sagemathgh-38490: prevent crash in order_from_multiple() due to round…

…ing error

Due to what appears to be rounding errors, the value of `k` here can be
zero, which results in the list `L` being split as `L1 == []` and `L2 ==
L`. This causes an error in the next recursive call.

Simple workaround: If either `L1` or `L2` would end up being empty, we
split the lists in the middle instead.

Resolves sagemath#38489.

URL: sagemath#38490
Reported by: Lorenz Panny
Reviewer(s):

build/pkgs/configure/checksums.ini

@@ -1,3 +1,3 @@
 tarball=configure-VERSION.tar.gz
-sha1=e162e0f52da5eca0c01ddf4831edcea1acd72033
-sha256=2033521228294e134368d69457d6e582706e84ff10bf3d6d0a57a2a4afad0a8b
+sha1=7ae6149d44ba78586d234861a18856430f89c439
+sha256=2417ae01c7f3ed65708a7fc937d9f2c4592252cbc35dceb3323445bd868bf8ee

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-b178c10a7401b381b8ed2daab5aaf026436452c9
+95fb8c3284c490325ef1e116f3a038a3467f5086

src/sage/groups/generic.py

@@ -1257,6 +1257,17 @@ def order_from_multiple(P, m, plist=None, factorization=None, check=True,
         sage: K.<a> = GF(3^60)
         sage: order_from_multiple(a, 3^60 - 1, operation='*', check=False)
         42391158275216203514294433200
+
+    TESTS:
+
+    Check that :issue:`38489` is fixed::
+
+        sage: from sage.groups.generic import order_from_multiple
+        sage: plist = [43, 257, 547, 881]
+        sage: m = prod(plist[:-1])
+        sage: elt = Zmod(m)(plist[-1])
+        sage: order_from_multiple(elt, m, plist=plist)
+        6044897
     """
     Z = integer_ring.ZZ
 
@@ -1325,6 +1336,8 @@ def _order_from_multiple_helper(Q, L, S):
                 if abs(sum_left + v - (S / 2)) > abs(sum_left - (S / 2)):
                     break
                 sum_left += v
+            if not 0 < k < l:
+                k = l // 2
             L1 = L[:k]
             L2 = L[k:]
             # recursive calls