1253 if (best_level == 0)
1280 gcdcAcB=
gcd (cA, cB);
1289 gcdlcAlcB=
gcd (lcA, lcB);
1296 coF=
N (ppA*(cA/gcdcAcB));
1297 coG=
N (ppB*(cB/gcdcAcB));
1308 coF=
N (ppA*(cA/gcdcAcB));
1309 coG=
N (ppB*(cB/gcdcAcB));
1314 CanonicalForm newtonPoly, coF_random_element, coG_random_element,
1315 coF_m, coG_m, ppCoF, ppCoG;
1325 bool inextension=
false;
1328 int bound1=
degree (ppA, 1);
1329 int bound2=
degree (ppB, 1);
1337 if (!fail && !inextension)
1342 modGCDFp (ppA (random_element,
x), ppB (random_element,
x),
1343 coF_random_element, coG_random_element,
topLevel,
1346 "time for recursive call: ");
1347 DEBOUTLN (cerr,
"G_random_element= " << G_random_element);
1349 else if (!fail && inextension)
1354 modGCDFq (ppA (random_element,
x), ppB (random_element,
x),
1355 coF_random_element, coG_random_element, V_buf,
1358 "time for recursive call: ");
1359 DEBOUTLN (cerr,
"G_random_element= " << G_random_element);
1361 else if (fail && !inextension)
1368 bool initialized=
false;
1387 modGCDFq (ppA (random_element,
x), ppB (random_element,
x),
1388 coF_random_element, coG_random_element,
alpha,
1391 "time for recursive call: ");
1392 DEBOUTLN (cerr,
"G_random_element= " << G_random_element);
1394 else if (fail && inextension)
1401 bool prim_fail=
false;
1406 if (V_buf3 !=
alpha)
1409 G_m=
mapDown (G_m, prim_elem, im_prim_elem,
alpha, source, dest);
1410 coF_m=
mapDown (coF_m, prim_elem, im_prim_elem,
alpha, source, dest);
1411 coG_m=
mapDown (coG_m, prim_elem, im_prim_elem,
alpha, source, dest);
1412 newtonPoly=
mapDown (newtonPoly, prim_elem, im_prim_elem,
alpha,
1414 ppA=
mapDown (ppA, prim_elem, im_prim_elem,
alpha, source, dest);
1415 ppB=
mapDown (ppB, prim_elem, im_prim_elem,
alpha, source, dest);
1416 gcdlcAlcB=
mapDown (gcdlcAlcB, prim_elem, im_prim_elem,
alpha, source,
1418 lcA=
mapDown (lcA, prim_elem, im_prim_elem,
alpha, source, dest);
1419 lcB=
mapDown (lcB, prim_elem, im_prim_elem,
alpha, source, dest);
1421 i.getItem()=
mapDown (
i.getItem(), prim_elem, im_prim_elem,
alpha,
1425 ASSERT (!prim_fail,
"failure in integer factorizer");
1435 i.getItem()=
mapUp (
i.getItem(),
alpha, V_buf, prim_elem,
1436 im_prim_elem, source, dest);
1437 m=
mapUp (
m,
alpha, V_buf, prim_elem, im_prim_elem, source, dest);
1438 G_m=
mapUp (G_m,
alpha, V_buf, prim_elem, im_prim_elem, source, dest);
1439 coF_m=
mapUp (coF_m,
alpha, V_buf, prim_elem, im_prim_elem, source, dest);
1440 coG_m=
mapUp (coG_m,
alpha, V_buf, prim_elem, im_prim_elem, source, dest);
1441 newtonPoly=
mapUp (newtonPoly,
alpha, V_buf, prim_elem, im_prim_elem,
1443 ppA=
mapUp (ppA,
alpha, V_buf, prim_elem, im_prim_elem, source, dest);
1444 ppB=
mapUp (ppB,
alpha, V_buf, prim_elem, im_prim_elem, source, dest);
1445 gcdlcAlcB=
mapUp (gcdlcAlcB,
alpha, V_buf, prim_elem, im_prim_elem,
1447 lcA=
mapUp (lcA,
alpha, V_buf, prim_elem, im_prim_elem, source, dest);
1448 lcB=
mapUp (lcB,
alpha, V_buf, prim_elem, im_prim_elem, source, dest);
1455 modGCDFq (ppA (random_element,
x), ppB (random_element,
x),
1456 coF_random_element, coG_random_element, V_buf,
1459 "time for recursive call: ");
1460 DEBOUTLN (cerr,
"G_random_element= " << G_random_element);
1474 coF=
N (ppA*(cA/gcdcAcB));
1475 coG=
N (ppB*(cB/gcdcAcB));
1481 if (!
find (
l, random_element))
1482 l.append (random_element);
1486 G_random_element= (gcdlcAlcB(random_element,
x)/
uni_lcoeff(G_random_element))
1489 coF_random_element= (lcA(random_element,
x)/
uni_lcoeff(coF_random_element))
1490 *coF_random_element;
1491 coG_random_element= (lcB(random_element,
x)/
uni_lcoeff(coG_random_element))
1492 *coG_random_element;
1511 H=
newtonInterp (random_element, G_random_element, newtonPoly, G_m,
x);
1512 coF=
newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,
x);
1513 coG=
newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,
x);
1515 "time for newton_interpolation: ");
1521 if (gcdlcAlcB.
isOne())
1540 coF=
N ((cA/gcdcAcB)*ppCoF);
1541 coG=
N ((cB/gcdcAcB)*ppCoG);
1543 "time for successful termination Fp: ");
1544 return N(gcdcAcB*ppH);
1547 "time for unsuccessful termination Fp: ");
1553 newtonPoly= newtonPoly*(
x - random_element);
1554 m=
m*(
x - random_element);
1555 if (!
find (
l, random_element))
1556 l.append (random_element);
const CanonicalForm CFMap CFMap & N
CanonicalForm modGCDFq(const CanonicalForm &F, const CanonicalForm &G, CanonicalForm &coF, CanonicalForm &coG, Variable &alpha, CFList &l, bool &topLevel)
GCD of F and G over , l and topLevel are only used internally, output is monic based on Alg....
const CanonicalForm const CanonicalForm const CanonicalForm & coG
int myCompress(const CanonicalForm &F, const CanonicalForm &G, CFMap &M, CFMap &N, bool topLevel)
compressing two polynomials F and G, M is used for compressing, N to reverse the compression
static Variable chooseExtension(const Variable &alpha)
static CanonicalForm uni_content(const CanonicalForm &F)
compute the content of F, where F is considered as an element of
static CanonicalForm uni_lcoeff(const CanonicalForm &F)
compute the leading coefficient of F, where F is considered as an element of , order on is dp.
const CanonicalForm const CanonicalForm & coF
static CanonicalForm randomElement(const CanonicalForm &F, const Variable &alpha, CFList &list, bool &fail)
compute a random element a of , s.t. F(a) , F is a univariate polynomial, returns fail if there are...
static CanonicalForm FpRandomElement(const CanonicalForm &F, CFList &list, bool &fail)
static CanonicalForm newtonInterp(const CanonicalForm &alpha, const CanonicalForm &u, const CanonicalForm &newtonPoly, const CanonicalForm &oldInterPoly, const Variable &x)
Newton interpolation - Incremental algorithm. Given a list of values alpha_i and a list of polynomial...
bool terminationTest(const CanonicalForm &F, const CanonicalForm &G, const CanonicalForm &coF, const CanonicalForm &coG, const CanonicalForm &cand)
bool fdivides(const CanonicalForm &f, const CanonicalForm &g)
bool fdivides ( const CanonicalForm & f, const CanonicalForm & g )
#define ASSERT(expression, message)
CanonicalForm randomIrredpoly(int i, const Variable &x)
computes a random monic irreducible univariate polynomial in x over Fp of degree i via NTL
CanonicalForm mapPrimElem(const CanonicalForm &primElem, const Variable &alpha, const Variable &beta)
compute the image of a primitive element of in . We assume .
CanonicalForm primitiveElement(const Variable &alpha, Variable &beta, bool &fail)
determine a primitive element of , is a primitive element of a field which is isomorphic to
static CanonicalForm mapDown(const CanonicalForm &F, const Variable &alpha, const CanonicalForm &G, CFList &source, CFList &dest)
the CanonicalForm G is the output of map_up, returns F considered as an element over ,...
static CanonicalForm mapUp(const Variable &alpha, const Variable &beta)
and is a primitive element, returns the image of
#define DEBOUTLN(stream, objects)
TIMING_END_AND_PRINT(fac_alg_resultant, "time to compute resultant0: ")
TIMING_START(fac_alg_resultant)
Variable rootOf(const CanonicalForm &, char name='@')
returns a symbolic root of polynomial with name name Use it to define algebraic variables
void prune(Variable &alpha)
CanonicalForm getMipo(const Variable &alpha, const Variable &x)
void setMipo(const Variable &alpha, const CanonicalForm &mipo)
template bool find(const List< CanonicalForm > &, const CanonicalForm &)