def p_multiplicative_expression(p):
"""multiplicative_expression : multiplicative_expression TIMES unary_expression
| multiplicative_expression DIVIDE unary_expression
| unary_expression """
if len(p) == 2:
p[0] = p[1]
else:
if p[2] == '*':
p[0] = Prod([p[1], p[3]], {})
elif p[2] == '/':
p[0] = Prod([p[1], Pow([p[3], Int(-1)], {})], {})
def p_postfix_expression_binary(p):
"""postfix_expression_binary : BINARY LBRACE argument_list RBRACE LBRACE argument_list RBRACE"""
# 0 1 2 3 4 5 6 7
if p[1] == '\\frac':
p[0] = Prod([p[3][0][0], Pow([p[6][0][0], Int(-1)], {})], {})
elif p[1] == '\\binom':
p[0] = C([p[3][0][0], p[6][0][0]], {})
def p_multiplicative_expression(p):
"""multiplicative_expression : multiplicative_expression TIMES unary_expression
| multiplicative_expression DIVIDE unary_expression
| multiplicative_expression MOD unary_expression
| BIGPROD DOWN LBRACE ID EQ expression RBRACE POW LBRACE expression RBRACE unary_expression
| unary_expression
"""
# 0 1 2 3 4 5 6 7 8 9 10 11 12
if len(p) == 13:
p[0] = BigProd([p[12], translate_id(p[4]), p[6], p[10]], {})
if len(p) == 2:
p[0] = p[1]
else:
if p[2] in ['*', '\\times']:
p[0] = Prod([p[1], p[3]], {})
elif p[2] == '/':
p[0] = Prod([p[1], Pow([p[3], Int(-1)], {})], {})
elif p[2] == '\\%':
p[0] = Mod([p[1], p[3]], {})
def p_additive_expression(p):
"""additive_expression : additive_expression PLUS multiplicative_expression
| additive_expression MINUS multiplicative_expression
| multiplicative_expression """
if len(p) == 2:
p[0] = p[1]
else:
if p[2] == '+':
p[0] = Sum([p[1], p[3]], {})
elif p[2] == '-':
p[0] = Sum([p[1], Prod([Int(-1), p[3]], {})], {})
def p_expr_unary(p):
"""unary_expression : MINUS unary_expression %prec NEG
| PLUS unary_expression %prec NEG
| pow_expression """
if len(p) == 2:
p[0] = p[1]
else:
if p[1] == '-':
p[0] = Prod([Int(-1), p[2]], {})
else:
p[0] = p[2]
def testSum(self):
test_list = [
(Sum([Int(1), Sum([Int(2), Int(3)], {})],
{}), Sum([Int(1), Int(2), Int(3)], {})),
(Sum([Int(0), Sum([Int(2), Sum([Int(3), Int(4)], {})], {})],
{}), Sum([Int(2), Int(3), Int(4)], {})),
(Sum([
Int(0),
Int(6),
Prod([Int(2),
Sum([Int(3), Sum([Int(4), Int(5)], {})], {})], {})
], {}),
Sum([
Int(6),
Prod([Int(2), Sum([Int(3), Int(4), Int(5)], {})], {})
], {})), (Sum([Id('x')], {}), Id('x'))
]
for (tree, ret) in test_list:
transformer = Transformer(tree)
simplifier = SimplifySum()
transformer.apply(simplifier)
self.assertEqual(transformer.get_tree(), ret)
def p_additive_expression(p):
"""additive_expression : additive_expression PLUS multiplicative_expression
| additive_expression MINUS multiplicative_expression
| BIGSUM DOWN LBRACE ID EQ expression RBRACE POW LBRACE expression RBRACE multiplicative_expression
| BIGINT DOWN LBRACE ID EQ expression RBRACE POW LBRACE expression RBRACE multiplicative_expression
| multiplicative_expression
"""
# 0 1 2 3 4 5 6 7 8 9 10 11 12
if len(p) == 13:
if p[1] == "\\int":
p[0] = Integrate([p[12], translate_id(p[4]), p[6], p[10]], {})
else:
p[0] = Series([p[12], translate_id(p[4]), p[6], p[10]], {})
elif len(p) == 2:
p[0] = p[1]
else:
if p[2] == '+':
p[0] = Sum([p[1], p[3]], {})
elif p[2] == '-':
p[0] = Sum([p[1], Prod([Int(-1), p[3]], {})], {})
def testParser(self):
a = Id('a')
i = Id('i')
n = Id('n')
x = Id('x')
y = Id('y')
test_list = [
("0", Int(0)),
("sin(x)", Sin([x], {})),
("\\sin{y}", Sin([y], {})),
("\\sqrt{4}", Sqrt([Int(4)], {})),
("\\sqrt{a}", Sqrt([a], {})),
("\\sqrt[n]{a}", Pow([a, Pow([n, Int(-1)], {})], {})),
("\\frac{1}{2}", Prod([Int(1), Pow([Int(2), Int(-1)], {})], {})),
("\\binom{6}{4}", C([Int(6), Int(4)], {})),
("\\lceil sin(x) \\rceil", Ceiling([Sin([x], {})], {})),
("\\lim_{x\\to 0} sin(x)/x",
Limit(
[Prod([Sin([x], {}), Pow([x, Int(-1)], {})], {}), x,
Int(0)], {})),
("\\sum _ { i = 0 } ^ { \\infty } (1)",
Series([Int(1), i, Int(0), infinity], {})),
("\\sum _ { i = 0 } ^ { \\infty } (1/i^{2}) ",
Series([
Prod(
[Int(1), Pow(
[Pow([i, Int(2)], {}), Int(-1)], {})], {}), i,
Int(0), infinity
], {})),
("\\frac { \\log ( \\frac { 1 } { 2 } ) } { 2 ^ {2} }",
Prod([
Log([Prod([Int(1), Pow([Int(2), Int(-1)], {})], {})], {}),
Pow([Pow([Int(2), Int(2)], {}),
Int(-1)], {})
], {})),
("2\\times(1+3)", Prod([Int(2), Sum([Int(1), Int(3)], {})], {})),
]
for e in test_list:
if len(e) == 3:
expr, res, d = e
else:
expr, res = e
d = False
self.assertEqual(
repr(latexParser.parse(expr, lexer=latexLexer, debug=d)),
repr(res))
def testParserWithImplicitBracesOrTimes(self):
a = Id('a')
b = Id('b')
c = Id('c')
d = Id('d')
f = Id('f')
g = Id('g')
i = Id('i')
j = Id('j')
n = Id('n')
x = Id('x')
test_list = [
("f ( a ) ", "f ( a ) ", Call(f, [a], {})),
("( a ) ", "( a ) ", a),
("( ( a ) ) ", "( ( a ) ) ", a),
("( ( a ) b ) ", "( ( a ) *b ) ", Prod([a, b], {})),
("( ( abc ) b a ^ {n} \\% b ! + c ) ",
"( ( abc ) *b *a ^ { n } \\% b ! + c ) ",
Sum([
Mod([
Prod([Prod([Id('abc'), b], {}),
Pow([a, n], {})], {}),
Fact([b], {})
], {}), c
], {})),
("f(x)a", "f ( x ) *a ", Prod([Call(f, [x], {}), a], {})),
("g f(n)", "g *f ( n ) ", Prod([g, Call(f, [n], {})], {})),
("((f(a)(a+b)a))a(c+d)d",
"( ( f ( a ) *( a + b ) *a ) ) *a ( c + d ) *d ",
Prod([
Prod([
Prod([Prod(
[Call(f, [a], {}), Sum([a, b], {})], {}), a], {}),
Call(a, [Sum([c, d], {})], {})
], {}), d
], {})),
("a 2", "a *2 ", Prod([a, Int(2)], {})),
("2 a", "2 *a ", Prod([Int(2), a], {})),
("2 4", "2 *4 ", Prod([Int(2), Int(4)], {})),
("2x", "2 *x ", Prod([Int(2), x], {})),
("x2", "x *2 ", Prod([x, Int(2)], {})),
("a-b", "a - b ", Sum([a, Prod([Int(-1), b], {})], {})),
("a/-b", "a / - b ",
Prod([a, Pow(
[Prod([Int(-1), b], {}), Int(-1)], {})], {})),
("-a/+b", "- a / + b ",
Prod([Prod([Int(-1), a], {}),
Pow([b, Int(-1)], {})], {})),
("a(b+c)", "a ( b + c ) ", Call(a, [Sum([b, c], {})], {})),
("42(b+c)", "42 *( b + c ) ",
Prod([Int(42), Sum([b, c], {})], {})),
("1/2\\pi", "1 / 2 *\\pi ",
Prod([Prod([Int(1), Pow([Int(2), Int(-1)], {})], {}), pi], {})),
("\\sum_{i=0}^\\infty i", "\sum _ { i = 0 } ^ { \infty } { i } ",
Series([i, i, Int(0), infinity], {})),
("\\sum\\limits_{j=0}^\\infty j",
"\sum _ { j = 0 } ^ { \infty } { j } ",
Series([j, j, Int(0), infinity], {})),
("\\sum_{i=0}^\\infty(1/i^2) ",
"\sum _ { i = 0 } ^ { \infty } ( 1 / i ^ { 2 } ) ",
Series([
Prod(
[Int(1), Pow(
[Pow([i, Int(2)], {}), Int(-1)], {})], {}), i,
Int(0), infinity
], {})),
("\\sqrt{a}", "\\sqrt { a } ", Sqrt([a], {})),
("\\sqrt[n]{a}", "\\sqrt [ n ] { a } ",
Pow([a, Pow([n, Int(-1)], {})], {})),
("\\sqrt {\\sqrt a}", "\\sqrt { \\sqrt { a } } ",
Sqrt([Sqrt([a], {})], {})),
]
for e in test_list:
if len(e) == 4:
expr, prep, res, d = e
else:
expr, prep, res = e
d = False
expr_ = preprocess_latex(expr)
self.assertEqual(expr_, prep)
self.assertEqual(
repr(latexParser.parse(expr_, lexer=latexLexer, debug=d)),
repr(res))
def testParser(self):
a = Id('a')
b = Id('b')
c = Id('c')
e = Id('e')
i = Id('i')
j = Id('j')
m = Id('m')
n = Id('n')
x = Id('x')
y = Id('y')
test_list = [
("0", Int(0)),
("Sin[x]", Sin([x], {})),
("Arctan[x]", Call(Id('Arctan'), [x], {})),
("Sqrt[4]", Call(Id('Sqrt'), [Int(4)], {})),
("ArcTan[x]", Call(Id('ArcTan'), [x], {})),
("x^2", Pow([x, Int(2)], {})),
("a+b", Sum([a, b], {})),
("a+b+c", Sum([Sum([a, b], {}), c], {})),
("a*b", Prod([a, b], {})),
("a!", Fact([a], {})),
("2*a!", Prod([Int(2), Fact([a], {})], {})),
("a!!", Fact([Fact([a], {})], {})),
("-a!", Prod([Int(-1), Fact([a], {})], {})),
("b+a!", Sum([b, Fact([a], {})], {})),
("-a-a", Sum([Prod([Int(-1), a], {}),
Prod([Int(-1), a], {})], {})),
("--a", Prod([Int(-1), Prod([Int(-1), a], {})], {})),
("+a", a),
("+-a", Prod([Int(-1), a], {})),
("-+a", Prod([Int(-1), a], {})),
("a*-b", Prod([a, Prod([Int(-1), b], {})], {})),
("-a*b", Prod([Prod([Int(-1), a], {}), b], {})),
("a/b", Prod([a, Pow([b, Int(-1)], {})], {})),
("a-b", Sum([a, Prod([Int(-1), b], {})], {})),
("a^b", Pow([a, b], {})),
("a^b/c",
Prod([Pow([a, b], {}), Pow([c, Int(-1)], {})], {})),
("-a^b/c",
Prod(
[Prod([Int(-1), Pow([a, b], {})], {}),
Pow([c, Int(-1)], {})], {})),
("(a+b)", Sum([a, b], {})),
("(a*b)", Prod([a, b], {})),
("(a/b)", Prod([a, Pow([b, Int(-1)], {})], {})),
("(a-b)", Sum([a, Prod([Int(-1), b], {})], {})),
("(a^b)", Pow([a, b], {})),
("(a)^b", Pow([a, b], {})),
("(a+b)*c", Prod([Sum([a, b], {}), c], {})),
("a+(b*c)", Sum([a, Prod([b, c], {})], {})),
("a+b*c", Sum([a, Prod([b, c], {})], {})),
("a^b^c", Pow([a, Pow([b, c], {})], {})),
("a*b/c",
Prod([Prod([a, b], {}), Pow([c, Int(-1)], {})], {})),
("a+b/c", Sum([a, Prod([b, Pow([c, Int(-1)], {})], {})], {})),
("x^n/n!",
Prod([Pow([x, n], {}),
Pow([Fact([n], {}), Int(-1)], {})], {})),
("a^G[x]", Pow([a, Call(Id('G'), [x], {})], {})),
("f[x]+f[x]",
Sum([Call(Id('f'), [x], {}),
Call(Id('f'), [x], {})], {})),
("f[x]^G[x]",
Pow([Call(Id('f'), [x], {}),
Call(Id('G'), [x], {})], {})),
("Sin[x]^2+Cos[x]^2",
Sum([
Pow([Sin([x], {}), Int(2)], {}),
Pow([Cos([x], {}), Int(2)], {})
], {})),
("Sum[1/i^6, {i, 1, Infinity}]",
Series([
Prod(
[Int(1), Pow(
[Pow([i, Int(6)], {}), Int(-1)], {})], {}), i,
Int(1), infinity
], {})),
("Sum[j/i^6, {i, 1, Infinity}, {j, 0 , m}]",
Series([
Series([
Prod([j, Pow(
[Pow([i, Int(6)], {}), Int(-1)], {})], {}), j,
Int(0), m
], {}), i,
Int(1), infinity
], {})),
("Integrate[1/(x^3 + 1), x]",
Integrate([
Prod([
Int(1),
Pow([Sum(
[Pow([x, Int(3)], {}), Int(1)], {}),
Int(-1)], {})
], {}), x
], {})),
("Integrate[1/(x^3 + 1), {x, 0, 1}]",
Integrate([
Prod([
Int(1),
Pow([Sum(
[Pow([x, Int(3)], {}), Int(1)], {}),
Int(-1)], {})
], {}), x,
Int(0),
Int(1)
], {})),
("Integrate[Sin[x*y], {x, 0, 1}, {y, 0, x}]",
Integrate([
Integrate([Sin([Prod([x, y], {})], {}), y,
Int(0), x], {}), x,
Int(0),
Int(1)
], {})),
("Limit[e, x->a]", Limit([e], {x: a})),
("Limit[Sin[x]/x, x->0]",
Limit([Prod([Sin([x], {}), Pow([x, Int(-1)], {})], {})],
{x: Int(0)})),
("Limit[(1+x/n)^n, x->Infinity]",
Limit([
Pow([
Sum([Int(1), Prod([x, Pow([n, Int(-1)], {})], {})], {}), n
], {})
], {x: infinity})),
("Solve[x^2==1, x]",
Solve([Eq([Pow([x, Int(2)], {}), Int(1)], {}), x], {})),
]
for test in test_list:
if len(test) == 2:
expr, res = test
d = False
else:
expr, res, d = test
self.assertEqual(
repr(
mathematicaParser.parse(expr,
lexer=mathematicaLexer,
debug=d)), repr(res))
def testParserWithImplicitMultiplication(self):
a = Id('a')
b = Id('b')
c = Id('c')
d = Id('d')
f = Id('f')
g = Id('g')
n = Id('n')
x = Id('x')
test_list = [
("(a)a^n%b!+c", "(a)*a^n%b!+c",
Sum([Mod([Prod([a, Pow([a, n], {})], {}),
Fact([b], {})], {}), c], {})),
("f(x)a", "f(x)*a", Prod([Call(f, [x], {}), a], {})),
("g f(n)", "g*f(n)", Prod([g, Call(f, [n], {})], {})),
("((f(a)(a+b)a))a(c+d)d", "((f(a)*(a+b)*a))*a(c+d)*d",
Prod([
Prod([
Prod([Prod(
[Call(f, [a], {}), Sum([a, b], {})], {}), a], {}),
Call(a, [Sum([c, d], {})], {})
], {}), d
], {})),
("a 2", "a*2", Prod([a, Int(2)], {})),
("2 a", "2*a", Prod([Int(2), a], {})),
("2 4", "2*4", Prod([Int(2), Int(4)], {})),
("2x", "2*x", Prod([Int(2), x], {})),
("x2", "x2", Id('x2')),
("a-b", "a-b", Sum([a, Prod([Int(-1), b], {})], {})),
("a/-b", "a/-b",
Prod([a, Pow(
[Prod([Int(-1), b], {}), Int(-1)], {})], {})),
("-a/+b", "-a/+b",
Prod([Prod([Int(-1), a], {}),
Pow([b, Int(-1)], {})], {})),
("a(b+c)", "a(b+c)", Call(a, [Sum([b, c], {})], {})),
("42(b+c)", "42*(b+c)", Prod([Int(42), Sum([b, c], {})], {})),
("1/2Pi", "1/2*Pi",
Prod([Prod([Int(1), Pow([Int(2), Int(-1)], {})], {}), pi], {})),
]
for e in test_list:
if len(e) == 4:
expr, prep, res, d = e
else:
expr, prep, res = e
d = False
expr_ = preprocess_natural(expr)
self.assertEqual(expr_, prep)
self.assertEqual(
repr(naturalParser.parse(expr_, lexer=naturalLexer, debug=d)),
repr(res))
def testParser(self):
a = Id('a')
b = Id('b')
c = Id('c')
d = Id('d')
f = Id('f')
g = Id('g')
i = Id('i')
j = Id('j')
m = Id('m')
n = Id('n')
x = Id('x')
y = Id('y')
z = Id('z')
_d0 = Id('_d0')
__1 = Int(-1)
_0 = Int(0)
_1 = Int(1)
_2 = Int(2)
_3 = Int(3)
_4 = Int(4)
_6 = Int(6)
_1024 = Int(1024)
self.maxDiff = None
test_list = [
("0", _0),
("Sin(x)", Sin([x], {})),
("Arctan(x)", Arctan([x], {})),
("Sqrt(4)", Sqrt([_4], {})),
("ArcTan(x)", Arctan([x], {})),
("x^2", Pow([x, _2], {})),
("a+b", Sum([a, b], {})),
("a*b", Prod([a, b], {})),
("a!", Fact([a], {})),
("2*a!", Prod([_2, Fact([a], {})], {})),
("a!!", Fact([Fact([a], {})], {})),
("-a!", Prod([__1, Fact([a], {})], {})),
("b+a!", Sum([b, Fact([a], {})], {})),
("-a-a",
Sum([Prod([__1, a], {}), Prod([__1, a], {})], {})),
("--a", Prod([__1, Prod([__1, a], {})], {})),
("+a", a),
("+-a", Prod([__1, a], {})),
("-+a", Prod([__1, a], {})),
("a*-b", Prod([a, Prod([__1, b], {})], {})),
("-a*b", Prod([Prod([__1, a], {}), b], {})),
("-a^b", Prod([__1, Pow([a, b], {})], {})),
("-c**d", Prod([__1, Pow([c, d], {})], {})),
("a/b", Prod([a, Pow([b, __1], {})], {})),
("a-b", Sum([a, Prod([__1, b], {})], {})),
("a^b", Pow([a, b], {})),
("a^b/c",
Prod([Pow([a, b], {}), Pow([c, __1], {})], {})),
("-a^b/c",
Prod([Prod([__1, Pow([a, b], {})], {}),
Pow([c, __1], {})], {})),
("(a+b)", Sum([a, b], {})),
("(a*b)", Prod([a, b], {})),
("(a/b)", Prod([a, Pow([b, __1], {})], {})),
("(a-b)", Sum([a, Prod([__1, b], {})], {})),
("(a^b)", Pow([a, b], {})),
("(a)^b", Pow([a, b], {})),
("(a+b)*c", Prod([Sum([a, b], {}), c], {})),
("a+(b*c)", Sum([a, Prod([b, c], {})], {})),
("a+b*c", Sum([a, Prod([b, c], {})], {})),
("a^b^c", Pow([a, Pow([b, c], {})], {})),
("a*b/c",
Prod([Prod([a, b], {}), Pow([c, __1], {})], {})),
("a+b/c", Sum([a, Prod([b, Pow([c, __1], {})], {})], {})),
("x^n/n!",
Prod([Pow([x, n], {}),
Pow([Fact([n], {}), __1], {})], {})),
("a^n%b!", Mod([Pow([a, n], {}), Fact([b], {})], {})),
("a!%b^c+d",
Sum([Mod([Fact([a], {}), Pow([b, c], {})], {}), d], {})),
("a^g(x)", Pow([a, Call(g, [x], {})], {})),
("f(x)+f(x)",
Sum([Call(f, [x], {}), Call(f, [x], {})], {})),
("f(x)^g(x)",
Pow([Call(f, [x], {}), Call(g, [x], {})], {})),
("Sin(x)^2+Cos(x)^2",
Sum([Pow([Sin([x], {}), _2], {}),
Pow([Cos([x], {}), _2], {})], {})),
("Sum(1/i^6, i, 1, Infinity)",
Series([
Prod([_1, Pow([Pow([i, _6], {}), __1], {})], {}), i, _1,
infinity
], {})),
("Sum(Sum(j/i^6, i, 1, Infinity), j, 0 , m)",
Series([
Series([
Prod([j, Pow([Pow([i, _6], {}), __1], {})], {}), i, _1,
infinity
], {}), j, _0, m
], {})),
("Integrate(1/(x^3 + 1), x)",
Integrate([
Prod([_1, Pow([Sum([Pow([x, _3], {}), _1], {}), __1], {})],
{}), x
], {})),
("Integrate(1/(x^3 + 1), x, 0, 1)",
Integrate([
Prod([_1, Pow([Sum([Pow([x, _3], {}), _1], {}), __1], {})],
{}), x, _0, _1
], {})),
("Integrate(Integrate(Sin(x*y), x, 0, 1), y, 0, x)",
Integrate([
Integrate([Sin([Prod([x, y], {})], {}), x, _0, _1], {}), y,
_0, x
], {})),
("Limit(Sin(x)/x, x, 0)",
Limit([Prod([Sin([x], {}), Pow([x, __1], {})], {}), x, _0], {})),
("Limit((1+x/n)^n, x, Infinity)",
Limit([
Pow([Sum([_1, Prod([x, Pow([n, __1], {})], {})], {}), n], {}),
x, infinity
], {})),
("Pow(1024, 1/2)",
Pow([_1024, Prod([_1, Pow([_2, __1], {})], {})], {})),
("cos'(x)", Call(Diff([Fun(_d0, Cos([_d0], {})), _1], {}), [x],
{})),
("cos''''(x)",
Call(Diff([Fun(_d0, Cos([_d0], {})), _4], {}), [x], {})),
("x | y", Or([x, y], {})),
("~ y", Not([y], {})),
("x & y", And([x, y], {})),
("x | ~z & ~ y",
Or([x, And([Not([z], {}), Not([y], {})], {})], {})),
]
for (expr, res) in test_list:
self.assertEqual(repr(parse_natural(expr)), repr(res))