def test_Domain_unify(): F3 = GF(3) assert unify(F3, F3) == F3 assert unify(F3, ZZ) == F3 assert unify(F3, QQ) == QQ assert unify(F3, ALG) == ALG assert unify(F3, RR) == RR assert unify(F3, CC) == CC assert unify(F3, ZZ.poly_ring(x)) == F3.poly_ring(x) assert unify(F3, ZZ.frac_field(x)) == F3.frac_field(x) assert unify(F3, EX) == EX assert unify(ZZ, F3) == F3 assert unify(ZZ, ZZ) == ZZ assert unify(ZZ, QQ) == QQ assert unify(ZZ, ALG) == ALG assert unify(ZZ, RR) == RR assert unify(ZZ, CC) == CC assert unify(ZZ, ZZ.poly_ring(x)) == ZZ.poly_ring(x) assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ, EX) == EX assert unify(QQ, F3) == QQ assert unify(QQ, ZZ) == QQ assert unify(QQ, QQ) == QQ assert unify(QQ, ALG) == ALG assert unify(QQ, RR) == RR assert unify(QQ, CC) == CC assert unify(QQ, ZZ.poly_ring(x)) == QQ.poly_ring(x) assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x) assert unify(QQ, EX) == EX assert unify(RR, F3) == RR assert unify(RR, ZZ) == RR assert unify(RR, QQ) == RR assert unify(RR, ALG) == RR assert unify(RR, RR) == RR assert unify(RR, CC) == CC assert unify(RR, ZZ.poly_ring(x)) == RR.poly_ring(x) assert unify(RR, ZZ.frac_field(x)) == RR.frac_field(x) assert unify(RR, EX) == EX assert unify(CC, F3) == CC assert unify(CC, ZZ) == CC assert unify(CC, QQ) == CC assert unify(CC, ALG) == CC assert unify(CC, RR) == CC assert unify(CC, CC) == CC assert unify(CC, ZZ.poly_ring(x)) == CC.poly_ring(x) assert unify(CC, ZZ.frac_field(x)) == CC.frac_field(x) assert unify(CC, EX) == EX CC2 = ComplexField(prec=20) assert unify(CC, CC2) == unify(CC2, CC) == ComplexField(prec=CC.precision, tol=CC2.tolerance) RR2 = RealField(prec=20) assert unify(RR, RR2) == unify(RR2, RR) == RealField(prec=RR.precision, tol=RR2.tolerance) assert unify(ZZ.poly_ring(x), F3) == F3.poly_ring(x) assert unify(ZZ.poly_ring(x), ZZ) == ZZ.poly_ring(x) assert unify(ZZ.poly_ring(x), QQ) == QQ.poly_ring(x) assert unify(ZZ.poly_ring(x), ALG) == ALG.poly_ring(x) assert unify(ZZ.poly_ring(x), RR) == RR.poly_ring(x) assert unify(ZZ.poly_ring(x), CC) == CC.poly_ring(x) assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x)) == ZZ.poly_ring(x) assert unify(ZZ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ.poly_ring(x), EX) == EX assert unify(ZZ.frac_field(x), F3) == F3.frac_field(x) assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x) assert unify(ZZ.frac_field(x), ALG) == ALG.frac_field(x) assert unify(ZZ.frac_field(x), RR) == RR.frac_field(x) assert unify(ZZ.frac_field(x), CC) == CC.frac_field(x) assert unify(ZZ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), EX) == EX assert unify(EX, F3) == EX assert unify(EX, ZZ) == EX assert unify(EX, QQ) == EX assert unify(EX, ALG) == EX assert unify(EX, RR) == EX assert unify(EX, CC) == EX assert unify(EX, ZZ.poly_ring(x)) == EX assert unify(EX, ZZ.frac_field(x)) == EX assert unify(EX, EX) == EX
def test_construct_domain(): assert construct_domain([1, 2, 3]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)]) assert construct_domain([1, 2, 3], field=True) == (QQ, [QQ(1), QQ(2), QQ(3)]) assert construct_domain([Integer(1), Integer(2), Integer(3)]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)]) assert construct_domain( [Integer(1), Integer(2), Integer(3)], field=True) == (QQ, [QQ(1), QQ(2), QQ(3)]) assert construct_domain([Rational(1, 2), Integer(2)]) == (QQ, [QQ(1, 2), QQ(2)]) assert construct_domain([3.14, 1, Rational(1, 2) ]) == (RR, [RR(3.14), RR(1.0), RR(0.5)]) assert construct_domain([3.14, sqrt(2)], extension=None) == (EX, [EX(3.14), EX(sqrt(2))]) assert construct_domain([3.14, sqrt(2)], extension=True) == (EX, [EX(3.14), EX(sqrt(2))]) assert construct_domain([sqrt(2), 3.14], extension=True) == (EX, [EX(sqrt(2)), EX(3.14)]) assert construct_domain([1, sqrt(2)], extension=None) == (EX, [EX(1), EX(sqrt(2))]) assert construct_domain([x, sqrt(x)]) == (EX, [EX(x), EX(sqrt(x))]) assert construct_domain([x, sqrt(x), sqrt(y) ]) == (EX, [EX(x), EX(sqrt(x)), EX(sqrt(y))]) alg = QQ.algebraic_field(sqrt(2)) assert (construct_domain( [7, Rational(1, 2), sqrt(2)], extension=True) == (alg, [alg(7), alg(Rational(1, 2)), alg(sqrt(2))])) alg = QQ.algebraic_field(sqrt(2) + sqrt(3)) assert (construct_domain([7, sqrt(2), sqrt(3)], extension=True) == (alg, [ alg(7), alg(sqrt(2)), alg(sqrt(3)) ])) dom = ZZ.poly_ring(x) assert construct_domain([2 * x, 3]) == (dom, [dom(2 * x), dom(3)]) dom = ZZ.poly_ring(x, y) assert construct_domain([2 * x, 3 * y]) == (dom, [dom(2 * x), dom(3 * y)]) dom = QQ.poly_ring(x) assert construct_domain([x / 2, 3]) == (dom, [dom(x / 2), dom(3)]) dom = QQ.poly_ring(x, y) assert construct_domain([x / 2, 3 * y]) == (dom, [dom(x / 2), dom(3 * y)]) dom = RR.poly_ring(x) assert construct_domain([x / 2, 3.5]) == (dom, [dom(x / 2), dom(3.5)]) dom = RR.poly_ring(x, y) assert construct_domain([x / 2, 3.5 * y]) == (dom, [dom(x / 2), dom(3.5 * y)]) dom = ZZ.frac_field(x) assert construct_domain([2 / x, 3]) == (dom, [dom(2 / x), dom(3)]) dom = ZZ.frac_field(x, y) assert construct_domain([2 / x, 3 * y]) == (dom, [dom(2 / x), dom(3 * y)]) dom = RR.frac_field(x) assert construct_domain([2 / x, 3.5]) == (dom, [dom(2 / x), dom(3.5)]) dom = RR.frac_field(x, y) assert construct_domain([2 / x, 3.5 * y]) == (dom, [dom(2 / x), dom(3.5 * y)]) assert construct_domain(2) == (ZZ, ZZ(2)) assert construct_domain(Rational(2, 3)) == (QQ, QQ(2, 3)) assert construct_domain({}) == (ZZ, {})
def test_Domain_unify(): F3 = GF(3) assert unify(F3, F3) == F3 assert unify(F3, ZZ) == F3 assert unify(F3, QQ) == QQ assert unify(F3, ALG) == ALG assert unify(F3, RR) == RR assert unify(F3, CC) == CC assert unify(F3, ZZ.poly_ring(x)) == F3.poly_ring(x) assert unify(F3, ZZ.frac_field(x)) == F3.frac_field(x) assert unify(F3, EX) == EX assert unify(ZZ, F3) == F3 assert unify(ZZ, ZZ) == ZZ assert unify(ZZ, QQ) == QQ assert unify(ZZ, ALG) == ALG assert unify(ZZ, RR) == RR assert unify(ZZ, CC) == CC assert unify(ZZ, ZZ.poly_ring(x)) == ZZ.poly_ring(x) assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ, EX) == EX assert unify(QQ, F3) == QQ assert unify(QQ, ZZ) == QQ assert unify(QQ, QQ) == QQ assert unify(QQ, ALG) == ALG assert unify(QQ, RR) == RR assert unify(QQ, CC) == CC assert unify(QQ, ZZ.poly_ring(x)) == QQ.poly_ring(x) assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x) assert unify(QQ, EX) == EX assert unify(RR, F3) == RR assert unify(RR, ZZ) == RR assert unify(RR, QQ) == RR assert unify(RR, ALG) == RR assert unify(RR, RR) == RR assert unify(RR, CC) == CC assert unify(RR, ZZ.poly_ring(x)) == RR.poly_ring(x) assert unify(RR, ZZ.frac_field(x)) == RR.frac_field(x) assert unify(RR, EX) == EX assert unify(CC, F3) == CC assert unify(CC, ZZ) == CC assert unify(CC, QQ) == CC assert unify(CC, ALG) == CC assert unify(CC, RR) == CC assert unify(CC, CC) == CC assert unify(CC, ZZ.poly_ring(x)) == CC.poly_ring(x) assert unify(CC, ZZ.frac_field(x)) == CC.frac_field(x) assert unify(CC, EX) == EX CC2 = ComplexField(prec=20) assert unify(CC, CC2) == unify(CC2, CC) == ComplexField(prec=CC.precision, tol=CC2.tolerance) RR2 = RealField(prec=20) assert unify(RR, RR2) == unify(RR2, RR) == RealField(prec=RR.precision, tol=RR2.tolerance) assert unify(ZZ.poly_ring(x), F3) == F3.poly_ring(x) assert unify(ZZ.poly_ring(x), ZZ) == ZZ.poly_ring(x) assert unify(ZZ.poly_ring(x), QQ) == QQ.poly_ring(x) assert unify(ZZ.poly_ring(x), ALG) == ALG.poly_ring(x) assert unify(ZZ.poly_ring(x), RR) == RR.poly_ring(x) assert unify(ZZ.poly_ring(x), CC) == CC.poly_ring(x) assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x)) == ZZ.poly_ring(x) assert unify(ZZ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ.poly_ring(x), EX) == EX assert unify(ZZ.frac_field(x), F3) == F3.frac_field(x) assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x) assert unify(ZZ.frac_field(x), ALG) == ALG.frac_field(x) assert unify(ZZ.frac_field(x), RR) == RR.frac_field(x) assert unify(ZZ.frac_field(x), CC) == CC.frac_field(x) assert unify(ZZ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), EX) == EX assert unify(EX, F3) == EX assert unify(EX, ZZ) == EX assert unify(EX, QQ) == EX assert unify(EX, ALG) == EX assert unify(EX, RR) == EX assert unify(EX, CC) == EX assert unify(EX, ZZ.poly_ring(x)) == EX assert unify(EX, ZZ.frac_field(x)) == EX assert unify(EX, EX) == EX