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authorFrédéric Chapoton <chapoton@math.univ-lyon1.fr>2015-03-09 22:26:44 +0100
committerFrédéric Chapoton <chapoton@math.univ-lyon1.fr>2015-03-09 22:26:44 +0100
commit5293a865dbe586928e7ed9f97a567e96eb7977a4 (patch)
treebced27f1b5d35e3e6b20f8b9e96de4c562d1ff2f
parenttrac #16449 inclusion into sage doc, plus correction to the doc (diff)
trac #16448 more doc improvements
-rw-r--r--src/sage/modular/jacobi/classical.py5
-rw-r--r--src/sage/modular/jacobi/classical_weak.py16
-rw-r--r--src/sage/modular/jacobi/higherrank.py8
-rw-r--r--src/sage/modular/jacobi/higherrank_dimension.py9
-rw-r--r--src/sage/modular/jacobi/vector_valued.py18
5 files changed, 30 insertions, 26 deletions
diff --git a/src/sage/modular/jacobi/classical.py b/src/sage/modular/jacobi/classical.py
index 9c3624d..401491a 100644
--- a/src/sage/modular/jacobi/classical.py
+++ b/src/sage/modular/jacobi/classical.py
@@ -97,9 +97,10 @@ def classical_jacobi_fe_indices(m, prec, reduced=False):
sage: list(classical_jacobi_fe_indices(2, 3, True))
[(1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (0, 0)]
sage: list(classical_jacobi_fe_indices(2, 3, False))
- [(1, 0), (1, 1), (1, -1), (1, 2), (1, -2), (2, 0), (2, 1), (2, -1), (2, 2), (2, -2), (2, 3), (2, -3), (0, 0), (2, 4), (2, -4)]
+ [(1, 0), (1, 1), (1, -1), (1, 2), (1, -2), (2, 0), (2, 1), (2, -1),
+ (2, 2), (2, -2), (2, 3), (2, -3), (0, 0), (2, 4), (2, -4)]
"""
- fm = Integer(4*m)
+ fm = Integer(4 * m)
if reduced :
# positive definite forms
diff --git a/src/sage/modular/jacobi/classical_weak.py b/src/sage/modular/jacobi/classical_weak.py
index 442f7dd..b1a7aca 100644
--- a/src/sage/modular/jacobi/classical_weak.py
+++ b/src/sage/modular/jacobi/classical_weak.py
@@ -435,7 +435,7 @@ class ClassicalWeakJacobiForms_factory:
INPUT:
- - ``wronskian_adjoint`` -- A list of lists of power series over `\Z`.
+ - ``wronskian_adjoint`` -- A list of lists of power series over `\ZZ`.
- ``weight_parity`` -- An integer (default: `0`).
@@ -460,7 +460,7 @@ class ClassicalWeakJacobiForms_factory:
def _wronskian_adjoint(self, weight_parity = 0) :
r"""
- The matrix `W^\# \pmod{p}`, mentioned on page 142 of [Sk84].
+ The matrix `W^\# \pmod{p}`, mentioned on page 142 of [Sk84]_.
This matrix is represented by a list of lists of q-expansions.
The q-expansion is shifted by `-(m + 1) (2*m + 1) / 24` in the
@@ -613,7 +613,7 @@ class ClassicalWeakJacobiForms_factory:
INPUT:
- ``wronskian_invdeterminant`` -- A power series over `\ZZ`.
-
+
- ``weight_parity`` -- An integer (default: `0`).
TESTS::
@@ -635,7 +635,7 @@ class ClassicalWeakJacobiForms_factory:
def _wronskian_invdeterminant(self, weight_parity = 0) :
r"""
The inverse determinant of `W`, which in the considered cases
- is always a negative power of the eta function. See [Sk84] for details.
+ is always a negative power of the eta function. See [Sk84]_ for details.
INPUT:
@@ -684,7 +684,7 @@ class ClassicalWeakJacobiForms_factory:
ALGORITHM:
We combine the theta decomposition and the heat operator as in
- [Sk84]. This yields a bijections of the space of weak Jacobi
+ [Sk84]_. This yields a bijections of the space of weak Jacobi
forms of weight `k` and index `m` with the product of spaces
of elliptic modular forms `M_k \times S_{k+2} \times .. \times
S_{k+2m}`.
@@ -692,9 +692,9 @@ class ClassicalWeakJacobiForms_factory:
INPUT:
- ``fs`` -- A list of functions that given an integer `p` return the
- q-expansion of a modular form with rational coefficients
- up to precision `p`. These modular forms correspond to
- the components of the above product.
+ q-expansion of a modular form with rational coefficients
+ up to precision `p`. These modular forms correspond to
+ the components of the above product.
- `k` -- An integer. The weight of the weak Jacobi form to be computed.
diff --git a/src/sage/modular/jacobi/higherrank.py b/src/sage/modular/jacobi/higherrank.py
index 2137050..316df62 100644
--- a/src/sage/modular/jacobi/higherrank.py
+++ b/src/sage/modular/jacobi/higherrank.py
@@ -121,7 +121,7 @@ def higherrank_jacobi_reduce_fe_index((n, r), m, r_classes, m_adj, m_span):
- ``r_classes`` -- A list of lists of vectors.
- - `m_adj` -- A quadratic form over `\ZZ`.
+ - ``m_adj`` -- A quadratic form over `\ZZ`.
- ``m_span`` -- The row (or column) span `m`.
@@ -216,7 +216,7 @@ def higherrank_jacobi_fe_indices(m, prec, r_classes, reduced=False):
OUTPUT:
- - A generator of pairs `(n, r)`, where `n` is an integer and `r` is a tupel.
+ - A generator of pairs `(n, r)`, where `n` is an integer and `r` is a tuple.
EXAMPLES::
@@ -337,7 +337,7 @@ def higherrank_jacobi_forms(k, m, prec, algorithm="restriction"):
ALGORITHM:
- See [Ra]. The algorithm in [Ra] is applied for precision
+ See [Ra]_. The algorithm in [Ra]_ is applied for precision
``relation_prec``. After this, the remaining Fourier coefficients
are determined using as few restrictions as possible.
@@ -354,7 +354,7 @@ def higherrank_jacobi_forms(k, m, prec, algorithm="restriction"):
OUTPUT:
A list of dictionaries, which describes the Fourier expansion of
- Jaocib forms.
+ Jacobi forms.
EXAMPLES::
diff --git a/src/sage/modular/jacobi/higherrank_dimension.py b/src/sage/modular/jacobi/higherrank_dimension.py
index 4804aa6..18d870f 100644
--- a/src/sage/modular/jacobi/higherrank_dimension.py
+++ b/src/sage/modular/jacobi/higherrank_dimension.py
@@ -6,7 +6,7 @@ that apply it to the case of Jacobi forms.
For Jacobi forms there is a much better way to implement this
formula. This is ongoing work by Ehlen et al. Replace this code by
- his work as soon as possible. However, for general vector valued
+ his work as soon as possible. However, for general vector valued
modular forms with diagonalizable representation matrix `\rho([1, 1; 0,
1])`, it is necessary to keep this method.
@@ -52,13 +52,14 @@ def jacobi_dimension(k, m):
- `k` -- An integer.
- - `m` -- A quadratic form or an even symmetric matrix (over `\Z`).
+ - `m` -- A quadratic form or an even symmetric matrix (over `\ZZ`).
TESTS::
sage: from sage.modular.jacobi.classical import _classical_jacobi_forms_as_weak_jacobi_forms
sage: from sage.modular.jacobi.higherrank_dimension import jacobi_dimension
- sage: assert all( len(_classical_jacobi_forms_as_weak_jacobi_forms(k, m)) == jacobi_dimension(k, matrix([[2 * m]])) for k in range(8, 16) for m in range(1, 10) ) # long time
+ sage: all(len(_classical_jacobi_forms_as_weak_jacobi_forms(k, m)) == jacobi_dimension(k, matrix([[2 * m]])) for k in range(8, 16) for m in range(1, 10) ) # long time
+ True
"""
from sage.matrix.matrix import is_Matrix
@@ -67,6 +68,7 @@ def jacobi_dimension(k, m):
else:
return vector_valued_dimension(k - ZZ(m.dim()) / 2, m.scale_by_factor(-1))
+
def nmb_isotropic_vectors(k, L):
r"""
Compute the number of isotropic vectors, which generically give
@@ -98,6 +100,7 @@ def nmb_isotropic_vectors(k, L):
return len([a for a in (singls + pairs if plus_basis else pairs)
if disc_quadratic(*a) in ZZ])
+
def vector_valued_dimension(k, L):
r"""
Compute the dimension of the space of weight `k` vector valued
diff --git a/src/sage/modular/jacobi/vector_valued.py b/src/sage/modular/jacobi/vector_valued.py
index 0380872..a17e9d1 100644
--- a/src/sage/modular/jacobi/vector_valued.py
+++ b/src/sage/modular/jacobi/vector_valued.py
@@ -62,7 +62,7 @@ def vector_valued_modular_forms(k, L, prec):
OUTPUT:
A list of dictionaries that encode the Fourier coefficients of
- vector valued modular forms. See `meth:theta_decomposition` for a
+ vector valued modular forms. See :meth:`theta_decomposition` for a
description of these expansions.
EXAMPLES::
@@ -176,23 +176,23 @@ def vector_valued_modular_forms_weakly_holomorphic(k, L, order, prec):
return wvvforms
-def vector_valued_modular_forms_weakly_holomorphic_with_principal_part( k, L, principal_part, prec ) :
+def vector_valued_modular_forms_weakly_holomorphic_with_principal_part(k, L, principal_part, prec):
r"""
Return a weak holomorphic vector valued modular form with given principal part.
- Raises ``ValueError`` if no such form exits.
+ Raises ``ValueError`` if no such form exists.
INPUT:
- - `k` -- A half-integral.
+ - `k` -- A half-integer.
- `L` -- A quadratic form over `\ZZ`.
- ``principal_part`` -- A dictionary whose keys represent elements
- of the discriminant group and whose values
- are dictionaries corresponding to Fourier
- expansions of a component. E.g.
- {(0,): {-2: 2, -1: 2}, (1,): {-1/4: 3}}
+ of the discriminant group and whose values
+ are dictionaries corresponding to Fourier
+ expansions of a component. E.g.
+ {(0,): {-2: 2, -1: 2}, (1,): {-1/4: 3}}
- ``prec`` -- A positive integer.
@@ -273,7 +273,7 @@ def theta_decomposition(phi, m, r_classes):
INPUT:
- ``phi`` -- A dictionary representing the Fourier expansion of a
- Jacobi form.
+ Jacobi form.
- `m` -- A quadratic form over `m`.