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sage: Normalize sign of polynomial factors in prover

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The prover, when run on recent sage versions,  failed to prove some of its
goals due to a change in sage. This commit adapts our code accordingly.
The prover passes again after this commit.
This commit is contained in:
Tim Ruffing 2022-02-03 12:46:42 +01:00
parent eae75869cf
commit 77cfa98dbc
1 changed files with 34 additions and 10 deletions
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44
sage/group_prover.sage
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@ -177,6 +177,30 @@ class constraints:
def __repr__(self):
return "%s" % self
def normalize_factor(p):
"""Normalizes the sign of primitive polynomials (as returned by factor())
This function ensures that the polynomial has a positive leading coefficient.
This is necessary because recent sage versions (starting with v9.3 or v9.4,
we don't know) are inconsistent about the placement of the minus sign in
polynomial factorizations:
```
sage: R.<ax,bx,ay,by,Az,Bz,Ai,Bi> = PolynomialRing(QQ,8,order='invlex')
sage: R((-2 * (bx - ax)) ^ 1).factor()
(-2) * (bx - ax)
sage: R((-2 * (bx - ax)) ^ 2).factor()
(4) * (-bx + ax)^2
sage: R((-2 * (bx - ax)) ^ 3).factor()
(8) * (-bx + ax)^3
```
"""
# Assert p is not 0 and that its non-zero coeffients are coprime.
# (We could just work with the primitive part p/p.content() but we want to be
# aware if factor() does not return a primitive part in future sage versions.)
assert p.content() == 1
# Ensure that the first non-zero coefficient is positive.
return p if p.lc() > 0 else -p
def conflicts(R, con):
"""Check whether any of the passed non-zero assumptions is implied by the zero assumptions"""
@ -204,10 +228,10 @@ def get_nonzero_set(R, assume):
nonzero = set()
for nz in map(numerator, assume.nonzero):
for (f,n) in nz.factor():
nonzero.add(f)
nonzero.add(normalize_factor(f))
rnz = zero.reduce(nz)
for (f,n) in rnz.factor():
nonzero.add(f)
nonzero.add(normalize_factor(f))
return nonzero
@ -222,27 +246,27 @@ def prove_nonzero(R, exprs, assume):
return (False, [exprs[expr]])
allexprs = reduce(lambda a,b: numerator(a)*numerator(b), exprs, 1)
for (f, n) in allexprs.factor():
if f not in nonzero:
if normalize_factor(f) not in nonzero:
ok = False
if ok:
return (True, None)
ok = True
for (f, n) in zero.reduce(allexprs).factor():
if f not in nonzero:
if normalize_factor(f) not in nonzero:
ok = False
if ok:
return (True, None)
ok = True
for expr in exprs:
for (f,n) in numerator(expr).factor():
if f not in nonzero:
if normalize_factor(f) not in nonzero:
ok = False
if ok:
return (True, None)
ok = True
for expr in exprs:
for (f,n) in zero.reduce(numerator(expr)).factor():
if f not in nonzero:
if normalize_factor(f) not in nonzero:
expl.add(exprs[expr])
if expl:
return (False, list(expl))
@ -279,8 +303,8 @@ def describe_extra(R, assume, assumeExtra):
if base not in zero:
add = []
for (f, n) in numerator(base).factor():
if f not in nonzero:
add += ["%s" % f]
if normalize_factor(f) not in nonzero:
add += ["%s" % normalize_factor(f)]
if add:
ret.add((" * ".join(add)) + " = 0 [%s]" % assumeExtra.zero[base])
# Iterate over the extra nonzero expressions
@ -288,8 +312,8 @@ def describe_extra(R, assume, assumeExtra):
nzr = zeroextra.reduce(numerator(nz))
if nzr not in zeroextra:
for (f,n) in nzr.factor():
if zeroextra.reduce(f) not in nonzero:
ret.add("%s != 0" % zeroextra.reduce(f))
if normalize_factor(zeroextra.reduce(f)) not in nonzero:
ret.add("%s != 0" % normalize_factor(zeroextra.reduce(f)))
return ", ".join(x for x in ret)