MLPY/Lib/site-packages/sympy/polys/tests/test_polyoptions.py

"""Tests for options manager for :class:`Poly` and public API functions. """

from sympy.polys.polyoptions import (
    Options, Expand, Gens, Wrt, Sort, Order, Field, Greedy, Domain,
    Split, Gaussian, Extension, Modulus, Symmetric, Strict, Auto,
    Frac, Formal, Polys, Include, All, Gen, Symbols, Method)

from sympy.polys.orderings import lex
from sympy.polys.domains import FF, GF, ZZ, QQ, QQ_I, RR, CC, EX

from sympy.polys.polyerrors import OptionError, GeneratorsError

from sympy.core.numbers import (I, Integer)
from sympy.core.symbol import Symbol
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.testing.pytest import raises
from sympy.abc import x, y, z


def test_Options_clone():
    opt = Options((x, y, z), {'domain': 'ZZ'})

    assert opt.gens == (x, y, z)
    assert opt.domain == ZZ
    assert ('order' in opt) is False

    new_opt = opt.clone({'gens': (x, y), 'order': 'lex'})

    assert opt.gens == (x, y, z)
    assert opt.domain == ZZ
    assert ('order' in opt) is False

    assert new_opt.gens == (x, y)
    assert new_opt.domain == ZZ
    assert ('order' in new_opt) is True


def test_Expand_preprocess():
    assert Expand.preprocess(False) is False
    assert Expand.preprocess(True) is True

    assert Expand.preprocess(0) is False
    assert Expand.preprocess(1) is True

    raises(OptionError, lambda: Expand.preprocess(x))


def test_Expand_postprocess():
    opt = {'expand': True}
    Expand.postprocess(opt)

    assert opt == {'expand': True}


def test_Gens_preprocess():
    assert Gens.preprocess((None,)) == ()
    assert Gens.preprocess((x, y, z)) == (x, y, z)
    assert Gens.preprocess(((x, y, z),)) == (x, y, z)

    a = Symbol('a', commutative=False)

    raises(GeneratorsError, lambda: Gens.preprocess((x, x, y)))
    raises(GeneratorsError, lambda: Gens.preprocess((x, y, a)))


def test_Gens_postprocess():
    opt = {'gens': (x, y)}
    Gens.postprocess(opt)

    assert opt == {'gens': (x, y)}


def test_Wrt_preprocess():
    assert Wrt.preprocess(x) == ['x']
    assert Wrt.preprocess('') == []
    assert Wrt.preprocess(' ') == []
    assert Wrt.preprocess('x,y') == ['x', 'y']
    assert Wrt.preprocess('x y') == ['x', 'y']
    assert Wrt.preprocess('x, y') == ['x', 'y']
    assert Wrt.preprocess('x , y') == ['x', 'y']
    assert Wrt.preprocess(' x, y') == ['x', 'y']
    assert Wrt.preprocess(' x,  y') == ['x', 'y']
    assert Wrt.preprocess([x, y]) == ['x', 'y']

    raises(OptionError, lambda: Wrt.preprocess(','))
    raises(OptionError, lambda: Wrt.preprocess(0))


def test_Wrt_postprocess():
    opt = {'wrt': ['x']}
    Wrt.postprocess(opt)

    assert opt == {'wrt': ['x']}


def test_Sort_preprocess():
    assert Sort.preprocess([x, y, z]) == ['x', 'y', 'z']
    assert Sort.preprocess((x, y, z)) == ['x', 'y', 'z']

    assert Sort.preprocess('x > y > z') == ['x', 'y', 'z']
    assert Sort.preprocess('x>y>z') == ['x', 'y', 'z']

    raises(OptionError, lambda: Sort.preprocess(0))
    raises(OptionError, lambda: Sort.preprocess({x, y, z}))


def test_Sort_postprocess():
    opt = {'sort': 'x > y'}
    Sort.postprocess(opt)

    assert opt == {'sort': 'x > y'}


def test_Order_preprocess():
    assert Order.preprocess('lex') == lex


def test_Order_postprocess():
    opt = {'order': True}
    Order.postprocess(opt)

    assert opt == {'order': True}


def test_Field_preprocess():
    assert Field.preprocess(False) is False
    assert Field.preprocess(True) is True

    assert Field.preprocess(0) is False
    assert Field.preprocess(1) is True

    raises(OptionError, lambda: Field.preprocess(x))


def test_Field_postprocess():
    opt = {'field': True}
    Field.postprocess(opt)

    assert opt == {'field': True}


def test_Greedy_preprocess():
    assert Greedy.preprocess(False) is False
    assert Greedy.preprocess(True) is True

    assert Greedy.preprocess(0) is False
    assert Greedy.preprocess(1) is True

    raises(OptionError, lambda: Greedy.preprocess(x))


def test_Greedy_postprocess():
    opt = {'greedy': True}
    Greedy.postprocess(opt)

    assert opt == {'greedy': True}


def test_Domain_preprocess():
    assert Domain.preprocess(ZZ) == ZZ
    assert Domain.preprocess(QQ) == QQ
    assert Domain.preprocess(EX) == EX
    assert Domain.preprocess(FF(2)) == FF(2)
    assert Domain.preprocess(ZZ[x, y]) == ZZ[x, y]

    assert Domain.preprocess('Z') == ZZ
    assert Domain.preprocess('Q') == QQ

    assert Domain.preprocess('ZZ') == ZZ
    assert Domain.preprocess('QQ') == QQ

    assert Domain.preprocess('EX') == EX

    assert Domain.preprocess('FF(23)') == FF(23)
    assert Domain.preprocess('GF(23)') == GF(23)

    raises(OptionError, lambda: Domain.preprocess('Z[]'))

    assert Domain.preprocess('Z[x]') == ZZ[x]
    assert Domain.preprocess('Q[x]') == QQ[x]
    assert Domain.preprocess('R[x]') == RR[x]
    assert Domain.preprocess('C[x]') == CC[x]

    assert Domain.preprocess('ZZ[x]') == ZZ[x]
    assert Domain.preprocess('QQ[x]') == QQ[x]
    assert Domain.preprocess('RR[x]') == RR[x]
    assert Domain.preprocess('CC[x]') == CC[x]

    assert Domain.preprocess('Z[x,y]') == ZZ[x, y]
    assert Domain.preprocess('Q[x,y]') == QQ[x, y]
    assert Domain.preprocess('R[x,y]') == RR[x, y]
    assert Domain.preprocess('C[x,y]') == CC[x, y]

    assert Domain.preprocess('ZZ[x,y]') == ZZ[x, y]
    assert Domain.preprocess('QQ[x,y]') == QQ[x, y]
    assert Domain.preprocess('RR[x,y]') == RR[x, y]
    assert Domain.preprocess('CC[x,y]') == CC[x, y]

    raises(OptionError, lambda: Domain.preprocess('Z()'))

    assert Domain.preprocess('Z(x)') == ZZ.frac_field(x)
    assert Domain.preprocess('Q(x)') == QQ.frac_field(x)

    assert Domain.preprocess('ZZ(x)') == ZZ.frac_field(x)
    assert Domain.preprocess('QQ(x)') == QQ.frac_field(x)

    assert Domain.preprocess('Z(x,y)') == ZZ.frac_field(x, y)
    assert Domain.preprocess('Q(x,y)') == QQ.frac_field(x, y)

    assert Domain.preprocess('ZZ(x,y)') == ZZ.frac_field(x, y)
    assert Domain.preprocess('QQ(x,y)') == QQ.frac_field(x, y)

    assert Domain.preprocess('Q<I>') == QQ.algebraic_field(I)
    assert Domain.preprocess('QQ<I>') == QQ.algebraic_field(I)

    assert Domain.preprocess('Q<sqrt(2), I>') == QQ.algebraic_field(sqrt(2), I)
    assert Domain.preprocess(
        'QQ<sqrt(2), I>') == QQ.algebraic_field(sqrt(2), I)

    raises(OptionError, lambda: Domain.preprocess('abc'))


def test_Domain_postprocess():
    raises(GeneratorsError, lambda: Domain.postprocess({'gens': (x, y),
           'domain': ZZ[y, z]}))

    raises(GeneratorsError, lambda: Domain.postprocess({'gens': (),
           'domain': EX}))
    raises(GeneratorsError, lambda: Domain.postprocess({'domain': EX}))


def test_Split_preprocess():
    assert Split.preprocess(False) is False
    assert Split.preprocess(True) is True

    assert Split.preprocess(0) is False
    assert Split.preprocess(1) is True

    raises(OptionError, lambda: Split.preprocess(x))


def test_Split_postprocess():
    raises(NotImplementedError, lambda: Split.postprocess({'split': True}))


def test_Gaussian_preprocess():
    assert Gaussian.preprocess(False) is False
    assert Gaussian.preprocess(True) is True

    assert Gaussian.preprocess(0) is False
    assert Gaussian.preprocess(1) is True

    raises(OptionError, lambda: Gaussian.preprocess(x))


def test_Gaussian_postprocess():
    opt = {'gaussian': True}
    Gaussian.postprocess(opt)

    assert opt == {
        'gaussian': True,
        'domain': QQ_I,
    }


def test_Extension_preprocess():
    assert Extension.preprocess(True) is True
    assert Extension.preprocess(1) is True

    assert Extension.preprocess([]) is None

    assert Extension.preprocess(sqrt(2)) == {sqrt(2)}
    assert Extension.preprocess([sqrt(2)]) == {sqrt(2)}

    assert Extension.preprocess([sqrt(2), I]) == {sqrt(2), I}

    raises(OptionError, lambda: Extension.preprocess(False))
    raises(OptionError, lambda: Extension.preprocess(0))


def test_Extension_postprocess():
    opt = {'extension': {sqrt(2)}}
    Extension.postprocess(opt)

    assert opt == {
        'extension': {sqrt(2)},
        'domain': QQ.algebraic_field(sqrt(2)),
    }

    opt = {'extension': True}
    Extension.postprocess(opt)

    assert opt == {'extension': True}


def test_Modulus_preprocess():
    assert Modulus.preprocess(23) == 23
    assert Modulus.preprocess(Integer(23)) == 23

    raises(OptionError, lambda: Modulus.preprocess(0))
    raises(OptionError, lambda: Modulus.preprocess(x))


def test_Modulus_postprocess():
    opt = {'modulus': 5}
    Modulus.postprocess(opt)

    assert opt == {
        'modulus': 5,
        'domain': FF(5),
    }

    opt = {'modulus': 5, 'symmetric': False}
    Modulus.postprocess(opt)

    assert opt == {
        'modulus': 5,
        'domain': FF(5, False),
        'symmetric': False,
    }


def test_Symmetric_preprocess():
    assert Symmetric.preprocess(False) is False
    assert Symmetric.preprocess(True) is True

    assert Symmetric.preprocess(0) is False
    assert Symmetric.preprocess(1) is True

    raises(OptionError, lambda: Symmetric.preprocess(x))


def test_Symmetric_postprocess():
    opt = {'symmetric': True}
    Symmetric.postprocess(opt)

    assert opt == {'symmetric': True}


def test_Strict_preprocess():
    assert Strict.preprocess(False) is False
    assert Strict.preprocess(True) is True

    assert Strict.preprocess(0) is False
    assert Strict.preprocess(1) is True

    raises(OptionError, lambda: Strict.preprocess(x))


def test_Strict_postprocess():
    opt = {'strict': True}
    Strict.postprocess(opt)

    assert opt == {'strict': True}


def test_Auto_preprocess():
    assert Auto.preprocess(False) is False
    assert Auto.preprocess(True) is True

    assert Auto.preprocess(0) is False
    assert Auto.preprocess(1) is True

    raises(OptionError, lambda: Auto.preprocess(x))


def test_Auto_postprocess():
    opt = {'auto': True}
    Auto.postprocess(opt)

    assert opt == {'auto': True}


def test_Frac_preprocess():
    assert Frac.preprocess(False) is False
    assert Frac.preprocess(True) is True

    assert Frac.preprocess(0) is False
    assert Frac.preprocess(1) is True

    raises(OptionError, lambda: Frac.preprocess(x))


def test_Frac_postprocess():
    opt = {'frac': True}
    Frac.postprocess(opt)

    assert opt == {'frac': True}


def test_Formal_preprocess():
    assert Formal.preprocess(False) is False
    assert Formal.preprocess(True) is True

    assert Formal.preprocess(0) is False
    assert Formal.preprocess(1) is True

    raises(OptionError, lambda: Formal.preprocess(x))


def test_Formal_postprocess():
    opt = {'formal': True}
    Formal.postprocess(opt)

    assert opt == {'formal': True}


def test_Polys_preprocess():
    assert Polys.preprocess(False) is False
    assert Polys.preprocess(True) is True

    assert Polys.preprocess(0) is False
    assert Polys.preprocess(1) is True

    raises(OptionError, lambda: Polys.preprocess(x))


def test_Polys_postprocess():
    opt = {'polys': True}
    Polys.postprocess(opt)

    assert opt == {'polys': True}


def test_Include_preprocess():
    assert Include.preprocess(False) is False
    assert Include.preprocess(True) is True

    assert Include.preprocess(0) is False
    assert Include.preprocess(1) is True

    raises(OptionError, lambda: Include.preprocess(x))


def test_Include_postprocess():
    opt = {'include': True}
    Include.postprocess(opt)

    assert opt == {'include': True}


def test_All_preprocess():
    assert All.preprocess(False) is False
    assert All.preprocess(True) is True

    assert All.preprocess(0) is False
    assert All.preprocess(1) is True

    raises(OptionError, lambda: All.preprocess(x))


def test_All_postprocess():
    opt = {'all': True}
    All.postprocess(opt)

    assert opt == {'all': True}


def test_Gen_postprocess():
    opt = {'gen': x}
    Gen.postprocess(opt)

    assert opt == {'gen': x}


def test_Symbols_preprocess():
    raises(OptionError, lambda: Symbols.preprocess(x))


def test_Symbols_postprocess():
    opt = {'symbols': [x, y, z]}
    Symbols.postprocess(opt)

    assert opt == {'symbols': [x, y, z]}


def test_Method_preprocess():
    raises(OptionError, lambda: Method.preprocess(10))


def test_Method_postprocess():
    opt = {'method': 'f5b'}
    Method.postprocess(opt)

    assert opt == {'method': 'f5b'}