 1: try: pts.append(X([ num/b for num in P ])) except: pass i = 0 m = ZZ(0) | 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... | |
Enumerates projective points on scheme X defined over a finite field | Enumerates projective points on scheme ``X`` defined over a finite field. | 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... |
- ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme | - ``X`` - a scheme defined over a finite field or a set of abstract rational points of such a scheme. | 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... |
- a list containing the projective points of X over the finite field, sorted | - a list containing the projective points of ``X`` over the finite field, sorted. | 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... |
NOTE: Warning:if X given as input is defined over an infinite field then this code will not finish! AUTHORS: John Cremona and Charlie Turner (06-2010) | .. WARNING:: If ``X`` is defined over an infinite field, this code will not finish! AUTHORS: - John Cremona and Charlie Turner (06-2010). | 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... |
except: | except TypeError: | 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... |
sage: cmp(N3, 3) -1 | sage: abs( cmp(N3, 3) ) 1 | def __cmp__(self, right): r""" Compare ``self`` and ``right``. |
``obj``, return a list of those names. If | ``obj``, return a sorted list of those names. If | def sage_getvariablename(obj, omit_underscore_names=True): """ Attempt to get the name of a Sage object. INPUT: - ``obj`` - an object - ``omit_underscore_names`` (optional, default True) If the user has assigned an object ``obj`` to a variable name, then return that variable name. If several variables point to ``ob... |
return result | return sorted(result) | def sage_getvariablename(obj, omit_underscore_names=True): """ Attempt to get the name of a Sage object. INPUT: - ``obj`` - an object - ``omit_underscore_names`` (optional, default True) If the user has assigned an object ``obj`` to a variable name, then return that variable name. If several variables point to ``ob... |
sage: M=E.modular_symbol() | def modular_symbol(self, sign=1, use_eclib = False, normalize = "L_ratio"): r""" Return the modular symbol associated to this elliptic curve, with given sign and base ring. This is the map that sends `r/s` to a fixed multiple of the integral of `2 \pi i f(z) dz` from `\infty` to `r/s`, normalized so that all values of... | |
1/5 | 2/5 | def modular_symbol(self, sign=1, use_eclib = False, normalize = "L_ratio"): r""" Return the modular symbol associated to this elliptic curve, with given sign and base ring. This is the map that sends `r/s` to a fixed multiple of the integral of `2 \pi i f(z) dz` from `\infty` to `r/s`, normalized so that all values of... |
Returns the Duursama data `v` and `m` of this formally s.d. code `C` | Returns the Duursma data `v` and `m` of this formally s.d. code `C` | def sd_duursma_data(C, i): r""" Returns the Duursama data `v` and `m` of this formally s.d. code `C` and the type number `i` in (1,2,3,4). Does *not* check if this code is actually sd. INPUT: - ``i`` - Type number OUTPUT: - Pair ``(v, m)`` as in Duursama [D]_ REFERENCES: - [D] - I. Duursma, "Extremal weight enum... |
- Pair ``(v, m)`` as in Duursama [D]_ | - Pair ``(v, m)`` as in Duursma [D]_ | def sd_duursma_data(C, i): r""" Returns the Duursama data `v` and `m` of this formally s.d. code `C` and the type number `i` in (1,2,3,4). Does *not* check if this code is actually sd. INPUT: - ``i`` - Type number OUTPUT: - Pair ``(v, m)`` as in Duursama [D]_ REFERENCES: - [D] - I. Duursma, "Extremal weight enum... |
- [D] - I. Duursma, "Extremal weight enumerators and ultraspherical polynomials" | .. [D] I. Duursma, "Extremal weight enumerators and ultraspherical polynomials" | def sd_duursma_data(C, i): r""" Returns the Duursama data `v` and `m` of this formally s.d. code `C` and the type number `i` in (1,2,3,4). Does *not* check if this code is actually sd. INPUT: - ``i`` - Type number OUTPUT: - Pair ``(v, m)`` as in Duursama [D]_ REFERENCES: - [D] - I. Duursma, "Extremal weight enum... |
- Coefficients `q_0, q_1, ...` of `q(T)` as in Duursama [D]_ | - Coefficients `q_0, q_1, ...` of `q(T)` as in Duursma [D]_ | def sd_duursma_q(C,i,d0): r""" INPUT: - ``C`` - sd code; does *not* check if `C` is actually an sd code - ``i`` - Type number, one of 1,2,3,4 - ``d0`` - Divisor, the smallest integer such that each `A_i > 0` iff `i` is divisible by `d0` OUTPUT: - Coefficients `q_0, q_1, ...` of `q(T)` as in Duursama [D]_ REFEREN... |
img = self(letter) | img = self.image(letter) | def is_identity(self): r""" Returns ``True`` if ``self`` is the identity morphism. EXAMPLES:: |
gens = [ "()" ] | k = max(self.entries()) gens = [range(1,k+1)] | def row_stabilizer(self): """ Return the PermutationGroup corresponding to the row stabilizer of self. EXAMPLES:: sage: rs = Tableau([[1,2,3],[4,5]]).row_stabilizer() sage: rs.order() == factorial(3)*factorial(2) True sage: PermutationGroupElement([(1,3,2),(4,5)]) in rs True sage: PermutationGroupElement([(1,4)]) in ... |
- ``algorithm`` - string (default: 'recursive') specifying which algorithm to be used when computing the iterated palindromic closure. It must be one of the two following values: - ``'definition'`` means that the iterated right palindromic closure is computed using the definition. - ``'recursive'`` is based on an eff... | - ``algorithm`` - string (default: ``'recursive'``) specifying which algorithm to be used when computing the iterated palindromic closure. It must be one of the two following values: - ``'definition'`` - computed using the definition - ``'recursive'`` - computation based on an efficient formula that recursively compu... | def iterated_right_palindromic_closure(self, f=None, algorithm='recursive'): r""" Returns the iterated (`f`-)palindromic closure of self. INPUT: |
l = len(sub) | L = len(sub) | 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: |
i = len(self) - l | i = len(self) - L | 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: |
i = start - l | i = start - L | 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: |
if self[i:i+l] == sub: return i | if self[i:i+L] == sub: return i | 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: |
l = len(sub) | L = len(sub) | 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: |
i = len(self) - l | i = len(self) - L | 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: |
i = end - l | i = end - L | 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: |
if self[i:i+l] == sub: return i | if self[i:i+L] == sub: return i | 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: |
""" qE = self._q | sage: T = EllipticCurve('14').tate_curve(7) sage: T.E2(30) 2 + 4*7 + 7^2 + 3*7^3 + 6*7^4 + 5*7^5 + 2*7^6 + 7^7 + 5*7^8 + 6*7^9 + 5*7^10 + 2*7^11 + 6*7^12 + 4*7^13 + 3*7^15 + 5*7^16 + 4*7^17 + 4*7^18 + 2*7^20 + 7^21 + 5*7^22 + 4*7^23 + 4*7^24 + 3*7^25 + 6*7^26 + 3*7^27 + 6*7^28 + O(7^30) """ | def E2(self,prec=20): r""" Returns the value of the `p`-adic Eisenstein series of weight 2 evaluated on the elliptic curve having split multiplicative reduction. |
Some cases that check on the negative twists:: | Some harder cases fail:: | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... |
-2 | 1 | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... |
Dlist = [5,8,12,13,17,21,24,28,29] | Dlist = [5,8,12,13,17,21,24,28,29, 33, 37, 40, 41, 44, 53, 56, 57, 60, 61, 65, 69, 73, 76, 77, 85, 88, 89, 92, 93, 97] | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... |
while j < 9 and at0 == 0 : | while j < 30 and at0 == 0 : | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... |
chtw = True for ell in prime_divisors(D): chtw = chtw and ( valuation(E.conductor(),ell)<= valuation(D,ell) ) if chtw : | if all( valuation(E.conductor(),ell)<= valuation(D,ell) for ell in prime_divisors(D) ) : | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... |
if j == 9 and at0 == 0: sc = 1 if not self._use_eclib : msn = ModularSymbolSage(self._E,sign = -1,normalize = "L_ratio") sc = msn._scaling if sc == 0 or self._use_eclib : self.__scale_by_periods_only__() else : self._scaling = sc | if j == 30 and at0 == 0: self.__scale_by_periods_only__() | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... |
verbose('scale modular symbols by %s'%(l1/at0)) | verbose('scale modular symbols by %s found at D=%s '%(l1/at0,D), level=2) | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... |
Dlist = [-3,-4,-7,-8,-11,-15,-19,-20,-23,-24] | Dlist = [-3,-4,-7,-8,-11,-15,-19,-20,-23,-24, -31, -35, -39, -40, -43, -47, -51, -52, -55, -56, -59, -67, -68, -71, -79, -83, -84, -87, -88, -91] | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... |
if j == 9 and at0 == 0: | if j == 30 and at0 == 0: | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... |
self._option["pdflatex"] = False | self._option["engine"] = "latex" self._option["engine_name"] = "LaTeX" | 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 _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): | def _run_latex_(filename, debug=False, density=150, engine=None, png=False, do_in_background=False): | 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... |
"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 the dvi file to png (because of postscript specials or other issues), then dvips is called, and the PS file is converted to a png file. | "filename.dvi" (or "filename.pdf"` if engine is either ``pdflatex`` or ``xelatex'') and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't convert the dvi file to png (because of postscript specials or other issues), then dvips is called, and the PS file is converted to a png file. | 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... |
- ``pdflatex`` - bool (optional, default False): whether to use pdflatex. | - ``engine`` - string: latex engine to use. | 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... |
``pdflatex`` is False, then a dvi file is created, but if there | engine is latex or None, then a dvi file is created, but if there | 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... |
returned.) If ``pdflatex`` is True and there are no errors, then | returned.) If engine is pdflatex or xelatex and there are no errors, then | 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... |
pdflatex, you must have 'convert' installed. | pdflatex or xelatex, you must have 'convert' installed. | 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... |
if pdflatex is None: pdflatex = _Latex_prefs._option["pdflatex"] if not pdflatex and not have_latex(): | if engine is None: engine = _Latex_prefs._option["engine"] if not engine and not have_latex(): | 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... |
if pdflatex and not have_pdflatex(): print "Error: PDFLaTeX does not seem to be installed. Download it from" | if engine and not have_pdflatex() and not have_xelatex(): print "Error: %s does not seem to be installed. Download it from" % _Latex_prefs._option["engine_name"] | 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... |
if not pdflatex and not (have_dvipng() or have_convert()): | if (not engine or engine == "latex") and not (have_dvipng() or have_convert()): | 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... |
print "appear to be installed. Displaying LaTeX or PDFLaTeX output" | print "appear to be installed. Displaying LaTeX, PDFLaTeX output" | 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... |
elif pdflatex and not have_convert(): | elif engine == "pdflatex" and not have_convert(): | 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... |
if pdflatex: | if not engine or engine == "latex": command = "latex" suffix = "ps" return_suffix = "dvi" elif engine == "pdflatex": | 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... |
command = "latex" suffix = "ps" return_suffix = "dvi" | raise ValueError, "Unsupported LaTeX engine." | 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... |
if pdflatex: | if engine == "pdflatex" or engine == "xelatex": | 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 __init__(self, debug=False, slide=False, density=150, pdflatex=None): | def __init__(self, debug=False, slide=False, density=150, pdflatex=None, engine=None): | def __init__(self, debug=False, slide=False, density=150, pdflatex=None): self.__debug = debug self.__slide = slide self.__pdflatex = pdflatex self.__density = density |
density=None, pdflatex=None, locals={}): | density=None, pdflatex=None, engine=None, locals={}): | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: |
- ``pdflatex`` - whether to use pdflatex. | - ``pdflatex`` - whether to use pdflatex. This is deprecated. Use ``engine`` option instead. - ``engine`` - latex engine to use. Currently latex, pdflatex, and xelatex are supported. | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: |
or this command won't work. When using pdflatex, you must | or this command won't work. When using pdflatex or xelatex, you must | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: |
if pdflatex is None: if self.__pdflatex is None: pdflatex = _Latex_prefs._option["pdflatex"] | if engine is None: if self.__engine is None: engine = _Latex_prefs._option["engine"] | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: |
pdflatex = bool(self.__pdflatex) | engine = self.__engine | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: |
density=density, pdflatex=pdflatex, png=True) | density=density, engine=engine, png=True) | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: |
def pdflatex(self, t = None): """ | def pdflatex(self, t = None): """ This is deprecated. Use engine("pdflatex") instead. | 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 |
sage: latex.pdflatex() | sage: latex.pdflatex() doctest:...: DeprecationWarning: Use engine() instead. | 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 |
sage: latex.pdflatex(False) | sage: latex.pdflatex(False) doctest:...: DeprecationWarning: Use engine("latex") instead. | 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 |
return _Latex_prefs._option["pdflatex"] _Latex_prefs._option["pdflatex"] = bool(t) | from sage.misc.misc import deprecation deprecation('Use engine() instead.') return _Latex_prefs._option["engine"] == "pdflatex" elif t: from sage.misc.misc import deprecation deprecation('Use engine("pdflatex") instead.') self.engine("pdflatex") else: from sage.misc.misc import deprecation deprecation('Use engine("late... | 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 view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, engine=None, viewer = None, tightpage = None, mode='inline', **kwds): | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... |
- ``pdflatex`` - bool (default: False): use pdflatex. | - ``pdflatex`` - bool (default: False): use pdflatex. This is deprecated. Use 'engine' option instead. - ``engine`` - 'latex', 'pdflatex', or 'xelatex' | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... |
If ``pdflatex`` is ``True``, then this produces a pdf file. Otherwise, it produces a dvi file, and if the program dvipng is | If ``pdflatex`` is ``True``, then the latex engine is set to pdflatex. If the engine is either pdflatex or xelatex, it produces a pdf file. Otherwise, it produces a dvi file, and if the program dvipng is | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... |
viewer, even in notebook mode. This also sets ``pdflatex`` to ``True``. | viewer, even in notebook mode. This also sets the latex engine to be ``pdflatex`` if the current engine is latex. | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... |
debug=debug, do_in_background=False, pdflatex=pdflatex) | debug=debug, do_in_background=False, engine=engine) | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... |
if viewer == "pdf": pdflatex = True if pdflatex is None: pdflatex = _Latex_prefs._option["pdflatex"] | if pdflatex: engine = "pdflatex" else: engine = _Latex_prefs._option["engine"] if viewer == "pdf" and engine == "latex": engine = "pdflatex" | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... |
suffix = _run_latex_(tex_file, debug=debug, pdflatex=pdflatex, png=False) | suffix = _run_latex_(tex_file, debug=debug, engine=engine, png=False) | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... |
do_in_background=False, tiny=False, pdflatex=True): | do_in_background=False, tiny=False, pdflatex=True, engine='pdflatex'): | def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... |
- ``pdflatex`` - bool (default: False): use pdflatex. | - ``pdflatex`` - bool (default: True): use pdflatex. This option is deprecated. Use ``engine`` option instead. See below. - ``engine`` - 'latex', 'pdflatex', or 'xelatex' (default: 'pdflatex') | def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... |
pdflatex=pdflatex) | engine=engine) | def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... |
""" | r""" | def FuzzyBallGraph(self, partition, q): """ Construct a Fuzzy Ball graph with the integer partition ``partition`` and ``q`` extra vertices. |
Let q be an integer and let m_1,m_2,...m_k be a set of positive integers. Let n=q+m_1+...+m_k. The Fuzzy Ball graph with partition m_1,m_2,...,m_k and q extra vertices is the graph constructed from the graph G=K_n by attaching, for each i=1,2,...,k, a new vertex a_i to m_i distinct vertices of G. For given positive ... | Let `q` be an integer and let `m_1,m_2,...,m_k` be a set of positive integers. Let `n=q+m_1+...+m_k`. The Fuzzy Ball graph with partition `m_1,m_2,...,m_k` and `q` extra vertices is the graph constructed from the graph `G=K_n` by attaching, for each `i=1,2,...,k`, a new vertex `a_i` to `m_i` distinct vertices of `G`.... | def FuzzyBallGraph(self, partition, q): """ Construct a Fuzzy Ball graph with the integer partition ``partition`` and ``q`` extra vertices. |
Pick positive integers m and k and a nonnegative integer q. All the FuzzyBallGraphs constructed from partitions of m with k parts should be cospectral with respect to the normalized | Pick positive integers `m` and `k` and a nonnegative integer `q`. All the FuzzyBallGraphs constructed from partitions of `m` with `k` parts should be cospectral with respect to the normalized | def FuzzyBallGraph(self, partition, q): """ Construct a Fuzzy Ball graph with the integer partition ``partition`` and ``q`` extra vertices. |
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