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
Example #2
0
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
Example #3
0
 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
Example #4
0
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