Merge remote-tracking branch 'origin/u/annasomoza/22173-shiodainv' in…

…to local-merge-22173

src/doc/en/reference/references/index.rst

@@ -3491,6 +3491,9 @@ REFERENCES:
             Reduction*. Advances in Cryptology - EUROCRYPT '95. LNCS
             Volume 921, 1995, pp 1-12.
 
+.. [Sh1967] \T. Shioda. *On the graded ring of invariants of binary octavics* in
+            American J. of Math., 89(4):1022-1046, 1967.
+
 .. [SHET2018] \O. Seker, P. Heggernes, T. Ekim, and Z. Caner Taskin.
               *Generation of random chordal graphs using subtrees of a tree*,
               :arxiv:`1810.13326v1`.

src/sage/schemes/hyperelliptic_curves/all.py

@@ -7,3 +7,5 @@
                         clebsch_invariants)
 from .mestre import (Mestre_conic, HyperellipticCurve_from_invariants)
 from . import monsky_washnitzer
+from sage.misc.lazy_import import lazy_import
+lazy_import('sage.schemes.hyperelliptic_curves.invariants', 'shioda_invariants')

src/sage/schemes/hyperelliptic_curves/constructor.py

@@ -5,6 +5,9 @@
 
 - David Kohel (2006): initial version
 
+- Sorina Ionica, Elisa Lorenzo Garcia, Anna Somoza (2017-01-11): Added
+  functionality for genus 3.
+
 - Anna Somoza (2019-04): dynamic class creation
 
 """
@@ -24,6 +27,7 @@
 from .hyperelliptic_rational_field import HyperellipticCurve_rational_field
 from .hyperelliptic_padic_field import HyperellipticCurve_padic_field
 from .hyperelliptic_g2 import HyperellipticCurve_g2
+from .hyperelliptic_g3 import HyperellipticCurve_g3
 
 from sage.rings.padics.all import is_pAdicField
 from sage.rings.rational_field import is_RationalField
@@ -228,7 +232,7 @@ def HyperellipticCurve(f, h=0, names=None, PP=None, check_squarefree=True):
     supercls = []
     cls_name = []
 
-    genus_class = {2:HyperellipticCurve_g2}
+    genus_class = {2:HyperellipticCurve_g2, 3:HyperellipticCurve_g3}
     if g in genus_class.keys():
         supercls.append(genus_class[g])
     cls_name.append("g"+str(g))

src/sage/schemes/hyperelliptic_curves/hyperelliptic_g3_finite_field.py

@@ -0,0 +1,20 @@
+"""
+Hyperelliptic curves of genus 3 over a finite field
+"""
+from __future__ import absolute_import
+
+#*****************************************************************************
+#  Copyright (C) 2017 Sorina Ionica <sorina.ionica@gmail.com>
+#                2017 Elisa Lorenzo Garcia <elisa.lorenzo@gmail.com>
+#                2017 Anna Somoza <anna.somoza@upc.edu>
+#  Distributed under the terms of the GNU General Public License (GPL)
+#                  http://www.gnu.org/licenses/
+#*****************************************************************************
+
+from . import hyperelliptic_finite_field, hyperelliptic_g3_generic
+
+class HyperellipticCurve_g3_finite_field(
+    hyperelliptic_g3_generic.HyperellipticCurve_g3_generic,
+    hyperelliptic_finite_field.HyperellipticCurve_finite_field):
+    pass
+

src/sage/schemes/hyperelliptic_curves/hyperelliptic_g3_generic.py

@@ -0,0 +1,54 @@
+r"""
+Hyperelliptic curves of genus 3 over a general ring
+
+AUTHORS:
+
+- Sorina Ionica, Elisa Lorenzo Garcia, Anna Somoza (2017-01-11): Initial version
+"""
+from __future__ import absolute_import
+#*****************************************************************************
+#  Copyright (C) 2017 Sorina Ionica <sorina.ionica@gmail.com>
+#                2017 Elisa Lorenzo Garcia <elisa.lorenzo@gmail.com>
+#                2017 Anna Somoza <anna.somoza@upc.edu>
+#  Distributed under the terms of the GNU General Public License (GPL)
+#                  http://www.gnu.org/licenses/
+#*****************************************************************************
+
+from . import hyperelliptic_generic
+from . import invariants
+
+
+class HyperellipticCurve_g3_generic(hyperelliptic_generic.HyperellipticCurve_generic):
+    def shioda_invariants(self):
+        r"""
+        Return the Shioda invariants `(J2, J3, J4, J5, J6, J7, J8, J9, J10)` of Shioda, [Sh1967]_.
+
+        .. SEEALSO::
+
+            :meth:`sage.schemes.hyperelliptic_curves.invariants`
+
+        EXAMPLES::
+
+            sage: R.<x> = QQ[]
+            sage: f = x^7 - x^4 + 3
+            sage: C = HyperellipticCurve(f)
+            sage: C.shioda_invariants()
+            [8/35, -144/8575, 32/7203, -128/84035, 128/1058841, 10673116768/12353145,
+            149423644992/1008840175, 85384936192/1815912315, 398463049216/49433168575]
+            sage: C = HyperellipticCurve(x^8 + 3*x^2 + 2*x +1)
+            sage: C.shioda_invariants()
+            [32, 648/49, 512/3, 6912/49, -8192/9, -24064/49, -89293312/36015,
+            69632/21, 1441134592/108045]
+            sage: C = HyperellipticCurve(x*(x^6 + 1))
+            sage: C.shioda_invariants()
+            [-4, 0, 1/6, 0, 1/36, 0, 1/70, 0, 1/420]
+            sage: C = HyperellipticCurve(x**8+4*x**4+5, x)
+            sage: C.shioda_invariants()
+            [5728/35, 1901607/17150, 29738480/7203, 95245904/16807, -114656031488/1058841,
+            -1832866169368/12353145, -4626584012971696/3026520525, 1415110141852160/363182463,
+            713601762721839616/17795940687]
+
+
+        """
+        f, h = self.hyperelliptic_polynomials()
+        return invariants.shioda_invariants(4*f + h**2)

src/sage/schemes/hyperelliptic_curves/hyperelliptic_g3_padic_field.py

@@ -0,0 +1,19 @@
+"""
+Hyperelliptic curves of genus 3 over a p-adic field
+"""
+from __future__ import absolute_import
+
+#*****************************************************************************
+#  Copyright (C) 2017 Sorina Ionica <sorina.ionica@gmail.com>
+#                2017 Elisa Lorenzo Garcia <elisa.lorenzo@gmail.com>
+#                2017 Anna Somoza <anna.somoza@upc.edu>
+#  Distributed under the terms of the GNU General Public License (GPL)
+#                  http://www.gnu.org/licenses/
+#*****************************************************************************
+
+from . import hyperelliptic_g3_generic, hyperelliptic_padic_field
+
+class HyperellipticCurve_g3_padic_field(
+    hyperelliptic_g3_generic.HyperellipticCurve_g3_generic,
+    hyperelliptic_padic_field.HyperellipticCurve_padic_field):
+    pass

src/sage/schemes/hyperelliptic_curves/hyperelliptic_g3_rational_field.py

@@ -0,0 +1,19 @@
+"""
+Hyperelliptic curves of genus 3 over the rationals
+"""
+from __future__ import absolute_import
+
+#*****************************************************************************
+#  Copyright (C) 2017 Sorina Ionica <sorina.ionica@gmail.com>
+#                2017 Elisa Lorenzo Garcia <elisa.lorenzo@gmail.com>
+#                2017 Anna Somoza <anna.somoza@upc.edu>
+#  Distributed under the terms of the GNU General Public License (GPL)
+#                  http://www.gnu.org/licenses/
+#*****************************************************************************
+
+from . import hyperelliptic_g3_generic, hyperelliptic_rational_field
+
+class HyperellipticCurve_g3_rational_field(
+    hyperelliptic_g3_generic.HyperellipticCurve_g3_generic,
+    hyperelliptic_rational_field.HyperellipticCurve_rational_field):
+    pass

src/sage/schemes/hyperelliptic_curves/invariants.py

@@ -1,17 +1,18 @@
 # -*- coding: utf-8 -*-
 r"""
-Compute invariants of quintics and sextics via 'Ueberschiebung'
+Compute invariants of genus 2 and 3 hyperelliptic curves via 'Ueberschiebung'.
 
 .. TODO::
 
     * Implement invariants in small positive characteristic.
 
     * Cardona-Quer and additional invariants for classifying automorphism groups.
 
-AUTHOR:
-
-- Nick Alexander
+AUTHORS:
 
+- Nick Alexander: Initial version
+- Sorina Ionica, Elisa Lorenzo Garcia, Anna Somoza (2017-01-11): Added
+  functionality for genus 3.
 """
 from sage.rings.all import ZZ
 from sage.rings.all import PolynomialRing
@@ -369,6 +370,12 @@ def absolute_igusa_invariants_kohel(f):
 
     `f` may be homogeneous in two variables or inhomogeneous in one.
 
+    REFERENCES:
+
+    .. [K] Kohel, David.  ECHIDNA: Databases for Elliptic Curves
+       and Higher Dimensional Analogues.
+       Available at http://echidna.maths.usyd.edu.au/~kohel/dbs/
+
     EXAMPLES::
 
         sage: R.<x> = QQ[]
@@ -397,3 +404,47 @@ def absolute_igusa_invariants_kohel(f):
     i2 = I2**3*I4/I10
     i3 = I2**2*I6/I10
     return (i1, i2, i3)
+
+def shioda_invariants(f):
+    r"""
+    Given a octavic form `f`, return the 9 Shioda invariants, [Sh1967]_.
+
+    `f` may be homogeneous in two variables or inhomogeneous in one.
+
+    EXAMPLES::
+
+        sage: R.<x> = QQ[]
+        sage: f = x^7 - x^4 + 3
+        sage: from sage.schemes.hyperelliptic_curves.invariants import shioda_invariants
+        sage: shioda_invariants(f)
+        [1/70,  -9/34300,  1/57624,  -1/672280,  1/33882912,  333534899/6324810240,
+        2334744453/1033052339200,  333534907/1859494210560,  778248143/101239129241600]
+        sage: R.<x,y> = QQ[]
+        sage: shioda_invariants(x^8 + 3*x^2*y^6 + 2*x*y^7 + y^8)
+        [2,  81/392,  2/3,  27/196,  -2/9,  -47/1568,  -174401/4609920,  17/1344,
+        703679/55319040]
+    """
+    F = f
+    if f.parent().ngens() == 1:
+        f = PolynomialRing(f.parent().base_ring(), 1, f.parent().variable_name())(f)
+        x1, x2 = f.homogenize().parent().gens()
+        F = sum([ f[i]*x1**i*x2**(8-i) for i in range(9)])
+    H = Ueberschiebung(F,F,2)
+    g = Ueberschiebung(F,F,4)
+    k = Ueberschiebung(F,F,6)
+    h = Ueberschiebung(k,k,2)
+    m = Ueberschiebung(F,k,4)
+    n = Ueberschiebung(F,h,4)
+    p = Ueberschiebung(g,k,4)
+    q = Ueberschiebung(g,h,4)
+    J2 = Ueberschiebung(F,F,8)
+    J3 = Ueberschiebung(F,g,8)
+    J4 = Ueberschiebung(k,k,4)
+    J5 = Ueberschiebung(m,k,4)
+    J6 = Ueberschiebung(k,h,4)
+    J7 = Ueberschiebung(m,h,4)
+    J8 = Ueberschiebung(p,h,4)
+    J9 = Ueberschiebung(n,h,4)
+    J10 = Ueberschiebung(q,h,4)
+    JI = [J2,J3,J4,J5,J6,J7,J8,J9,J10]
+    return [j.constant_coefficient() for j in JI]