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| from sympy import sin, Function, symbols, Dummy, Lambda, cos | |
| from sympy.parsing.mathematica import parse_mathematica, MathematicaParser | |
| from sympy.core.sympify import sympify | |
| from sympy.abc import n, w, x, y, z | |
| from sympy.testing.pytest import raises | |
| def test_mathematica(): | |
| d = { | |
| '- 6x': '-6*x', | |
| 'Sin[x]^2': 'sin(x)**2', | |
| '2(x-1)': '2*(x-1)', | |
| '3y+8': '3*y+8', | |
| 'ArcSin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x', | |
| 'x+y': 'x+y', | |
| '355/113': '355/113', | |
| '2.718281828': '2.718281828', | |
| 'Cos(1/2 * π)': 'Cos(π/2)', | |
| 'Sin[12]': 'sin(12)', | |
| 'Exp[Log[4]]': 'exp(log(4))', | |
| '(x+1)(x+3)': '(x+1)*(x+3)', | |
| 'Cos[ArcCos[3.6]]': 'cos(acos(3.6))', | |
| 'Cos[x]==Sin[y]': 'Eq(cos(x), sin(y))', | |
| '2*Sin[x+y]': '2*sin(x+y)', | |
| 'Sin[x]+Cos[y]': 'sin(x)+cos(y)', | |
| 'Sin[Cos[x]]': 'sin(cos(x))', | |
| '2*Sqrt[x+y]': '2*sqrt(x+y)', # Test case from the issue 4259 | |
| '+Sqrt[2]': 'sqrt(2)', | |
| '-Sqrt[2]': '-sqrt(2)', | |
| '-1/Sqrt[2]': '-1/sqrt(2)', | |
| '-(1/Sqrt[3])': '-(1/sqrt(3))', | |
| '1/(2*Sqrt[5])': '1/(2*sqrt(5))', | |
| 'Mod[5,3]': 'Mod(5,3)', | |
| '-Mod[5,3]': '-Mod(5,3)', | |
| '(x+1)y': '(x+1)*y', | |
| 'x(y+1)': 'x*(y+1)', | |
| 'Sin[x]Cos[y]': 'sin(x)*cos(y)', | |
| 'Sin[x]^2Cos[y]^2': 'sin(x)**2*cos(y)**2', | |
| 'Cos[x]^2(1 - Cos[y]^2)': 'cos(x)**2*(1-cos(y)**2)', | |
| 'x y': 'x*y', | |
| 'x y': 'x*y', | |
| '2 x': '2*x', | |
| 'x 8': 'x*8', | |
| '2 8': '2*8', | |
| '4.x': '4.*x', | |
| '4. 3': '4.*3', | |
| '4. 3.': '4.*3.', | |
| '1 2 3': '1*2*3', | |
| ' - 2 * Sqrt[ 2 3 * ( 1 + 5 ) ] ': '-2*sqrt(2*3*(1+5))', | |
| 'Log[2,4]': 'log(4,2)', | |
| 'Log[Log[2,4],4]': 'log(4,log(4,2))', | |
| 'Exp[Sqrt[2]^2Log[2, 8]]': 'exp(sqrt(2)**2*log(8,2))', | |
| 'ArcSin[Cos[0]]': 'asin(cos(0))', | |
| 'Log2[16]': 'log(16,2)', | |
| 'Max[1,-2,3,-4]': 'Max(1,-2,3,-4)', | |
| 'Min[1,-2,3]': 'Min(1,-2,3)', | |
| 'Exp[I Pi/2]': 'exp(I*pi/2)', | |
| 'ArcTan[x,y]': 'atan2(y,x)', | |
| 'Pochhammer[x,y]': 'rf(x,y)', | |
| 'ExpIntegralEi[x]': 'Ei(x)', | |
| 'SinIntegral[x]': 'Si(x)', | |
| 'CosIntegral[x]': 'Ci(x)', | |
| 'AiryAi[x]': 'airyai(x)', | |
| 'AiryAiPrime[5]': 'airyaiprime(5)', | |
| 'AiryBi[x]': 'airybi(x)', | |
| 'AiryBiPrime[7]': 'airybiprime(7)', | |
| 'LogIntegral[4]': ' li(4)', | |
| 'PrimePi[7]': 'primepi(7)', | |
| 'Prime[5]': 'prime(5)', | |
| 'PrimeQ[5]': 'isprime(5)', | |
| 'Rational[2,19]': 'Rational(2,19)', # test case for issue 25716 | |
| } | |
| for e in d: | |
| assert parse_mathematica(e) == sympify(d[e]) | |
| # The parsed form of this expression should not evaluate the Lambda object: | |
| assert parse_mathematica("Sin[#]^2 + Cos[#]^2 &[x]") == sin(x)**2 + cos(x)**2 | |
| d1, d2, d3 = symbols("d1:4", cls=Dummy) | |
| assert parse_mathematica("Sin[#] + Cos[#3] &").dummy_eq(Lambda((d1, d2, d3), sin(d1) + cos(d3))) | |
| assert parse_mathematica("Sin[#^2] &").dummy_eq(Lambda(d1, sin(d1**2))) | |
| assert parse_mathematica("Function[x, x^3]") == Lambda(x, x**3) | |
| assert parse_mathematica("Function[{x, y}, x^2 + y^2]") == Lambda((x, y), x**2 + y**2) | |
| def test_parser_mathematica_tokenizer(): | |
| parser = MathematicaParser() | |
| chain = lambda expr: parser._from_tokens_to_fullformlist(parser._from_mathematica_to_tokens(expr)) | |
| # Basic patterns | |
| assert chain("x") == "x" | |
| assert chain("42") == "42" | |
| assert chain(".2") == ".2" | |
| assert chain("+x") == "x" | |
| assert chain("-1") == "-1" | |
| assert chain("- 3") == "-3" | |
| assert chain("α") == "α" | |
| assert chain("+Sin[x]") == ["Sin", "x"] | |
| assert chain("-Sin[x]") == ["Times", "-1", ["Sin", "x"]] | |
| assert chain("x(a+1)") == ["Times", "x", ["Plus", "a", "1"]] | |
| assert chain("(x)") == "x" | |
| assert chain("(+x)") == "x" | |
| assert chain("-a") == ["Times", "-1", "a"] | |
| assert chain("(-x)") == ["Times", "-1", "x"] | |
| assert chain("(x + y)") == ["Plus", "x", "y"] | |
| assert chain("3 + 4") == ["Plus", "3", "4"] | |
| assert chain("a - 3") == ["Plus", "a", "-3"] | |
| assert chain("a - b") == ["Plus", "a", ["Times", "-1", "b"]] | |
| assert chain("7 * 8") == ["Times", "7", "8"] | |
| assert chain("a + b*c") == ["Plus", "a", ["Times", "b", "c"]] | |
| assert chain("a + b* c* d + 2 * e") == ["Plus", "a", ["Times", "b", "c", "d"], ["Times", "2", "e"]] | |
| assert chain("a / b") == ["Times", "a", ["Power", "b", "-1"]] | |
| # Missing asterisk (*) patterns: | |
| assert chain("x y") == ["Times", "x", "y"] | |
| assert chain("3 4") == ["Times", "3", "4"] | |
| assert chain("a[b] c") == ["Times", ["a", "b"], "c"] | |
| assert chain("(x) (y)") == ["Times", "x", "y"] | |
| assert chain("3 (a)") == ["Times", "3", "a"] | |
| assert chain("(a) b") == ["Times", "a", "b"] | |
| assert chain("4.2") == "4.2" | |
| assert chain("4 2") == ["Times", "4", "2"] | |
| assert chain("4 2") == ["Times", "4", "2"] | |
| assert chain("3 . 4") == ["Dot", "3", "4"] | |
| assert chain("4. 2") == ["Times", "4.", "2"] | |
| assert chain("x.y") == ["Dot", "x", "y"] | |
| assert chain("4.y") == ["Times", "4.", "y"] | |
| assert chain("4 .y") == ["Dot", "4", "y"] | |
| assert chain("x.4") == ["Times", "x", ".4"] | |
| assert chain("x0.3") == ["Times", "x0", ".3"] | |
| assert chain("x. 4") == ["Dot", "x", "4"] | |
| # Comments | |
| assert chain("a (* +b *) + c") == ["Plus", "a", "c"] | |
| assert chain("a (* + b *) + (**)c (* +d *) + e") == ["Plus", "a", "c", "e"] | |
| assert chain("""a + (* | |
| + b | |
| *) c + (* d | |
| *) e | |
| """) == ["Plus", "a", "c", "e"] | |
| # Operators couples + and -, * and / are mutually associative: | |
| # (i.e. expression gets flattened when mixing these operators) | |
| assert chain("a*b/c") == ["Times", "a", "b", ["Power", "c", "-1"]] | |
| assert chain("a/b*c") == ["Times", "a", ["Power", "b", "-1"], "c"] | |
| assert chain("a+b-c") == ["Plus", "a", "b", ["Times", "-1", "c"]] | |
| assert chain("a-b+c") == ["Plus", "a", ["Times", "-1", "b"], "c"] | |
| assert chain("-a + b -c ") == ["Plus", ["Times", "-1", "a"], "b", ["Times", "-1", "c"]] | |
| assert chain("a/b/c*d") == ["Times", "a", ["Power", "b", "-1"], ["Power", "c", "-1"], "d"] | |
| assert chain("a/b/c") == ["Times", "a", ["Power", "b", "-1"], ["Power", "c", "-1"]] | |
| assert chain("a-b-c") == ["Plus", "a", ["Times", "-1", "b"], ["Times", "-1", "c"]] | |
| assert chain("1/a") == ["Times", "1", ["Power", "a", "-1"]] | |
| assert chain("1/a/b") == ["Times", "1", ["Power", "a", "-1"], ["Power", "b", "-1"]] | |
| assert chain("-1/a*b") == ["Times", "-1", ["Power", "a", "-1"], "b"] | |
| # Enclosures of various kinds, i.e. ( ) [ ] [[ ]] { } | |
| assert chain("(a + b) + c") == ["Plus", ["Plus", "a", "b"], "c"] | |
| assert chain(" a + (b + c) + d ") == ["Plus", "a", ["Plus", "b", "c"], "d"] | |
| assert chain("a * (b + c)") == ["Times", "a", ["Plus", "b", "c"]] | |
| assert chain("a b (c d)") == ["Times", "a", "b", ["Times", "c", "d"]] | |
| assert chain("{a, b, 2, c}") == ["List", "a", "b", "2", "c"] | |
| assert chain("{a, {b, c}}") == ["List", "a", ["List", "b", "c"]] | |
| assert chain("{{a}}") == ["List", ["List", "a"]] | |
| assert chain("a[b, c]") == ["a", "b", "c"] | |
| assert chain("a[[b, c]]") == ["Part", "a", "b", "c"] | |
| assert chain("a[b[c]]") == ["a", ["b", "c"]] | |
| assert chain("a[[b, c[[d, {e,f}]]]]") == ["Part", "a", "b", ["Part", "c", "d", ["List", "e", "f"]]] | |
| assert chain("a[b[[c,d]]]") == ["a", ["Part", "b", "c", "d"]] | |
| assert chain("a[[b[c]]]") == ["Part", "a", ["b", "c"]] | |
| assert chain("a[[b[[c]]]]") == ["Part", "a", ["Part", "b", "c"]] | |
| assert chain("a[[b[c[[d]]]]]") == ["Part", "a", ["b", ["Part", "c", "d"]]] | |
| assert chain("a[b[[c[d]]]]") == ["a", ["Part", "b", ["c", "d"]]] | |
| assert chain("x[[a+1, b+2, c+3]]") == ["Part", "x", ["Plus", "a", "1"], ["Plus", "b", "2"], ["Plus", "c", "3"]] | |
| assert chain("x[a+1, b+2, c+3]") == ["x", ["Plus", "a", "1"], ["Plus", "b", "2"], ["Plus", "c", "3"]] | |
| assert chain("{a+1, b+2, c+3}") == ["List", ["Plus", "a", "1"], ["Plus", "b", "2"], ["Plus", "c", "3"]] | |
| # Flat operator: | |
| assert chain("a*b*c*d*e") == ["Times", "a", "b", "c", "d", "e"] | |
| assert chain("a +b + c+ d+e") == ["Plus", "a", "b", "c", "d", "e"] | |
| # Right priority operator: | |
| assert chain("a^b") == ["Power", "a", "b"] | |
| assert chain("a^b^c") == ["Power", "a", ["Power", "b", "c"]] | |
| assert chain("a^b^c^d") == ["Power", "a", ["Power", "b", ["Power", "c", "d"]]] | |
| # Left priority operator: | |
| assert chain("a/.b") == ["ReplaceAll", "a", "b"] | |
| assert chain("a/.b/.c/.d") == ["ReplaceAll", ["ReplaceAll", ["ReplaceAll", "a", "b"], "c"], "d"] | |
| assert chain("a//b") == ["a", "b"] | |
| assert chain("a//b//c") == [["a", "b"], "c"] | |
| assert chain("a//b//c//d") == [[["a", "b"], "c"], "d"] | |
| # Compound expressions | |
| assert chain("a;b") == ["CompoundExpression", "a", "b"] | |
| assert chain("a;") == ["CompoundExpression", "a", "Null"] | |
| assert chain("a;b;") == ["CompoundExpression", "a", "b", "Null"] | |
| assert chain("a[b;c]") == ["a", ["CompoundExpression", "b", "c"]] | |
| assert chain("a[b,c;d,e]") == ["a", "b", ["CompoundExpression", "c", "d"], "e"] | |
| assert chain("a[b,c;,d]") == ["a", "b", ["CompoundExpression", "c", "Null"], "d"] | |
| # New lines | |
| assert chain("a\nb\n") == ["CompoundExpression", "a", "b"] | |
| assert chain("a\n\nb\n (c \nd) \n") == ["CompoundExpression", "a", "b", ["Times", "c", "d"]] | |
| assert chain("\na; b\nc") == ["CompoundExpression", "a", "b", "c"] | |
| assert chain("a + \nb\n") == ["Plus", "a", "b"] | |
| assert chain("a\nb; c; d\n e; (f \n g); h + \n i") == ["CompoundExpression", "a", "b", "c", "d", "e", ["Times", "f", "g"], ["Plus", "h", "i"]] | |
| assert chain("\n{\na\nb; c; d\n e (f \n g); h + \n i\n\n}\n") == ["List", ["CompoundExpression", ["Times", "a", "b"], "c", ["Times", "d", "e", ["Times", "f", "g"]], ["Plus", "h", "i"]]] | |
| # Patterns | |
| assert chain("y_") == ["Pattern", "y", ["Blank"]] | |
| assert chain("y_.") == ["Optional", ["Pattern", "y", ["Blank"]]] | |
| assert chain("y__") == ["Pattern", "y", ["BlankSequence"]] | |
| assert chain("y___") == ["Pattern", "y", ["BlankNullSequence"]] | |
| assert chain("a[b_.,c_]") == ["a", ["Optional", ["Pattern", "b", ["Blank"]]], ["Pattern", "c", ["Blank"]]] | |
| assert chain("b_. c") == ["Times", ["Optional", ["Pattern", "b", ["Blank"]]], "c"] | |
| # Slots for lambda functions | |
| assert chain("#") == ["Slot", "1"] | |
| assert chain("#3") == ["Slot", "3"] | |
| assert chain("#n") == ["Slot", "n"] | |
| assert chain("##") == ["SlotSequence", "1"] | |
| assert chain("##a") == ["SlotSequence", "a"] | |
| # Lambda functions | |
| assert chain("x&") == ["Function", "x"] | |
| assert chain("#&") == ["Function", ["Slot", "1"]] | |
| assert chain("#+3&") == ["Function", ["Plus", ["Slot", "1"], "3"]] | |
| assert chain("#1 + #2&") == ["Function", ["Plus", ["Slot", "1"], ["Slot", "2"]]] | |
| assert chain("# + #&") == ["Function", ["Plus", ["Slot", "1"], ["Slot", "1"]]] | |
| assert chain("#&[x]") == [["Function", ["Slot", "1"]], "x"] | |
| assert chain("#1 + #2 & [x, y]") == [["Function", ["Plus", ["Slot", "1"], ["Slot", "2"]]], "x", "y"] | |
| assert chain("#1^2#2^3&") == ["Function", ["Times", ["Power", ["Slot", "1"], "2"], ["Power", ["Slot", "2"], "3"]]] | |
| # Strings inside Mathematica expressions: | |
| assert chain('"abc"') == ["_Str", "abc"] | |
| assert chain('"a\\"b"') == ["_Str", 'a"b'] | |
| # This expression does not make sense mathematically, it's just testing the parser: | |
| assert chain('x + "abc" ^ 3') == ["Plus", "x", ["Power", ["_Str", "abc"], "3"]] | |
| assert chain('"a (* b *) c"') == ["_Str", "a (* b *) c"] | |
| assert chain('"a" (* b *) ') == ["_Str", "a"] | |
| assert chain('"a [ b] "') == ["_Str", "a [ b] "] | |
| raises(SyntaxError, lambda: chain('"')) | |
| raises(SyntaxError, lambda: chain('"\\"')) | |
| raises(SyntaxError, lambda: chain('"abc')) | |
| raises(SyntaxError, lambda: chain('"abc\\"def')) | |
| # Invalid expressions: | |
| raises(SyntaxError, lambda: chain("(,")) | |
| raises(SyntaxError, lambda: chain("()")) | |
| raises(SyntaxError, lambda: chain("a (* b")) | |
| def test_parser_mathematica_exp_alt(): | |
| parser = MathematicaParser() | |
| convert_chain2 = lambda expr: parser._from_fullformlist_to_fullformsympy(parser._from_fullform_to_fullformlist(expr)) | |
| convert_chain3 = lambda expr: parser._from_fullformsympy_to_sympy(convert_chain2(expr)) | |
| Sin, Times, Plus, Power = symbols("Sin Times Plus Power", cls=Function) | |
| full_form1 = "Sin[Times[x, y]]" | |
| full_form2 = "Plus[Times[x, y], z]" | |
| full_form3 = "Sin[Times[x, Plus[y, z], Power[w, n]]]]" | |
| full_form4 = "Rational[Rational[x, y], z]" | |
| assert parser._from_fullform_to_fullformlist(full_form1) == ["Sin", ["Times", "x", "y"]] | |
| assert parser._from_fullform_to_fullformlist(full_form2) == ["Plus", ["Times", "x", "y"], "z"] | |
| assert parser._from_fullform_to_fullformlist(full_form3) == ["Sin", ["Times", "x", ["Plus", "y", "z"], ["Power", "w", "n"]]] | |
| assert parser._from_fullform_to_fullformlist(full_form4) == ["Rational", ["Rational", "x", "y"], "z"] | |
| assert convert_chain2(full_form1) == Sin(Times(x, y)) | |
| assert convert_chain2(full_form2) == Plus(Times(x, y), z) | |
| assert convert_chain2(full_form3) == Sin(Times(x, Plus(y, z), Power(w, n))) | |
| assert convert_chain3(full_form1) == sin(x*y) | |
| assert convert_chain3(full_form2) == x*y + z | |
| assert convert_chain3(full_form3) == sin(x*(y + z)*w**n) | |