def add_simple_poly(p,i):
p=Polynomial(p)
if p.is_zero():
return
res_p=Polynomial(res.get(i, Polynomial(0, p.ring())))
res[i]=res_p+p
if res[i].is_zero():
del res[i]
inter=BooleSet(res_p).intersect(BooleSet(p))
add_simple_poly(inter, i+1)
return
def proofll(ifthen, reductors, redsb=True, prot=True):
if prot and (not ifthen.supposedToBeValid):
print "THIS THEOREM IS NOT SUPPOSED TO BE VALID"
ip_pre = ifthen.ifpart
ip = []
for p in ip_pre:
p = Polynomial(p)
if p.is_zero():
continue
li = list(p.lead().variables())
if len(li) == 1 and (not (li[0] in list(Polynomial(reductors).lead().
variables()))):
assert not Polynomial(reductors).is_zero()
lead_index = li[0]
if redsb:
p = ll_red_nf_redsb(p, reductors)
reductors = ll_red_nf_redsb(Polynomial(reductors), BooleSet(p.
set()))
p_nav = p.navigation()
reductors = recursively_insert(p_nav.else_branch(), p_nav.value(),
reductors)
else:
ip.append(p)
it = ifthen.thenpart
if prot:
print "proofing:", ifthen
ip = logicaland(ip)
for c in it:
if prot:
print "proofing part:", c
c = logicalor([BooleConstant(1) + ip, c])
if c.is_zero():
if prot:
print "TRUE (trivial)"
return True
else:
c_orig = c
if redsb:
c = ll_red_nf_redsb(c, reductors)
else:
c = ll_red_nf_noredsb(c, reductors)
if c.is_zero():
if prot:
print "TRUE"
return True
else:
if prot:
print "FAILED"
print "can construct COUNTER EXAMPLE with:", find_one(c)
return False
def add_simple_poly(p, i):
p = Polynomial(p)
if p.is_zero():
return
res_p = Polynomial(res.get(i, Polynomial(0, p.ring())))
res[i] = res_p + p
if res[i].is_zero():
del res[i]
inter = BooleSet(res_p).intersect(BooleSet(p))
add_simple_poly(inter, i + 1)
return
def proofll(ifthen, reductors, redsb=True, prot=True):
if prot and (not ifthen.supposedToBeValid):
print "THIS THEOREM IS NOT SUPPOSED TO BE VALID"
ip_pre = ifthen.ifpart
ip = []
for p in ip_pre:
p = Polynomial(p)
if p.is_zero():
continue
li = list(p.lead().variables())
if len(li) == 1 and (not (li[0] in list(
Polynomial(reductors).lead().variables()))):
assert not Polynomial(reductors).is_zero()
lead_index = li[0]
if redsb:
p = ll_red_nf_redsb(p, reductors)
reductors = ll_red_nf_redsb(Polynomial(reductors),
BooleSet(p.set()))
p_nav = p.navigation()
reductors = recursively_insert(p_nav.else_branch(), p_nav.value(),
reductors)
else:
ip.append(p)
it = ifthen.thenpart
if prot:
print "proofing:", ifthen
ip = logicaland(ip)
for c in it:
if prot:
print "proofing part:", c
c = logicalor([BooleConstant(1) + ip, c])
if c.is_zero():
if prot:
print "TRUE (trivial)"
return True
else:
c_orig = c
if redsb:
c = ll_red_nf_redsb(c, reductors)
else:
c = ll_red_nf_noredsb(c, reductors)
if c.is_zero():
if prot:
print "TRUE"
return True
else:
if prot:
print "FAILED"
print "can construct COUNTER EXAMPLE with:", find_one(c)
return False