/** Test module and polynomial and module list. */
public void testModulePolynomialModuleList() {
List<List<GenPolynomial<BigRational>>> l = new ArrayList<List<GenPolynomial<BigRational>>>();
for (int i = 0; i < 4; i++) {
List<GenPolynomial<BigRational>> r = new ArrayList<GenPolynomial<BigRational>>();
for (int j = 0; j < 3; j++) {
a = pfac.random(kl, ll, el, q);
assertTrue("length( a" + i + " ) <> 0", a.length() >= 0);
assertTrue(" not isZERO( a" + i + " )", !a.isZERO());
assertTrue(" not isONE( a" + i + " )", !a.isONE());
r.add(a);
}
l.add(r);
}
m = new ModuleList<BigRational>(pfac, l);
// System.out.println("m = "+m);
assertTrue("m == m", m.equals(m));
assertEquals("m.length", 4, m.list.size());
p = m.getPolynomialList();
// System.out.println("p = "+p);
assertTrue("p == p", p.equals(p));
assertEquals("p.length", 4, p.list.size());
ModuleList<BigRational> m2 = null;
m2 = p.getModuleList(3);
// System.out.println("m2 = "+m2);
assertTrue("m2 == m2", m2.equals(m2));
assertEquals("m2.length", 4, m2.list.size());
assertTrue("m == m2", m.equals(m2));
}
/** Test polynomial list. */
public void testPolynomialList() {
List<GenPolynomial<BigRational>> l = new ArrayList<GenPolynomial<BigRational>>();
for (int i = 0; i < 7; i++) {
a = pfac.random(kl, ll + i, el, q);
assertTrue("length( a" + i + " ) <> 0", a.length() >= 0);
assertTrue(" not isZERO( a" + i + " )", !a.isZERO());
assertTrue(" not isONE( a" + i + " )", !a.isONE());
l.add(a);
}
p = new PolynomialList<BigRational>(pfac, l);
// System.out.println("p = "+p);
assertTrue("p == p", p.equals(p));
assertEquals("p.length", 7, p.list.size());
}
/**
* Random solvable polynomial.
*
* @param k size of random coefficients.
* @param l number of terms.
* @param d maximal degree in each variable.
* @param q density of nozero exponents.
* @param rnd is a source for random bits.
* @return a random solvable polynomial.
*/
@Override
public GenSolvablePolynomial<C> random(int k, int l, int d, float q, Random rnd) {
GenSolvablePolynomial<C> r = getZERO(); // .clone();
// copy( ZERO );
// new GenPolynomial<C>( this, getZERO().val );
ExpVector e;
C a;
// add random coeffs and exponents
for (int i = 0; i < l; i++) {
e = ExpVector.EVRAND(nvar, d, q, rnd);
a = coFac.random(k, rnd);
r = (GenSolvablePolynomial<C>) r.sum(a, e);
// somewhat inefficient but clean
}
return r;
}
/**
* Query if this ring is associative. Test if the relations define an associative solvable ring.
*
* @return true, if this ring is associative, else false.
*/
@Override
public boolean isAssociative() {
GenSolvablePolynomial<C> Xi, Xj, Xk, p, q;
for (int i = 0; i < nvar; i++) {
Xi = univariate(i);
for (int j = i + 1; j < nvar; j++) {
Xj = univariate(j);
for (int k = j + 1; k < nvar; k++) {
Xk = univariate(k);
p = Xk.multiply(Xj).multiply(Xi);
q = Xk.multiply(Xj.multiply(Xi));
if (!p.equals(q)) {
if (true || debug) {
logger.info("Xi = " + Xi + ", Xj = " + Xj + ", Xk = " + Xk);
logger.info("p = ( Xk * Xj ) * Xi = " + p);
logger.info("q = Xk * ( Xj * Xi ) = " + q);
}
return false;
}
}
}
}
return coFac.isAssociative();
}
/** Test module and polynomial and module and polynomial list with WeylRelations. */
public void testWeylModulePolynomialModuleListPolynomial() {
int rloc = 4;
pfac = new GenSolvablePolynomialRing<BigRational>(cfac, rloc);
RelationGenerator<BigRational> wl = new WeylRelations<BigRational>();
wl.generate(pfac);
RelationTable table1 = pfac.table;
RelationTable table2 = null;
RelationTable table3 = null;
RelationTable table4 = null;
RelationTable table5 = null;
// System.out.println("table 1 = " + table1);
// System.out.println("ring = " + ring);
List<List<GenPolynomial<BigRational>>> l = new ArrayList<List<GenPolynomial<BigRational>>>();
for (int i = 0; i < 4; i++) {
List<GenPolynomial<BigRational>> r = new ArrayList<GenPolynomial<BigRational>>();
for (int j = 0; j < 3; j++) {
a = pfac.random(kl, ll, el, q);
assertTrue("length( a" + i + " ) <> 0", a.length() >= 0);
assertTrue(" not isZERO( a" + i + " )", !a.isZERO());
assertTrue(" not isONE( a" + i + " )", !a.isONE());
r.add(a);
}
l.add(r);
}
m = new ModuleList<BigRational>(pfac, l);
// System.out.println("m = "+m);
assertTrue("m == m", m.equals(m));
assertEquals("m.length", 4, m.list.size());
table2 = ((GenSolvablePolynomialRing<BigRational>) m.ring).table;
// System.out.println("table 2 = " + table2);
assertEquals("table1 == table2", table1, table2);
p = m.getPolynomialList();
// System.out.println("p = "+p);
assertTrue("p == p", p.equals(p));
assertEquals("p.length", 4, p.list.size());
table3 = ((GenSolvablePolynomialRing<BigRational>) p.ring).table;
// System.out.println("table 3 = " + table3);
ModuleList<BigRational> m2 = null;
m2 = p.getModuleList(3);
// System.out.println("m2 = "+m2);
assertTrue("m2 == m2", m2.equals(m2));
assertEquals("m2.length", 4, m2.list.size());
assertTrue("m == m2", m.equals(m2));
table4 = ((GenSolvablePolynomialRing<BigRational>) m2.ring).table;
// System.out.println("table 4 = " + table4);
assertEquals("table2 == table4", table2, table4);
assertEquals("table1 == table4", table1, table4);
PolynomialList<BigRational> p2 = null;
p2 = m2.getPolynomialList();
// System.out.println("p2 = "+p2);
assertTrue("p2 == p2", p2.equals(p2));
assertEquals("p2.length", 4, p2.list.size());
assertTrue("p == p2", p.list.equals(p2.list));
table5 = ((GenSolvablePolynomialRing<BigRational>) p2.ring).table;
// System.out.println("table 5= " + table5);
assertEquals("table2 == table4", table3.table, table5.table);
}