src/sage/sat/boolean_polynomials.py: Use file-level # optional/needs

src/sage/sat/boolean_polynomials.py

@@ -1,4 +1,4 @@
-# sage.doctest: needs sage.rings.polynomial.pbori
+# sage.doctest: optional - pycryptosat, needs sage.modules sage.rings.polynomial.pbori
 """
 SAT Functions for Boolean Polynomials
 
@@ -72,8 +72,8 @@ def solve(F, converter=None, solver=None, n=1, target_variables=None, **kwds):
 
  We construct a very small-scale AES system of equations::
 
- sage: sr = mq.SR(1, 1, 1, 4, gf2=True, polybori=True) # needs sage.modules sage.rings.finite_rings
- sage: while True: # workaround (see :trac:`31891`) # needs sage.modules sage.rings.finite_rings
+ sage: sr = mq.SR(1, 1, 1, 4, gf2=True, polybori=True)
+ sage: while True: # workaround (see :trac:`31891`)
  ....: try:
  ....: F, s = sr.polynomial_system()
  ....: break
@@ -83,57 +83,56 @@ def solve(F, converter=None, solver=None, n=1, target_variables=None, **kwds):
  and pass it to a SAT solver::
 
  sage: from sage.sat.boolean_polynomials import solve as solve_sat
- sage: s = solve_sat(F) # optional - pycryptosat # needs sage.modules sage.rings.finite_rings
- sage: F.subs(s[0]) # optional - pycryptosat # needs sage.modules sage.rings.finite_rings
+ sage: s = solve_sat(F)
+ sage: F.subs(s[0])
  Polynomial Sequence with 36 Polynomials in 0 Variables
 
  This time we pass a few options through to the converter and the solver::
 
- sage: s = solve_sat(F, c_max_vars_sparse=4, c_cutting_number=8) # optional - pycryptosat, needs sage.modules sage.rings.finite_rings
- sage: F.subs(s[0]) # optional - pycryptosat # needs sage.modules sage.rings.finite_rings
+ sage: s = solve_sat(F, c_max_vars_sparse=4, c_cutting_number=8)
+ sage: F.subs(s[0])
  Polynomial Sequence with 36 Polynomials in 0 Variables
 
  We construct a very simple system with three solutions
  and ask for a specific number of solutions::
 
- sage: # optional - pycryptosat, needs sage.modules
  sage: B.<a,b> = BooleanPolynomialRing()
  sage: f = a*b
  sage: l = solve_sat([f],n=1)
  sage: len(l) == 1, f.subs(l[0])
  (True, 0)
 
- sage: l = solve_sat([a*b],n=2) # optional - pycryptosat # needs sage.modules
- sage: len(l) == 2, f.subs(l[0]), f.subs(l[1]) # optional - pycryptosat # needs sage.modules
+ sage: l = solve_sat([a*b],n=2)
+ sage: len(l) == 2, f.subs(l[0]), f.subs(l[1])
  (True, 0, 0)
 
- sage: sorted((d[a], d[b]) for d in solve_sat([a*b], n=3)) # optional - pycryptosat, needs sage.modules
+ sage: sorted((d[a], d[b]) for d in solve_sat([a*b], n=3))
  [(0, 0), (0, 1), (1, 0)]
- sage: sorted((d[a], d[b]) for d in solve_sat([a*b], n=4)) # optional - pycryptosat, needs sage.modules
+ sage: sorted((d[a], d[b]) for d in solve_sat([a*b], n=4))
  [(0, 0), (0, 1), (1, 0)]
- sage: sorted((d[a], d[b]) for d in solve_sat([a*b], n=infinity)) # optional - pycryptosat, needs sage.modules
+ sage: sorted((d[a], d[b]) for d in solve_sat([a*b], n=infinity))
  [(0, 0), (0, 1), (1, 0)]
 
  In the next example we see how the ``target_variables`` parameter works::
 
  sage: from sage.sat.boolean_polynomials import solve as solve_sat
- sage: R.<a,b,c,d> = BooleanPolynomialRing() # optional - pycryptosat # needs sage.modules
- sage: F = [a + b, a + c + d] # optional - pycryptosat # needs sage.modules
+ sage: R.<a,b,c,d> = BooleanPolynomialRing()
+ sage: F = [a + b, a + c + d]
 
  First the normal use case::
 
- sage: sorted((D[a], D[b], D[c], D[d]) # optional - pycryptosat # needs sage.modules
+ sage: sorted((D[a], D[b], D[c], D[d])
  ....: for D in solve_sat(F, n=infinity))
  [(0, 0, 0, 0), (0, 0, 1, 1), (1, 1, 0, 1), (1, 1, 1, 0)]
 
  Now we are only interested in the solutions of the variables a and b::
 
- sage: solve_sat(F, n=infinity, target_variables=[a,b]) # optional - pycryptosat, needs sage.modules
+ sage: solve_sat(F, n=infinity, target_variables=[a,b])
  [{b: 0, a: 0}, {b: 1, a: 1}]
 
  Here, we generate and solve the cubic equations of the AES SBox (see :trac:`26676`)::
 
- sage: # long time, optional - pycryptosat, needs sage.modules
+ sage: # long time
  sage: from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence
  sage: from sage.sat.boolean_polynomials import solve as solve_sat
  sage: sr = sage.crypto.mq.SR(1, 4, 4, 8,
@@ -145,7 +144,7 @@ def solve(F, converter=None, solver=None, n=1, target_variables=None, **kwds):
  sage: variables = ",".join(variables)
  sage: R = BooleanPolynomialRing(16, variables)
  sage: eqs = [R(eq) for eq in eqs]
- sage: sls_aes = solve_sat(eqs, n = infinity)
+ sage: sls_aes = solve_sat(eqs, n=infinity)
  sage: len(sls_aes)
  256
 
@@ -168,7 +167,7 @@ def solve(F, converter=None, solver=None, n=1, target_variables=None, **kwds):
  ....: k9 + k28,
  ....: k11 + k20]
  sage: from sage.sat.boolean_polynomials import solve as solve_sat
- sage: solve_sat(keqs, n=1, solver=SAT('cryptominisat')) # optional - pycryptosat
+ sage: solve_sat(keqs, n=1, solver=SAT('cryptominisat'))
  [{k28: 0,
  k26: 1,
  k24: 0,
@@ -342,16 +341,16 @@ def learn(F, converter=None, solver=None, max_learnt_length=3, interreduction=Fa
 
  EXAMPLES::
 
- sage: from sage.sat.boolean_polynomials import learn as learn_sat # optional - pycryptosat
+  sage: from sage.sat.boolean_polynomials import learn as learn_sat
 
  We construct a simple system and solve it::
 
- sage: set_random_seed(2300)
- sage: sr = mq.SR(1, 2, 2, 4, gf2=True, polybori=True) # optional - pycryptosat, needs sage.modules sage.rings.finite_rings
- sage: F,s = sr.polynomial_system() # optional - pycryptosat # needs sage.modules sage.rings.finite_rings
- sage: H = learn_sat(F) # optional - pycryptosat # needs sage.modules sage.rings.finite_rings
- sage: H[-1] # optional - pycryptosat # needs sage.modules sage.rings.finite_rings
- k033 + 1
+  sage: set_random_seed(2300)
+  sage: sr = mq.SR(1, 2, 2, 4, gf2=True, polybori=True)
+  sage: F,s = sr.polynomial_system()
+  sage: H = learn_sat(F)
+  sage: H[-1]
+  k033 + 1
  """
  try:
  len(F)