From 0b7dd8f0eb2c98139565c6ccc7e3e9b903c27e62 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= Date: Wed, 27 Jun 2018 22:13:51 +0200 Subject: [PATCH] adding more pari roles in the doc --- src/sage/matrix/matrix_integer_dense.pyx | 2 +- src/sage/matrix/matrix_integer_sparse.pyx | 2 +- src/sage/rings/complex_double.pyx | 4 +++- src/sage/rings/complex_number.pyx | 2 +- src/sage/rings/number_field/number_field_ideal.py | 4 ++-- 5 files changed, 8 insertions(+), 6 deletions(-) diff --git a/src/sage/matrix/matrix_integer_dense.pyx b/src/sage/matrix/matrix_integer_dense.pyx index 07eec923212..04858d4b4d8 100644 --- a/src/sage/matrix/matrix_integer_dense.pyx +++ b/src/sage/matrix/matrix_integer_dense.pyx @@ -2507,7 +2507,7 @@ cdef class Matrix_integer_dense(Matrix_dense): - ``algorithm`` - determines which algorithm to use, options are: - 'flint' - use the algorithm from the FLINT library - - 'pari' - use the ``matkerint()`` function from the PARI library + - 'pari' - use the :pari:`matkerint` function from the PARI library - 'padic' - use the p-adic algorithm from the IML library - 'default' - use a heuristic to decide which of the three above routines is fastest. This is the default value. diff --git a/src/sage/matrix/matrix_integer_sparse.pyx b/src/sage/matrix/matrix_integer_sparse.pyx index f0ea3d8d400..a901e2aa51b 100644 --- a/src/sage/matrix/matrix_integer_sparse.pyx +++ b/src/sage/matrix/matrix_integer_sparse.pyx @@ -339,7 +339,7 @@ cdef class Matrix_integer_sparse(Matrix_sparse): - ``algorithm`` - determines which algorithm to use, options are: - - 'pari' - use the ``matkerint()`` function from the PARI library + - 'pari' - use the :pari:`matkerint` function from the PARI library - 'padic' - use the p-adic algorithm from the IML library - 'default' - use a heuristic to decide which of the two above routines is fastest. This is the default value. diff --git a/src/sage/rings/complex_double.pyx b/src/sage/rings/complex_double.pyx index a47af748358..766f39a2b27 100644 --- a/src/sage/rings/complex_double.pyx +++ b/src/sage/rings/complex_double.pyx @@ -2240,7 +2240,7 @@ cdef class ComplexDoubleElement(FieldElement): this is a multi-valued function, and the algorithm used affects the value returned, as follows: - - ``'pari'``: Call the agm function from the pari library. + - ``'pari'``: Call the :pari:`agm` function from the pari library. - ``'optimal'``: Use the AGM sequence such that at each stage `(a,b)` is replaced by `(a_1,b_1)=((a+b)/2,\pm\sqrt{ab})` @@ -2253,6 +2253,8 @@ cdef class ComplexDoubleElement(FieldElement): where the sign is chosen so that `\Re(b_1/a_1) \geq 0` (the so-called principal branch of the square root). + See :wikipedia:`Arithmetic-geometric mean` + EXAMPLES:: sage: i = CDF(I) diff --git a/src/sage/rings/complex_number.pyx b/src/sage/rings/complex_number.pyx index a52d6c01a63..46221714f5e 100644 --- a/src/sage/rings/complex_number.pyx +++ b/src/sage/rings/complex_number.pyx @@ -1744,7 +1744,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement): this is a multi-valued function, and the algorithm used affects the value returned, as follows: - - "pari": Call the sgm function from the pari library. + - "pari": Call the :pari:`agm` function from the pari library. - "optimal": Use the AGM sequence such that at each stage `(a,b)` is replaced by `(a_1,b_1)=((a+b)/2,\pm\sqrt{ab})` diff --git a/src/sage/rings/number_field/number_field_ideal.py b/src/sage/rings/number_field/number_field_ideal.py index d422ffc5ad9..8acd60f7190 100644 --- a/src/sage/rings/number_field/number_field_ideal.py +++ b/src/sage/rings/number_field/number_field_ideal.py @@ -687,7 +687,7 @@ def reduce_equiv(self): not always) if self is principal then this function returns the unit ideal. - ALGORITHM: Calls pari's idealred function. + ALGORITHM: Calls :pari:`idealred` function. EXAMPLES:: @@ -2119,7 +2119,7 @@ def invertible_residues(self, reduce=True): `I`, i.e. a list of elements in the ring of integers `R` representing the elements of `(R/I)^*`. - ALGORITHM: Use pari's ``idealstar`` to find the group structure and + ALGORITHM: Use :pari:`idealstar` to find the group structure and generators of the multiplicative group modulo the ideal. EXAMPLES::