def test_unitize():
assert p("Unitize[Pi]") == 1
assert p("Unitize[Sqrt[2] + Sqrt[3] - Sqrt[5 + 2 Sqrt[6]]]") == 0
assert p(
"m = {{-2, 1, 0, 1}, {1, -2, 1, 0}, {0, 1, -2, 1}, {1, 0, -2, 1}}; Unitize[m]"
) == List(List(1, 1, 0, 1), List(1, 1, 1, 0), List(0, 1, 1, 1),
List(1, 0, 1, 1))
def test_rescale():
assert p_str("Rescale[2.5, {-10, 10}]").startswith("0.6250")
assert p_str("Rescale[12.5, {-10, 10}]").startswith("1.1250")
assert p("Rescale[-3/2, {-2, 2}]") == f(1, 8)
assert p_str("N[Rescale[Pi, {0, 2.5}]]").startswith("1.2566")
assert p("Rescale[3, {-9, 7}, {11, 28}]") == f(95, 4)
assert p("Expand[Rescale[1 + 2 I, {0, 5}]]") == f(1, 5) + 2 * s.I / 5
assert p("Expand[Rescale[1 + 2 I, {0, 1 + I}]]") == f(3, 2) + s.I / 2
assert p("Rescale[{-2, 0, 2}]") == List(0, f(1, 2), 1)
assert p("Rescale[{-2, 0, 2}, {-5, 5}]") == List(f(3, 10), f(1, 2),
f(7, 10))
assert p("Rescale[{-2, 0, 2}, {-5, 5}, {-1, 1}]") == List(
f(-2, 5), 0, f(2, 5))
def thread(func, *args, **kwargs):
"""
Internal threading function
keyword args are not threaded
"""
length = None
for arg in args:
if isinstance(arg, iterables):
if length is not None:
if length != len(arg):
raise FunctionException(
"General::thread",
"Cannot Thread over Lists of Unequal Length.",
)
else:
length = len(arg)
if length is None:
return func(*args, **kwargs)
chained = list(args)
for i in range(len(chained)):
if not isinstance(chained[i], iterables):
chained[i] = (chained[i],) * length
return List.create(thread(func, *z, **kwargs) for z in zip(*chained))
def test_ramp():
assert p("Ramp[-1]") == 0
assert p_str("Ramp[3.7]").startswith("3.70")
assert p("Ramp[1/2]") == f(1, 2)
assert p("Ramp[-E]") == 0
assert p("Ramp[-1.55]") == 0
assert p("Ramp[{-5, -1.5, 0, 1/3, Pi}]") == List(0, 0, 0, f(1, 3), s.pi)
def test_sign():
assert p("Sign[-2.5]") == -1
assert p("Sign[3.14]") == 1
assert p("Sign[1 + I]") == (1 + s.I) / s.sqrt(2)
assert p("Sign[{1.2, 1.5, -1.8}]") == List(1, 1, -1)
assert p("Sign[0]") == 0
assert p("Sign[Infinity]") == 1
assert p("Sign[-Infinity]") == -1
def test_clip():
assert p("Clip[8.5]") == 1
assert p("Clip[-5/2, {-2, 2}]") == -2
assert p("Clip[Pi, {-9, 7}, {11, 28}]") == s.pi
assert p("Clip[3 Pi, {-9, 7}, {11, 28}]") == 28
assert p("Clip[{-2, 0, 2}]") == List(-1, 0, 1)
assert p("Clip[0]") == 0
assert p("Clip[Infinity]") == 1
def test_int_part():
assert p("IntegerPart[2.4]") == 2
assert p("IntegerPart[-2.4]") == -2
assert p("IntegerPart[456.457]") == 456
assert p("IntegerPart[-5/4]") == -1
assert p("IntegerPart[Pi + E]") == 5
assert p("IntegerPart[78/47 - 4.2 I]") == 1 - 4 * s.I
assert p("IntegerPart[{2.4, 2.5, 3.0}]") == List(2, 2, 3)
assert p("IntegerPart[0]") == 0
assert p("IntegerPart[Infinity]") == s.oo
def test_round():
assert p("Round[2.4]") == 2
assert p("Round[2.6]") == 3
assert p("Round[226, 10]") == 230
assert p("Round[-3.7]") == -4
assert p_str("Round[-10.3, 3.5]").startswith("-10.50")
assert p("Round[2 Pi - E, 5/4]") == f("15/4")
assert p("Round[5.37 - 1.3 I]") == 5 - s.I
assert p("Round[{2.4, 2.5, 2.6}]") == List(2, 2, 3)
assert p("Round[0]") == 0
assert p("Round[Infinity]") == s.oo
def r_thread(func, to_thread, *args, rule=True, **kwargs):
if isinstance(to_thread, iterables):
return List(*(r_thread(func, x, *args, **kwargs) for x in to_thread))
if rule and isinstance(to_thread, Rule):
return Rule(
r_thread(func, to_thread.lhs, *args, **kwargs),
r_thread(func, to_thread.rhs, *args, **kwargs),
)
return func(to_thread, *args, **kwargs)
def evaluate_no_lazy(expr):
"""
Evaluate an expression with current definitions.
Does not evaluate any LazyFunctions in given expression.
"""
# if is iterable, apply for each element
if isinstance(expr, iterables) and not isinstance(expr, s.Matrix):
return List.create(evaluate_no_lazy(x) for x in expr)
# if expr does not have ability to perform substitutions, return
if not hasattr(expr, "xreplace"):
return expr
def extend(ex):
# if ex is a number, return
if hasattr(ex, "is_Number") and ex.is_Number:
return ex
# if ex is a symbol, return definitions if present
if isinstance(ex, s.Symbol):
st = ex.name
if st in r.refs.OwnValues:
return r.refs.OwnValues[st]
elif st in r.refs.Constants.Dict:
return r.refs.Constants.Dict[st]
# if ex does not have any arguments, return
if not hasattr(ex, "args") or not isinstance(ex.args, iterables):
return ex
# ex is supposed to be a function at this point (since args are present)
f_name = type(ex).__name__
# do not make substitutions if function is explicit
# since explicit functions require unevaluated args
if Functions.is_explicit(f_name):
return ex
# evaluate args
rep = {x: extend(x) for x in ex.args}
ex = ex.xreplace(rep)
# built-ins are automatically re-evaluated
# when replacements are made by sympy
# apply definitions if function has any
if Functions.is_not_builtin(f_name):
ex = Functions.apply_definitions(ex)
return ex
# evaluate inside-out
return extend(expr)
def test_rule():
assert p("1 -> 2") == Rule(1, 2)
assert p("2 -> 3").lhs == 2
r = p("1 -> 2")
r.lhs += 1
assert p("2 -> 2") == r
assert (p("1 -> 2") == r) is False
assert (r.lhs, r.rhs) == (r[0], r[1])
assert list(r) == [2, 2]
assert Rule(1, 2).__repr__() == Rule(1, 2).__str__() == "1 -> 2"
assert Rule.from_dict({1: 2, 3: 4}, head=List) == List(Rule(1, 2), Rule(3, 4))
def test_floor():
assert p("Floor[2.4]") == 2
assert p("Floor[2.6]") == 2
assert p("Floor[226, 10]") == 220
assert p("Floor[5.37]") == 5
assert p("Floor[-3.7]") == -4
assert p_str("Floor[-10.3, 3.5]").startswith("-10.50")
assert p("Floor[2 Pi - E, 5/4]") == f("5/2")
assert p("Floor[5.37 - 1.3 I]") == 5 - 2 * s.I
assert p("Floor[{2.4, 2.5, 2.6}]") == List(2, 2, 2)
assert p("Floor[0]") == 0
assert p("Floor[Infinity]") == s.oo
assert p("Simplify[Floor[x + 1]]") == p("1 + Floor[x]")
def test_ceiling():
assert p("Ceiling[2.4]") == 3
assert p("Ceiling[2.6]") == 3
assert p("Ceiling[226, 10]") == 230
assert p("Ceiling[5.37]") == 6
assert p("Ceiling[-3.7]") == -3
assert p_str("Ceiling[-10.3, 3.5]").startswith("-7.0")
assert p("Ceiling[2 Pi - E, 5/4]") == f("15/4")
assert p("Ceiling[5.37 - 1.3 I]") == 6 - s.I
assert p("Ceiling[{2.4, 2.5, 2.6}]") == List(3, 3, 3)
assert p("Ceiling[0]") == 0
assert p("Ceiling[Infinity]") == s.oo
assert p("Simplify[Ceiling[x + 1]]") == p("1 + Ceiling[x]")
def operate(tree: Tree):
if not isinstance(tree, Tree):
return tree
if tree.data == "symbol":
return symbol(tree.children[0])
if tree.data in basic_ops:
return basic(tree.data, [operate(x) for x in tree.children],
lazy_call=False)
if tree.data == "function":
name = str(tree.children[0].children[0])
if Functions.is_explicit(name):
return Functions.call(name, *(lazy(x) for x in tree.children[1:]))
return Functions.call(name, *(operate(x) for x in tree.children[1:]))
if tree.data == "list":
return List(*(operate(x) for x in tree.children))
if tree.data == "rule":
return Rule(*(operate(x) for x in tree.children))
if tree.data == "part":
return Functions.call("Part", *(operate(x) for x in tree.children))
if tree.data == "out":
return out(tree.children)
if tree.data == "set":
return Functions.call("Set", lazy(tree.children[0]),
operate(tree.children[1]))
if tree.data == "set_delayed":
return Functions.call("SetDelayed", lazy(tree.children[0]),
lazy(tree.children[1]))
if tree.data == "replace": # see ReplaceAll
return Functions.call("Replace", *(operate(x) for x in tree.children))
if tree.data == "unset":
return Functions.call("Unset", lazy(tree.children[0]))
if tree.data == "semicolon_statement":
return Functions.call("SemicolonStatement",
*(lazy(x) for x in tree.children))
if tree.data == "compound_statement":
return Functions.call("CompoundExpression",
*(lazy(x) for x in tree.children))
if tree.data == "postfix":
name = str(tree.children[-1].children[0])
if Functions.is_explicit(name):
return Functions.call(name, *(lazy(x) for x in tree.children[:-1]))
return Functions.call(name, *(operate(x) for x in tree.children[:-1]))
if tree.data == "RELATIONAL":
return str(tree.children[0])
if tree.data == "relation":
return relations([operate(x) for x in tree.children])
if tree.data == "tag":
return tag(*(operate(x) for x in tree.children))
if tree.data == "span":
return spanner(tree.children, operate)
return tree
def lazy(tree: Tree):
if not isinstance(tree, Tree):
return tree
if tree.data == "symbol":
return s.Symbol(tree.children[0])
if tree.data in basic_ops:
return basic(tree.data, [lazy(x) for x in tree.children],
lazy_call=True)
if tree.data == "function":
return Functions.lazy_call(
str(tree.children[0].children[0]),
*(lazy(x) for x in tree.children[1:]),
)
if tree.data == "list":
return List(*(lazy(x) for x in tree.children))
if tree.data == "rule":
return Rule(*(lazy(x) for x in tree.children))
if tree.data == "part":
return Functions.lazy_call("Part", *(lazy(x) for x in tree.children))
if tree.data == "out":
return out(tree.children)
if tree.data == "set":
return Functions.lazy_call("Set", lazy(tree.children[0]),
lazy(tree.children[1]))
if tree.data == "set_delayed":
return Functions.lazy_call("SetDelayed", lazy(tree.children[0]),
lazy(tree.children[1]))
if tree.data == "replace":
return Functions.lazy_call("Replace",
*(lazy(x) for x in tree.children))
if tree.data == "semicolon_statement":
return Functions.lazy_call("SemicolonStatement",
*(lazy(x) for x in tree.children))
if tree.data == "compound_statement":
return Functions.lazy_call("CompoundExpression",
*(lazy(x) for x in tree.children))
if tree.data == "postfix":
return Functions.lazy_call(
str(tree.children[-1].children[0]),
*(lazy(x) for x in tree.children[:-1]),
)
if tree.data == "RELATIONAL":
return str(tree.children[0])
if tree.data == "relation":
return relations([lazy(x) for x in tree.children])
if tree.data == "tag":
return lazy_tag(*(lazy(x) for x in tree.children))
if tree.data == "span":
return spanner(tree.children, lazy)
def evaluate(expr):
"""
Evaluate an expression with current definitions.
Evaluates all LazyFunctions in given expression.
"""
# see evaluate_no_lazy for explanation
if isinstance(expr, iterables) and not isinstance(expr, s.Matrix):
return List.create(LazyFunction.evaluate(x) for x in expr)
if not hasattr(expr, "subs"):
return expr
def extend(ex):
if hasattr(ex, "is_Number") and ex.is_Number:
return ex
if isinstance(ex, s.Symbol):
st = ex.name
if st in r.refs.OwnValues:
return r.refs.OwnValues[st]
elif st in r.refs.Constants.Dict:
return r.refs.Constants.Dict[st]
if not hasattr(ex, "args") or not isinstance(ex.args, iterables):
return ex
f_name = type(ex).__name__
if Functions.is_explicit(f_name):
# if explicit lazy function, call with args un-evaluated
if isinstance(ex, LazyFunction):
return ex.land()
return ex
rep = {x: extend(x) for x in ex.args}
ex = ex.xreplace(rep)
if Functions.is_not_builtin(f_name):
ex = Functions.apply_definitions(ex)
# if lazy function, call actual function
if isinstance(ex, LazyFunction):
return ex.land()
return ex
return extend(expr)
def exec(cls, expr, replacements):
if not isinstance(replacements, iterables):
replacements = (replacements,)
else:
if isinstance(replacements[0], iterables):
if not all(isinstance(x, iterables) for x in replacements):
raise FunctionException(
"Replace::subs",
f"{replacements} is a mixture of Lists and Non-Lists.",
)
return List(
*(cls.exec(expr, replacement) for replacement in replacements)
)
else:
if not all(not isinstance(x, iterables) for x in replacements):
raise FunctionException(
"Replace::subs",
f"{replacements} is a mixture of Lists and Non-Lists.",
)
if isinstance(expr, iterables) and not isinstance(expr, s.Matrix):
return List(*(cls.do_subs(x, replacements) for x in expr))
return cls.do_subs(expr, replacements)
def __init__(self):
self.In = []
self.Out = []
self.Messages = [List()]
self.OwnValues = OwnValues()
self.NoCache = NoCache
self.BuiltIns = DownValues()
self.DownValues = DownValues()
self.TagValues = TagValues()
self.FunctionWrappers = FunctionWrappers
self.Constants = Constants
self.Protected = Protected
self.Line = 1
self.CacheClearQueued = False # dirty, but works
self.Parser = None
self.Messenger = None
self.DefaultPrecision = 9
self.ExtraPrecision = 5
self.WorkingPrecision = self.DefaultPrecision + self.ExtraPrecision
def add_def(self, _in, out):
self.In.append(_in)
self.Out.append(out)
self.Messages.append(List())
self.Line += 1
def test_part():
a, b, c, d, e, f, g, h, i = s.var("a b c d e f g h i")
assert p("Part[{a, b, c, d, e}, 3]") == c
assert p("{a, b, c, d, e, f}[[3]]") == c
assert p("{{a, b, c}, {d, e, f}}[[1]][[2]]") == b
assert p("{{a, b, c}, {d, e, f}}[[1, 2]]") == b
assert p("{{a, b, c}, {d, e, f}, {g, h, i}}[[{1, 3}]]") == List(
List(a, b, c), List(g, h, i))
assert p("{{a, b, c}, {d, e, f}, {g, h, i}}[[{1, 3}, {2, 3}]]") == List(
List(b, c), List(h, i))
assert p("{{a, b, c}, {d, e, f}, {g, h, i}}[[2, 3]]") == f
assert p("{{a, b, c}, {d, e, f}, {g, h, i}}[[2]]") == List(d, e, f)
assert p("{{a, b, c}, {d, e, f}, {g, h, i}}[[All, 2]]") == List(b, e, h)
assert p("{a, b, c, d, e, f}[[-2]]") == e
assert p("{a, b, c, d, e, f}[[{1, 3, 1, 2, -1, -1}]]") == List(
a, c, a, b, f, f)
assert p("{a, b, c, d, e, f}[[2 ;; 4]]") == List(b, c, d)
assert (p("{a, b, c, d, e, f}[[1 ;; -3]]") ==
p("{a, b, c, d, e, f}[[;; -3]]") == List(a, b, c, d))
assert p("{a, b, c, d, e, f, g, h, i, j}[[3 ;; -3 ;; 2]]") == List(c, e, g)
assert p("{a, b, c, d, e, f, g, h, i, j}[[;; ;; 2]]") == List(
a, c, e, g, i)
assert p("{{a, b}, {c, d}, {e, f}}[[1;;2]][[2]]") == List(c, d)
assert p("{{a, b}, {c, d}, {e, f}}[[1;;2, 2]]") == List(b, d)
assert p("f[g[a, b], g[c, d]][[2, 1]]") == c
assert p("(1 + 2 a^2 + b^2)[[2]]") == b**2
assert p("{a -> c, b -> d}[[1, 2]]") == c
assert p("(a/b)[[2]]") == 1 / b
assert p("{a, b, c}[[0]]") == p("List")
assert p("f[a, b, c][[{2, 3}]] == f[b, c]")
assert p("f[g[a, b], h[c, d]][[{1, 2}, {2}]] == f[g[b], h[d]]")
def test_take():
a, b, c, d, e, f, t, u = s.var("a b c d e f t u")
assert p("Take[{a, b, c, d, e, f}, 4]") == List(a, b, c, d)
assert p("Take[{a, b, c, d, e, f}, -3]") == List(d, e, f)
assert p("Take[{a, b, c, d, e, f}, {2, -2}]") == List(b, c, d, e)
assert p("Take[{a, b, c, d, e, f}, {1, -1, 2}]") == List(a, c, e)
assert p("Take[{a, b, c, d, e}, -1]") == List(e)
assert p("Take[{{11, 12, 13}, {21, 22, 23}, {31, 32, 33}}, 2]") == List(
List(11, 12, 13), List(21, 22, 23))
assert p(
"Take[{{11, 12, 13}, {21, 22, 23}, {31, 32, 33}}, All, 2]") == List(
List(11, 12), List(21, 22), List(31, 32))
assert p(
"Take[{{11, 12, 13}, {21, 22, 23}, {31, 32, 33}}, 2, -1]") == List(
List(13), List(23))
m = "{{11,12,13,14,15},{21,22,23,24,25},{31,32,33,34,35},{41,42,43,44,45},{51,52,53,54,55}}"
assert p("Take[" + m + ", {2, 4}, {3, 5}]") == List(
List(23, 24, 25), List(33, 34, 35), List(43, 44, 45))
assert p("Take[" + m + ", {1, -1, 2}, {1, -1, 2}]") == p(
"{{11,13,15},{31,33,35},{51,53,55}}")
assert p("Take[a + b + c + d + e + f, 3]") == a + b + c
assert p("Take[{a + b + c, t + u + v, x + y + z}, 2, 2]") == List(
a + b, t + u)
def do_set(x, n):
"""Handles assignment"""
refs = r.refs
if isinstance(x, s.Symbol):
if not is_assignable(x.name):
raise FunctionException(
"Set::setx",
f"Symbol {x} is protected and cannot be assigned to.",
)
if isinstance(x, Tag):
set_tag_value(x, n)
return n
if isinstance(n, s.Expr):
if x in n.atoms():
return None # TODO: raise
refs.OwnValues[x.name] = n
return n
if isinstance(x, s.Function):
name = type(x).__name__
# handle part assignment
if name == "Part":
return set_part(x, n)
if not is_assignable(name):
raise FunctionException("Set::set", f"Symbol {x} cannot be Assigned to.")
# create dict of patterns if not present
if name not in refs.DownValues:
refs.DownValues[name] = {ArgsPattern(*x.args): n}
# else add pattern to existing dict
else:
pat = ArgsPattern(*x.args)
# remove duplicate if present
remove_duplicate_pattern(refs.DownValues[name], pat)
# update in place
refs.DownValues[name].update({pat: n})
# sort dict when done
# sorting is done during assignment to keep function calls fast
refs.DownValues[name] = OrderedDict(
sorted(
refs.DownValues[name].items(),
key=lambda z: z[0].importance,
reverse=True,
)
)
return n
if isinstance(x, iterables):
if isinstance(n, iterables) and len(x) == len(n):
return List.create(Set(a, b) for a, b in zip(x, n))
else:
raise FunctionException("Set::shape")
return None
def exec(cls, n):
if isinstance(n, iterables):
return List.create(Unset(x) for x in n)
if isinstance(n, s.Symbol) and str(n) in r.refs.OwnValues:
del r.refs.OwnValues[str(n)]
return NoOutput(None)
def test_list():
assert p("{}") == List()
assert p("{1, 2, 3}") == List(1, 2, 3)
d = p("{1, 2, 3, 4, 5}")
assert d[0] == 1
assert d[:2] == List(1, 2)
d[0] = 2
assert d[0] == 2
d = d.concat(List(6))
assert d == List(2, 2, 3).concat(List(4, 5, 6))
assert p("{1, 2} + {3, 4}") == List(4, 6)
assert p("{1, 2} - {3, 4}") == List(-2, -2)
assert p("{1, 2} * 2") == List(2, 4)
assert p("2 * {1, 2}") == List(2, 4)
assert p("{1, 2} * {3, 4}") == List(3, 8)
assert p("{1, 2} / 2") == List(f(1, 2), 1)
assert p("2 / {1, 2}") == List(2, 1)
assert p("{1, 2} / {4, 3}") == List(f(1, 4), f(2, 3))
assert p("1 + {1, 2, 3, 4}") == List(2, 3, 4, 5)
assert p("{1, 2, 3, 4} + 1") == List(2, 3, 4, 5)
assert p("1 - {1, 2, 3, 4}") == List(0, -1, -2, -3)
assert p("{1, 2, 3, 4} - 1") == List(0, 1, 2, 3)
assert p("{1, 2, 3}").evalf() == List(1, 2, 3)
assert p("N[{1, 2, 3}]") == List(1, 2, 3)
assert p("2 ^ {1, 2, 3}") == List(2, 4, 8)
assert p("{1, 2, 3} ^ 2") == List(1, 4, 9)
assert p("{1, 2, 3} ^ {3, 2, 1}") == List(1, 4, 3)
assert p("{1, 2, 3, x}") == p("{2 - 1, 2, 2 + 1, x}")
assert p("{1, 2}").__repr__() == p("{1, 2}").__str__() == "{1, 2}"
assert list(p("{1, 2, 3}")) == [1, 2, 3]