Add transformation feature to BKZ

CITATION.cff

@@ -4,8 +4,8 @@ title: SageMath
 abstract: SageMath is a free open-source mathematics software system.
 authors:
 - name: "The SageMath Developers"
-version: 10.6.rc0
+version: 10.6.rc1
 doi: 10.5281/zenodo.8042260
-date-released: 2025-03-22
+date-released: 2025-03-27
 repository-code: "https://github.com/sagemath/sage"
 url: "https://www.sagemath.org/"

VERSION.txt

@@ -1 +1 @@
-SageMath version 10.6.rc0, Release Date: 2025-03-22
+SageMath version 10.6.rc1, Release Date: 2025-03-27

build/pkgs/configure/checksums.ini

@@ -1,3 +1,3 @@
 tarball=configure-VERSION.tar.gz
-sha1=9743f84f12c5cef218137fc45ee258620ded9fe5
-sha256=7b2b9d2fef25fa69918ecb1f5b6eca1fccf22960ce2a235e0baf99d096e625b7
+sha1=b864ca0eb94c01c9e724699ac6d797a65b5acbb0
+sha256=5aa6946e6a99eeac2b829f2146338eeef8537a3134b4289078c8417092ecaaf2

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-9320452a3de4e261d779f159315c25d3dbe8f57d
+8dab37468c9feb4a5a1fcc22bbccc12321aaa475

build/pkgs/fpylll/distros/conda.txt

@@ -1 +1 @@
-fpylll>=0.5.9
+fpylll>=0.6.3

build/pkgs/fpylll/version_requirements.txt

@@ -1 +1 @@
-fpylll >=0.5.9
+fpylll >=0.6.3

build/pkgs/sage_conf/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sage-conf ~= 10.6rc0
+sage-conf ~= 10.6rc1

build/pkgs/sage_docbuild/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sage-docbuild ~= 10.6rc0
+sage-docbuild ~= 10.6rc1

build/pkgs/sage_setup/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sage-setup ~= 10.6rc0
+sage-setup ~= 10.6rc1

build/pkgs/sage_sws2rst/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sage-sws2rst ~= 10.6rc0
+sage-sws2rst ~= 10.6rc1

build/pkgs/sagelib/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-standard ~= 10.6rc0
+sagemath-standard ~= 10.6rc1

build/pkgs/sagemath_bliss/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-bliss ~= 10.6rc0
+sagemath-bliss ~= 10.6rc1

build/pkgs/sagemath_categories/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-categories ~= 10.6rc0
+sagemath-categories ~= 10.6rc1

build/pkgs/sagemath_coxeter3/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-coxeter3 ~= 10.6rc0
+sagemath-coxeter3 ~= 10.6rc1

build/pkgs/sagemath_environment/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-environment ~= 10.6rc0
+sagemath-environment ~= 10.6rc1

build/pkgs/sagemath_mcqd/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-mcqd ~= 10.6rc0
+sagemath-mcqd ~= 10.6rc1

build/pkgs/sagemath_meataxe/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-meataxe ~= 10.6rc0
+sagemath-meataxe ~= 10.6rc1

build/pkgs/sagemath_objects/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-objects ~= 10.6rc0
+sagemath-objects ~= 10.6rc1

build/pkgs/sagemath_repl/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-repl ~= 10.6rc0
+sagemath-repl ~= 10.6rc1

build/pkgs/sagemath_sirocco/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-sirocco ~= 10.6rc0
+sagemath-sirocco ~= 10.6rc1

build/pkgs/sagemath_tdlib/version_requirements.txt

@@ -1,2 +1,2 @@
 # This file is updated on every release by the sage-update-version script
-sagemath-tdlib ~= 10.6rc0
+sagemath-tdlib ~= 10.6rc1

environment-3.11-linux-aarch64.yml

@@ -90,7 +90,7 @@ dependencies:
   - fonttools=4.56.0=py311h58d527c_0
   - fortran-compiler=1.9.0=h25a59a9_0
   - fplll=5.5.0=h45c7457_0
-  - fpylll=0.6.2=py311h2dc1a0e_0
+  - fpylll=0.6.3=py311h2dc1a0e_0
   - freetype=2.13.3=he93130f_0
   - furo=2024.8.6=pyhd8ed1ab_2
   - gap-core=4.14.0=h1754e88_2

environment-3.11-linux.yml

@@ -91,7 +91,7 @@ dependencies:
   - fonttools=4.56.0=py311h2dc5d0c_0
   - fortran-compiler=1.9.0=h36df796_0
   - fplll=5.5.0=hd20a173_0
-  - fpylll=0.6.2=py311hf0b6740_0
+  - fpylll=0.6.3=py311hf0b6740_0
   - freetype=2.13.3=h48d6fc4_0
   - furo=2024.8.6=pyhd8ed1ab_2
   - gap-core=4.14.0=h3b03731_2

environment-3.11-macos-x86_64.yml

@@ -91,7 +91,7 @@ dependencies:
   - fonttools=4.56.0=py311ha3cf9ac_0
   - fortran-compiler=1.9.0=h02557f8_0
   - fplll=5.5.0=h6ede486_0
-  - fpylll=0.6.2=py311h793c761_0
+  - fpylll=0.6.3=py311h793c761_0
   - freetype=2.13.3=h40dfd5c_0
   - furo=2024.8.6=pyhd8ed1ab_2
   - gap-core=4.14.0=hb9686a1_2

environment-3.11-macos.yml

@@ -91,7 +91,7 @@ dependencies:
   - fonttools=4.56.0=py311h4921393_0
   - fortran-compiler=1.9.0=h5692697_0
   - fplll=5.5.0=h2a2278a_0
-  - fpylll=0.6.2=py311h4044dbd_0
+  - fpylll=0.6.3=py311h4044dbd_0
   - freetype=2.13.3=h1d14073_0
   - furo=2024.8.6=pyhd8ed1ab_2
   - gap-core=4.14.0=h25f1785_2

environment-3.12-linux-aarch64.yml

@@ -90,7 +90,7 @@ dependencies:
   - fonttools=4.56.0=py312hcc812fe_0
   - fortran-compiler=1.9.0=h25a59a9_0
   - fplll=5.5.0=h45c7457_0
-  - fpylll=0.6.2=py312h37c3976_0
+  - fpylll=0.6.3=py312h37c3976_0
   - freetype=2.13.3=he93130f_0
   - furo=2024.8.6=pyhd8ed1ab_2
   - gap-core=4.14.0=h1754e88_2

environment-3.12-linux.yml

@@ -91,7 +91,7 @@ dependencies:
   - fonttools=4.56.0=py312h178313f_0
   - fortran-compiler=1.9.0=h36df796_0
   - fplll=5.5.0=hd20a173_0
-  - fpylll=0.6.2=py312ha4ee43a_0
+  - fpylll=0.6.3=py312ha4ee43a_0
   - freetype=2.13.3=h48d6fc4_0
   - furo=2024.8.6=pyhd8ed1ab_2
   - gap-core=4.14.0=h3b03731_2

environment-3.12-macos-x86_64.yml

@@ -91,7 +91,7 @@ dependencies:
   - fonttools=4.56.0=py312h3520af0_0
   - fortran-compiler=1.9.0=h02557f8_0
   - fplll=5.5.0=h6ede486_0
-  - fpylll=0.6.2=py312hfffdf69_0
+  - fpylll=0.6.3=py312hfffdf69_0
   - freetype=2.13.3=h40dfd5c_0
   - furo=2024.8.6=pyhd8ed1ab_2
   - gap-core=4.14.0=hb9686a1_2

environment-3.12-macos.yml

@@ -91,7 +91,7 @@ dependencies:
   - fonttools=4.56.0=py312h998013c_0
   - fortran-compiler=1.9.0=h5692697_0
   - fplll=5.5.0=h2a2278a_0
-  - fpylll=0.6.2=py312h03fe13c_0
+  - fpylll=0.6.3=py312h03fe13c_0
   - freetype=2.13.3=h1d14073_0
   - furo=2024.8.6=pyhd8ed1ab_2
   - gap-core=4.14.0=h25f1785_2

pkgs/sage-conf/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sage-conf_conda/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sage-conf_pypi/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sage-docbuild/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sage-setup/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sage-sws2rst/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-bliss/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-categories/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-coxeter3/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-environment/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-mcqd/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-meataxe/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-objects/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-repl/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-sirocco/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pkgs/sagemath-tdlib/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

pyproject.toml

@@ -46,7 +46,7 @@ dependencies = [
     'ipykernel >=5.2.1',
     'jupyter-client',
     'ipywidgets >=7.5.1',
-    'fpylll >=0.5.9',
+    'fpylll >=0.6.3',
     'ptyprocess > 0.5',
     # TODO: Remove this once the migration to meson is complete
     'pkgconfig'

src/VERSION.txt

@@ -1 +1 @@
-10.6.rc0
+10.6.rc1

src/bin/sage-version.sh

@@ -4,6 +4,6 @@
 # which stops "setup.py develop" from rewriting it as a Python file.
 :
 # This file is auto-generated by the sage-update-version script, do not edit!
-SAGE_VERSION='10.6.rc0'
-SAGE_RELEASE_DATE='2025-03-22'
-SAGE_VERSION_BANNER='SageMath version 10.6.rc0, Release Date: 2025-03-22'
+SAGE_VERSION='10.6.rc1'
+SAGE_RELEASE_DATE='2025-03-27'
+SAGE_VERSION_BANNER='SageMath version 10.6.rc1, Release Date: 2025-03-27'

src/sage/matrix/matrix_integer_dense.pyx

@@ -2729,7 +2729,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
     #######################################################################
 
     def BKZ(self, delta=None, algorithm='fpLLL', fp=None, block_size=10, prune=0,
-            use_givens=False, precision=0, proof=None, **kwds):
+            use_givens=False, precision=0, proof=None, transformation=False, **kwds):
         """
         Return the result of running Block Korkin-Zolotarev reduction on
         ``self`` interpreted as a lattice.
@@ -2795,6 +2795,8 @@ cdef class Matrix_integer_dense(Matrix_dense):
         - ``precision`` -- (default: ``0`` for automatic choice) bit
           precision to use if ``fp='rr'`` is set
 
+        - ``transformation`` -- boolean (default: ``False``); also return transformation
+
         - ``**kwds`` -- keywords to be passed to :mod:`fpylll`; see
           :class:`fpylll.BKZ.Param` for details
 
@@ -2821,6 +2823,13 @@ cdef class Matrix_integer_dense(Matrix_dense):
             [ 2  1  0]
             [-1  1  3]
 
+        We return the transformation matrix::
+
+            sage: A = random_matrix(ZZ, 10, 20)
+            sage: R, U = A.BKZ(transformation=True)
+            sage: U * A == R
+            True
+
         ALGORITHM:
 
         Calls either NTL or fpLLL.
@@ -2859,48 +2868,59 @@ cdef class Matrix_integer_dense(Matrix_dense):
                 raise TypeError("fp parameter not understood.")
 
             A = self._ntl_()
+            UNTL = None
+            if transformation:
+                import sage.libs.ntl.ntl_mat_ZZ
+                _I = matrix_space.MatrixSpace(ZZ, self.nrows()).identity_matrix()
+                UNTL = sage.libs.ntl.ntl_mat_ZZ.ntl_mat_ZZ(self.nrows(),
+                        self.nrows(), _I.list())
 
             if algorithm == "BKZ_FP":
                 if not use_givens:
-                    r = A.BKZ_FP(U=None, delta=delta, BlockSize=block_size,
+                    r = A.BKZ_FP(U=UNTL, delta=delta, BlockSize=block_size,
                                  prune=prune, verbose=verbose)
                 else:
-                    r = A.G_BKZ_FP(U=None, delta=delta, BlockSize=block_size,
+                    r = A.G_BKZ_FP(U=UNTL, delta=delta, BlockSize=block_size,
                                    prune=prune, verbose=verbose)
 
             elif algorithm == "BKZ_QP":
                 if not use_givens:
-                    r = A.BKZ_QP(U=None, delta=delta, BlockSize=block_size,
+                    r = A.BKZ_QP(U=UNTL, delta=delta, BlockSize=block_size,
                                  prune=prune, verbose=verbose)
                 else:
-                    r = A.G_BKZ_QP(U=None, delta=delta, BlockSize=block_size,
+                    r = A.G_BKZ_QP(U=UNTL, delta=delta, BlockSize=block_size,
                                    prune=prune, verbose=verbose)
 
             elif algorithm == "BKZ_QP1":
                 if not use_givens:
-                    r = A.BKZ_QP1(U=None, delta=delta, BlockSize=block_size,
+                    r = A.BKZ_QP1(U=UNTL, delta=delta, BlockSize=block_size,
                                   prune=prune, verbose=verbose)
                 else:
-                    r = A.G_BKZ_QP1(U=None, delta=delta, BlockSize=block_size,
+                    r = A.G_BKZ_QP1(U=UNTL, delta=delta, BlockSize=block_size,
                                     prune=prune, verbose=verbose)
 
             elif algorithm == "BKZ_XD":
                 if not use_givens:
-                    r = A.BKZ_XD(U=None, delta=delta, BlockSize=block_size,
+                    r = A.BKZ_XD(U=UNTL, delta=delta, BlockSize=block_size,
                                  prune=prune, verbose=verbose)
                 else:
-                    r = A.G_BKZ_XD(U=None, delta=delta, BlockSize=block_size,
+                    r = A.G_BKZ_XD(U=UNTL, delta=delta, BlockSize=block_size,
                                    prune=prune, verbose=verbose)
 
             elif algorithm == "BKZ_RR":
                 if not use_givens:
-                    r = A.BKZ_RR(U=None, delta=delta, BlockSize=block_size,
+                    r = A.BKZ_RR(U=UNTL, delta=delta, BlockSize=block_size,
                                  prune=prune, verbose=verbose)
                 else:
-                    r = A.G_BKZ_RR(U=None, delta=delta, BlockSize=block_size,
+                    r = A.G_BKZ_RR(U=UNTL, delta=delta, BlockSize=block_size,
                                    prune=prune, verbose=verbose)
 
             self.cache("rank",ZZ(r))
+
+            if transformation:
+                U = self.new_matrix(self.nrows(), self.nrows(),
+                                    entries=[ZZ(z) for z in UNTL.list()])
+
             R = <Matrix_integer_dense>self.new_matrix(
                     entries=[ZZ(z) for z in A.list()])
 
@@ -2929,12 +2949,23 @@ cdef class Matrix_integer_dense(Matrix_dense):
                     kwds["auto_abort"] = True
 
             A = IntegerMatrix.from_matrix(self)
-            BKZ.reduction(A, BKZ.Param(block_size=block_size, delta=delta, **kwds),
+            Ufplll = None
+            if transformation:
+                _I = matrix_space.MatrixSpace(ZZ, self.nrows()).identity_matrix()
+                Ufplll = IntegerMatrix.from_matrix(_I)
+            BKZ.reduction(A,
+                          BKZ.Param(block_size=block_size, delta=delta, **kwds),
+                          U=Ufplll,
                           float_type=fp_,
                           precision=precision)
 
             R = A.to_matrix(self.new_matrix())
-        return R
+            if transformation:
+                U = Ufplll.to_matrix(self.new_matrix(Ufplll.nrows, Ufplll.ncols))
+        if transformation:
+            return R, U
+        else:
+            return R
 
     def LLL(self, delta=None, eta=None, algorithm='fpLLL:wrapper', fp=None, prec=0, early_red=False, use_givens=False, use_siegel=False, transformation=False, **kwds):
         r"""
@@ -3260,7 +3291,8 @@ cdef class Matrix_integer_dense(Matrix_dense):
             A = IntegerMatrix.from_matrix(self)
             Ufplll = None
             if transformation:
-                Ufplll = IntegerMatrix(A.nrows, A.nrows)
+                _I = matrix_space.MatrixSpace(ZZ, self.nrows()).identity_matrix()
+                Ufplll = IntegerMatrix.from_matrix(_I)
 
             method = algorithm.replace("fpLLL:","")
             if verb:

src/sage/matrix/matrix_rational_dense.pyx

@@ -2930,13 +2930,19 @@ cdef class Matrix_rational_dense(Matrix_dense):
             [ 1/28 -1/40 -1/18]
             [ 1/28 -1/40  1/18]
             [-1/14 -1/40     0]
+            sage: L, U = A.BKZ(transformation=True)
+            sage: U * A == L
+            True
 
             sage: A = random_matrix(QQ, 10, 10)
             sage: d = lcm(a.denom() for a in A.list())
             sage: A.BKZ() == (A * d).change_ring(ZZ).BKZ() / d
             True
         """
         A, d = self._clear_denom()
+        if kwargs.get('transformation', False):
+            L, U = A.BKZ(*args, **kwargs)
+            return L / d, U
         return A.BKZ(*args, **kwargs) / d
 
     def LLL(self, *args, **kwargs):

src/sage/version.py

@@ -1,5 +1,5 @@
 # Sage version information for Python scripts
 # This file is auto-generated by the sage-update-version script, do not edit!
-version = '10.6.rc0'
-date = '2025-03-22'
-banner = 'SageMath version 10.6.rc0, Release Date: 2025-03-22'
+version = '10.6.rc1'
+date = '2025-03-27'
+banner = 'SageMath version 10.6.rc1, Release Date: 2025-03-27'