gh-35855: Extend MAX_MODULUS of matrix_modn_dense_double.pyx

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### 📚 Description

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Assign to `MAX_MODULUS` of `matrix_modn_dense_double.pyx` the actual
limit for LinBox `Modular<double>` (Givaro's `maxCardinality`)
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It allows better speed performances for matrices over the integers mod
N, for N having 24 to 27 bits.
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Fixes #35806
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### ⌛ Dependencies

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URL: #35855
Reported by: Marie Bonboire
Reviewer(s): Vincent Neiger

build/pkgs/configure/checksums.ini

@@ -1,4 +1,4 @@
 tarball=configure-VERSION.tar.gz
-sha1=b3604052037bc57fb64fcbe347b289dcd959366c
-md5=603842fccbd68e1125d32fed8d81ca86
-cksum=2053680048
+sha1=2852935b61f22d59a640dfe33a5f5bab10512296
+md5=b87baf9857489d7a70f5d9bee8322b64
+cksum=3781755388

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-4fa9c1c33b69fc6c3b948e9df3f7688b61b70589
+0779dd250ceb081a3a116c34a0a6b732de215bdf

src/sage/matrix/matrix_modn_dense_double.pyx

@@ -4,7 +4,7 @@
 # distutils: include_dirs = CBLAS_INCDIR
 # distutils: extra_compile_args = -D_XPG6
 r"""
-Dense matrices over `\ZZ/n\ZZ` for `n < 2^{23}` using LinBox's ``Modular<double>``
+Dense matrices over `\ZZ/n\ZZ` for `n < 94906266` using LinBox's ``Modular<double>``
 
 AUTHORS:
 
@@ -38,7 +38,7 @@ from sage.libs.linbox.fflas cimport \
 ctypedef Poly1Dom[ModField, Dense] ModDensePolyRing
 
 # Limit for LinBox Modular<double>
-MAX_MODULUS = 2**23
+MAX_MODULUS = 94906266
 
 from sage.rings.finite_rings.integer_mod cimport IntegerMod_int64
 
@@ -47,11 +47,11 @@ include "matrix_modn_dense_template.pxi"
 
 cdef class Matrix_modn_dense_double(Matrix_modn_dense_template):
     r"""
-    Dense matrices over `\ZZ/n\ZZ` for `n < 2^{23}` using LinBox's ``Modular<double>``
+    Dense matrices over `\ZZ/n\ZZ` for `n < 94906266` using LinBox's ``Modular<double>``
 
     These are matrices with integer entries mod ``n`` represented as
     floating-point numbers in a 64-bit word for use with LinBox routines.
-    This allows for ``n`` up to `2^{23}`. By default, the analogous
+    This allows for ``n`` up to `94906266`. By default, the analogous
     ``Matrix_modn_dense_float`` class is used for smaller moduli, specifically
     for ``n`` up to `2^{8}`.
 
@@ -70,7 +70,7 @@ cdef class Matrix_modn_dense_double(Matrix_modn_dense_template):
             <class 'sage.rings.finite_rings.integer_mod.IntegerMod_int64'>
         """
         self._get_template = self._base_ring.zero()
-        # note that INTEGER_MOD_INT32_LIMIT is ceil(sqrt(2^31-1)) < 2^23
+        # note that INTEGER_MOD_INT32_LIMIT is ceil(sqrt(2^31-1)) < 94906266
         self._fits_int32 = ((<Matrix_modn_dense_template>self).p <= INTEGER_MOD_INT32_LIMIT)
 
     cdef void set_unsafe_int(self, Py_ssize_t i, Py_ssize_t j, int value):

src/sage/matrix/matrix_space.py

@@ -166,7 +166,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
         sage: get_matrix_class(Zmod(2**30), 2, 2, False, 'linbox-double')
         Traceback (most recent call last):
         ...
-        ValueError: 'linbox-double' matrices can only deal with order < 8388608
+        ValueError: 'linbox-double' matrices can only deal with order < 94906266
 
         sage: type(matrix(SR, 2, 2, 0))
         <class 'sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense'>
@@ -617,7 +617,8 @@ def __init__(self, base_ring, nrows, ncols, sparse, implementation):
 
            - ``linbox-float`` - for integer mod rings up to `2^8 = 256`
 
-           - ``linbox-double`` - for integer mod rings up to `2^23 = 8388608`
+           - ``linbox-double`` - for integer mod rings up to
+             `floor(2^26*sqrt(2) + 1/2) = 94906266`
 
            - ``numpy`` - for real and complex floating point numbers