SL2Z.random_element unstable, ZZ.random_element does not ignore bounds not needed for distribution

[kliem]

sage: for _ in range(1000): _ = SL2Z.random_element(5, distribution='1/n')
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-18-454018fc8ca8> in <module>
----> 1 for _ in range(Integer(1000)): _ = SL2Z.random_element(Integer(5), distribution='1/n')

~/Applications/sage/local/lib/python3.8/site-packages/sage/modular/arithgroup/congroup_sl2z.py in random_element(self, bound, *args, **kwds)
    212         d = ZZ.random_element(1-bound, bound, *args, **kwds)
    213         if gcd(c,d) != 1: # try again
--> 214             return self.random_element(bound, *args, **kwds)
    215         else:
    216             a,b,c,d = lift_to_sl2z(c,d,0)

~/Applications/sage/local/lib/python3.8/site-packages/sage/modular/arithgroup/congroup_sl2z.py in random_element(self, bound, *args, **kwds)
    231                 wlo = min(wlo, ((bound - b)/ZZ(-d)).ceil())
    232 
--> 233             w = ZZ.random_element(1-wlo, whi, *args, **kwds)
    234             a += c*w
    235             b += d*w

~/Applications/sage/local/lib/python3.8/site-packages/sage/rings/integer_ring.pyx in sage.rings.integer_ring.IntegerRing_class.random_element (build/cythonized/sage/rings/integer_ring.c:6515)()
    715             raise TypeError("x must be > 0")
    716         if x is not None and y is not None and x >= y:
--> 717             raise TypeError("x must be < y")
    718         self._randomize_mpz(z.value, x, y, distribution)
    719         return z

TypeError: x must be < y

sage: ZZ.random_element(-10, -5, distribution="mpz_rrandomb")                                                                                                                       
---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)
<ipython-input-1-6e917954ddfe> in <module>
----> 1 ZZ.random_element(-Integer(10), -Integer(5), distribution="mpz_rrandomb")

/srv/public/kliem/sage/local/lib/python3.7/site-packages/sage/rings/integer_ring.pyx in sage.rings.integer_ring.IntegerRing_class.random_element (build/cythonized/sage/rings/integer_ring.c:6533)()
    733         if x is not None and y is not None and x >= y:
    734             raise TypeError("x must be < y")
--> 735         self._randomize_mpz(z.value, x, y, distribution)
    736         return z
    737 

/srv/public/kliem/sage/local/lib/python3.7/site-packages/sage/rings/integer_ring.pyx in sage.rings.integer_ring.IntegerRing_class._randomize_mpz (build/cythonized/sage/rings/integer_ring.c:7036)()
    778             if x is None:
    779                 raise ValueError("must specify x to use 'distribution=mpz_rrandomb'")
--> 780             mpz_rrandomb(value, rstate.gmp_state, int(x))
    781         elif distribution == "gaussian":
    782             global _prev_discrete_gaussian_integer_sampler

OverflowError: can't convert negative value to unsigned long

Component: modular forms

Author: Jonathan Kliem

Branch/Commit: e6a697a

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/32124

[kliem]

comment:1

I would say the problem is in ZZ.random_element. It claims that x and y are ignored, if the distribution is '1/n'. However, it still raises an error if y >= x, which is not what I would call ignoring x and y.

[kliem]

Description changed:

--- 
+++ 
@@ -29,3 +29,27 @@
 
 TypeError: x must be < y
 ```
+
+```
+sage: ZZ.random_element(-10, -5, distribution="mpz_rrandomb")                                                                                                                       
+---------------------------------------------------------------------------
+OverflowError                             Traceback (most recent call last)
+<ipython-input-1-6e917954ddfe> in <module>
+----> 1 ZZ.random_element(-Integer(10), -Integer(5), distribution="mpz_rrandomb")
+
+/srv/public/kliem/sage/local/lib/python3.7/site-packages/sage/rings/integer_ring.pyx in sage.rings.integer_ring.IntegerRing_class.random_element (build/cythonized/sage/rings/integer_ring.c:6533)()
+    733         if x is not None and y is not None and x >= y:
+    734             raise TypeError("x must be < y")
+--> 735         self._randomize_mpz(z.value, x, y, distribution)
+    736         return z
+    737 
+
+/srv/public/kliem/sage/local/lib/python3.7/site-packages/sage/rings/integer_ring.pyx in sage.rings.integer_ring.IntegerRing_class._randomize_mpz (build/cythonized/sage/rings/integer_ring.c:7036)()
+    778             if x is None:
+    779                 raise ValueError("must specify x to use 'distribution=mpz_rrandomb'")
+--> 780             mpz_rrandomb(value, rstate.gmp_state, int(x))
+    781         elif distribution == "gaussian":
+    782             global _prev_discrete_gaussian_integer_sampler
+
+OverflowError: can't convert negative value to unsigned long
+```

[kliem]

New commits:

e6a697a

truely ignore ignored bounds for ZZ.random_element

[kliem]

Author: Jonathan Kliem

[kliem]

Branch: public/32124

[kliem]

Commit: e6a697a

[dimpase]

comment:4

good catch!

[fchapoton]

comment:5

ok, let it be

[fchapoton]

Reviewer: Frédéric Chapoton