move private doctests to pytests in mathics.builtin.numeric

mathics/builtin/numbers/algebra.py

@@ -373,12 +373,6 @@ class Apart(Builtin):
     But it does not touch other expressions:
     >> Sin[1 / (x ^ 2 - y ^ 2)] // Apart
      = Sin[1 / (x ^ 2 - y ^ 2)]
-
-    #> Attributes[f] = {HoldAll}; Apart[f[x + x]]
-     = f[x + x]
-
-    #> Attributes[f] = {}; Apart[f[x + x]]
-     = f[2 x]
     """
 
     attributes = A_LISTABLE | A_PROTECTED
@@ -504,25 +498,9 @@ class Coefficient(Builtin):
     >> Coefficient[a x^2 + b y^3 + c x + d y + 5, x, 0]
      = 5 + b y ^ 3 + d y
 
-    ## Errors:
-    #> Coefficient[x + y + 3]
-     : Coefficient called with 1 argument; 2 or 3 arguments are expected.
-     = Coefficient[3 + x + y]
-    #> Coefficient[x + y + 3, 5]
-     : 5 is not a valid variable.
-     = Coefficient[3 + x + y, 5]
-
-    ## This is known bug of Sympy 1.0, next Sympy version will fix it by this commit
-    ## https://github.com/sympy/sympy/commit/25bf64b64d4d9a2dc563022818d29d06bc740d47
-    ## #> Coefficient[x * y, z, 0]
-    ##  = x y
-    ##  ## Sympy 1.0 retuns 0
-
     ## ## TODO: Support Modulus
     ## >> Coefficient[(x + 2)^3 + (x + 3)^2, x, 0, Modulus -> 3]
     ##  = 2
-    ## #> Coefficient[(x + 2)^3 + (x + 3)^2, x, 0, {Modulus -> 3, Modulus -> 2, Modulus -> 10}]
-    ##  = {2, 1, 7}
     """
 
     attributes = A_LISTABLE | A_PROTECTED
@@ -910,21 +888,11 @@ class CoefficientList(Builtin):
      = {2 / (-3 + y), 1 / (-3 + y) + 1 / (-2 + y)}
     >> CoefficientList[(x + y)^3, z]
      = {(x + y) ^ 3}
-    #> CoefficientList[x + y, 5]
-     : 5 is not a valid variable.
-     = CoefficientList[x + y, 5]
-
     ## Form 2 CoefficientList[poly, {var1, var2, ...}]
     >> CoefficientList[a x^2 + b y^3 + c x + d y + 5, {x, y}]
      = {{5, d, 0, b}, {c, 0, 0, 0}, {a, 0, 0, 0}}
     >> CoefficientList[(x - 2 y + 3 z)^3, {x, y, z}]
      = {{{0, 0, 0, 27}, {0, 0, -54, 0}, {0, 36, 0, 0}, {-8, 0, 0, 0}}, {{0, 0, 27, 0}, {0, -36, 0, 0}, {12, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 9, 0, 0}, {-6, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{1, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}
-    #> CoefficientList[(x - 2 y)^4, {x, 2}]
-     : 2 is not a valid variable.
-     = CoefficientList[(x - 2 y) ^ 4, {x, 2}]
-    #> CoefficientList[x / y, {x, y}]
-     : x / y is not a polynomial.
-     = CoefficientList[x / y, {x, y}]
     """
 
     messages = {
@@ -1182,22 +1150,6 @@ class Expand(_Expand):
 
     >> Expand[(1 + a)^12, Modulus -> 4]
      = 1 + 2 a ^ 2 + 3 a ^ 4 + 3 a ^ 8 + 2 a ^ 10 + a ^ 12
-
-    #> Expand[x, Modulus -> -1]  (* copy odd MMA behaviour *)
-     = 0
-    #> Expand[x, Modulus -> x]
-     : Value of option Modulus -> x should be an integer.
-     = Expand[x, Modulus -> x]
-
-    #> a(b(c+d)+e) // Expand
-     = a b c + a b d + a e
-
-    #> (y^2)^(1/2)/(2x+2y)//Expand
-     = Sqrt[y ^ 2] / (2 x + 2 y)
-
-
-    #> 2(3+2x)^2/(5+x^2+3x)^3 // Expand
-     = 24 x / (5 + 3 x + x ^ 2) ^ 3 + 8 x ^ 2 / (5 + 3 x + x ^ 2) ^ 3 + 18 / (5 + 3 x + x ^ 2) ^ 3
     """
 
     summary_text = "expand out products and powers"
@@ -1303,15 +1255,6 @@ class ExpandDenominator(_Expand):
 
     >> ExpandDenominator[(a + b) ^ 2 / ((c + d)^2 (e + f))]
      = (a + b) ^ 2 / (c ^ 2 e + c ^ 2 f + 2 c d e + 2 c d f + d ^ 2 e + d ^ 2 f)
-
-    ## Modulus option
-    #> ExpandDenominator[1 / (x + y)^3, Modulus -> 3]
-     = 1 / (x ^ 3 + y ^ 3)
-    #> ExpandDenominator[1 / (x + y)^6, Modulus -> 4]
-     = 1 / (x ^ 6 + 2 x ^ 5 y + 3 x ^ 4 y ^ 2 + 3 x ^ 2 y ^ 4 + 2 x y ^ 5 + y ^ 6)
-
-    #> ExpandDenominator[2(3+2x)^2/(5+x^2+3x)^3]
-     = 2 (3 + 2 x) ^ 2 / (125 + 225 x + 210 x ^ 2 + 117 x ^ 3 + 42 x ^ 4 + 9 x ^ 5 + x ^ 6)
     """
 
     summary_text = "expand just the denominator of a rational expression"
@@ -1354,11 +1297,6 @@ class Exponent(Builtin):
      = -Infinity
     >> Exponent[1, x]
      = 0
-
-    ## errors:
-    #> Exponent[x^2]
-     : Exponent called with 1 argument; 2 or 3 arguments are expected.
-     = Exponent[x ^ 2]
     """
 
     attributes = A_LISTABLE | A_PROTECTED
@@ -1422,10 +1360,6 @@ class Factor(Builtin):
     You can use Factor to find when a polynomial is zero:
     >> x^2 - x == 0 // Factor
      = x (-1 + x) == 0
-
-    ## Issue659
-    #> Factor[{x+x^2}]
-     = {x (1 + x)}
     """
 
     attributes = A_LISTABLE | A_PROTECTED
@@ -1467,9 +1401,6 @@ class FactorTermsList(Builtin):
      = {2, -1 + x ^ 2}
     >> FactorTermsList[x^2 - 2 x + 1]
      = {1, 1 - 2 x + x ^ 2}
-    #> FactorTermsList[2 x^2 - 2, x]
-     = {2, 1, -1 + x ^ 2}
-
     >> f = 3 (-1 + 2 x) (-1 + y) (1 - a)
      = 3 (-1 + 2 x) (-1 + y) (1 - a)
     >> FactorTermsList[f]
@@ -1775,17 +1706,6 @@ class MinimalPolynomial(Builtin):
      = -2 - 2 x ^ 2 + x ^ 4
     >> MinimalPolynomial[Sqrt[I + Sqrt[6]], x]
      = 49 - 10 x ^ 4 + x ^ 8
-
-    #> MinimalPolynomial[7a, x]
-     : 7 a is not an explicit algebraic number.
-     = MinimalPolynomial[7 a, x]
-    #> MinimalPolynomial[3x^3 + 2x^2 + y^2 + ab, x]
-     : ab + 2 x ^ 2 + 3 x ^ 3 + y ^ 2 is not an explicit algebraic number.
-     = MinimalPolynomial[ab + 2 x ^ 2 + 3 x ^ 3 + y ^ 2, x]
-
-    ## PurePoly
-    #> MinimalPolynomial[Sqrt[2 + Sqrt[3]]]
-     = 1 - 4 #1 ^ 2 + #1 ^ 4
     """
 
     attributes = A_LISTABLE | A_PROTECTED
@@ -1874,37 +1794,6 @@ class PolynomialQ(Builtin):
      = True
     >> PolynomialQ[x^2 + axy^2 - bSin[c], {a, b, c}]
      = False
-
-    #> PolynomialQ[x, x, y]
-     : PolynomialQ called with 3 arguments; 1 or 2 arguments are expected.
-     = PolynomialQ[x, x, y]
-
-    ## Always return True if argument is Null
-    #> PolynomialQ[x^3 - 2 x/y + 3xz,]
-     : Warning: comma encountered with no adjacent expression. The expression will be treated as Null (line 1 of "<test>").
-     = True
-    #> PolynomialQ[, {x, y, z}]
-     : Warning: comma encountered with no adjacent expression. The expression will be treated as Null (line 1 of "<test>").
-     = True
-    #> PolynomialQ[, ]
-     : Warning: comma encountered with no adjacent expression. The expression will be treated as Null (line 1 of "<test>").
-     : Warning: comma encountered with no adjacent expression. The expression will be treated as Null (line 1 of "<test>").
-     = True
-
-    ## TODO: MMA and Sympy handle these cases differently
-    ## #> PolynomialQ[x^(1/2) + 6xyz]
-    ##  : No variable is not supported in PolynomialQ.
-    ##  = True
-    ## #> PolynomialQ[x^(1/2) + 6xyz, {}]
-    ##  : No variable is not supported in PolynomialQ.
-    ##  = True
-
-    ## #> PolynomialQ[x^3 - 2 x/y + 3xz]
-    ##  : No variable is not supported in PolynomialQ.
-    ##  = False
-    ## #> PolynomialQ[x^3 - 2 x/y + 3xz, {}]
-    ##  : No variable is not supported in PolynomialQ.
-    ##  = False
     """
 
     messages = {
@@ -1994,9 +1883,6 @@ class Together(Builtin):
     But it does not touch other functions:
     >> Together[f[a / c + b / c]]
      = f[a / c + b / c]
-
-    #> f[x]/x+f[x]/x^2//Together
-     = f[x] (1 + x) / x ^ 2
     """
 
     attributes = A_LISTABLE | A_PROTECTED
@@ -2030,9 +1916,6 @@ class Variables(Builtin):
      = {a, b, c, x, y}
     >> Variables[x + Sin[y]]
      = {x, Sin[y]}
-    ## failing test case from MMA docs
-    #> Variables[E^x]
-     = {}
     """
     summary_text = "list of variables in a polynomial"
 

mathics/builtin/numbers/calculus.py

@@ -172,24 +172,6 @@ class D(SympyFunction):
     Hesse matrix:
     >> D[Sin[x] * Cos[y], {{x,y}, 2}]
      = {{-Cos[y] Sin[x], -Cos[x] Sin[y]}, {-Cos[x] Sin[y], -Cos[y] Sin[x]}}
-
-    #> D[2/3 Cos[x] - 1/3 x Cos[x] Sin[x] ^ 2,x]//Expand
-     = -2 x Cos[x] ^ 2 Sin[x] / 3 + x Sin[x] ^ 3 / 3 - 2 Sin[x] / 3 - Cos[x] Sin[x] ^ 2 / 3
-
-    #> D[f[#1], {#1,2}]
-     = f''[#1]
-    #> D[(#1&)[t],{t,4}]
-     = 0
-
-    #> Attributes[f] ={HoldAll}; Apart[f''[x + x]]
-     = f''[2 x]
-
-    #> Attributes[f] = {}; Apart[f''[x + x]]
-     = f''[2 x]
-
-    ## Issue #375
-    #> D[{#^2}, #]
-     = {2 #1}
     """
 
     # TODO
@@ -416,16 +398,6 @@ class Derivative(PostfixOperator, SympyFunction):
      = Derivative[2, 1][h]
     >> Derivative[2, 0, 1, 0][h[g]]
      = Derivative[2, 0, 1, 0][h[g]]
-
-    ## Parser Tests
-    #> Hold[f''] // FullForm
-     = Hold[Derivative[2][f]]
-    #> Hold[f ' '] // FullForm
-     = Hold[Derivative[2][f]]
-    #> Hold[f '' ''] // FullForm
-     = Hold[Derivative[4][f]]
-    #> Hold[Derivative[x][4] '] // FullForm
-     = Hold[Derivative[1][Derivative[x][4]]]
     """
 
     attributes = A_N_HOLD_ALL
@@ -866,12 +838,8 @@ class FindRoot(_BaseFinder):
      = FindRoot[Sin[x] - x, {x, 0}]
 
 
-    #> FindRoot[2.5==x,{x,0}]
-     = {x -> 2.5}
-
     >> FindRoot[x^2 - 2, {x, 1,3}, Method->"Secant"]
      = {x -> 1.41421}
-
     """
 
     rules = {
@@ -972,20 +940,6 @@ class Integrate(SympyFunction):
     >> Integrate[f[x], {x, a, b}] // TeXForm
      = \int_a^b f\left[x\right] \, dx
 
-    #> DownValues[Integrate]
-     = {}
-    #> Definition[Integrate]
-     = Attributes[Integrate] = {Protected, ReadProtected}
-     .
-     . Options[Integrate] = {Assumptions -> $Assumptions, GenerateConditions -> Automatic, PrincipalValue -> False}
-    #> Integrate[Hold[x + x], {x, a, b}]
-     = Integrate[Hold[x + x], {x, a, b}]
-    #> Integrate[sin[x], x]
-     = Integrate[sin[x], x]
-
-    #> Integrate[x ^ 3.5 + x, x]
-     = x ^ 2 / 2 + 0.222222 x ^ 4.5
-
     Sometimes there is a loss of precision during integration.
     You can check the precision of your result with the following sequence
     of commands.
@@ -994,20 +948,6 @@ class Integrate(SympyFunction):
      >> % // Precision
      = MachinePrecision
 
-    #> Integrate[1/(x^5+1), x]
-     = RootSum[1 + 5 #1 + 25 #1 ^ 2 + 125 #1 ^ 3 + 625 #1 ^ 4&, Log[x + 5 #1] #1&] + Log[1 + x] / 5
-
-    #> Integrate[ArcTan(x), x]
-     = x ^ 2 ArcTan / 2
-    #> Integrate[E[x], x]
-     = Integrate[E[x], x]
-
-    #> Integrate[Exp[-(x/2)^2],{x,-Infinity,+Infinity}]
-     = 2 Sqrt[Pi]
-
-    #> Integrate[Exp[-1/(x^2)], x]
-     = x E ^ (-1 / x ^ 2) + Sqrt[Pi] Erf[1 / x]
-
     >> Integrate[ArcSin[x / 3], x]
      = x ArcSin[x / 3] + Sqrt[9 - x ^ 2]
 

mathics/builtin/numbers/diffeqns.py

@@ -42,48 +42,6 @@ class DSolve(Builtin):
 
     >> DSolve[D[y[x, t], t] + 2 D[y[x, t], x] == 0, y[x, t], {x, t}]
      = {{y[x, t] -> C[1][x - 2 t]}}
-
-    ## FIXME: sympy solves this as `Function[{x}, C[1] + Integrate[ArcSin[f[2 x]], x]]`
-    ## #> Attributes[f] = {HoldAll};
-    ## #> DSolve[f[x + x] == Sin[f'[x]], f, x]
-    ##  : To avoid possible ambiguity, the arguments of the dependent variable in f[x + x] == Sin[f'[x]] should literally match the independent variables.
-    ##  = DSolve[f[x + x] == Sin[f'[x]], f, x]
-
-    ## #> Attributes[f] = {};
-    ## #> DSolve[f[x + x] == Sin[f'[x]], f, x]
-    ##  : To avoid possible ambiguity, the arguments of the dependent variable in f[2 x] == Sin[f'[x]] should literally match the independent variables.
-    ##  = DSolve[f[2 x] == Sin[f'[x]], f, x]
-
-    #> DSolve[f'[x] == f[x], f, x] // FullForm
-     = {{Rule[f, Function[{x}, Times[C[1], Power[E, x]]]]}}
-
-    #> DSolve[f'[x] == f[x], f, x] /. {C[1] -> 1}
-     = {{f -> (Function[{x}, 1 E ^ x])}}
-
-    #> DSolve[f'[x] == f[x], f, x] /. {C -> D}
-     = {{f -> (Function[{x}, D[1] E ^ x])}}
-
-    #> DSolve[f'[x] == f[x], f, x] /. {C[1] -> C[0]}
-     = {{f -> (Function[{x}, C[0] E ^ x])}}
-
-    #> DSolve[f[x] == 0, f, {}]
-     : {} cannot be used as a variable.
-     = DSolve[f[x] == 0, f, {}]
-
-    ## Order of arguments shoudn't matter
-    #> DSolve[D[f[x, y], x] == D[f[x, y], y], f, {x, y}]
-     = {{f -> (Function[{x, y}, C[1][-x - y]])}}
-    #> DSolve[D[f[x, y], x] == D[f[x, y], y], f[x, y], {x, y}]
-     = {{f[x, y] -> C[1][-x - y]}}
-    #> DSolve[D[f[x, y], x] == D[f[x, y], y], f[x, y], {y, x}]
-     = {{f[x, y] -> C[1][-x - y]}}
-    """
-
-    # XXX sympy #11669 test
-    """
-    #> DSolve[\\[Gamma]'[x] == 0, \\[Gamma], x]
-     : Hit sympy bug #11669.
-     = ...
     """
 
     # TODO: GeneratedParameters option

mathics/builtin/numbers/exp.py

@@ -176,9 +176,6 @@ class Exp(MPMathFunction):
 
     >> Plot[Exp[x], {x, 0, 3}]
      = -Graphics-
-    #> Exp[1.*^20]
-     : Overflow occurred in computation.
-     = Overflow[]
     """
 
     rules = {
@@ -206,21 +203,6 @@ class Log(MPMathFunction):
      = Indeterminate
     >> Plot[Log[x], {x, 0, 5}]
      = -Graphics-
-
-    #> Log[1000] / Log[10] // Simplify
-     = 3
-
-    #> Log[1.4]
-     = 0.336472
-
-    #> Log[Exp[1.4]]
-     = 1.4
-
-    #> Log[-1.4]
-     = 0.336472 + 3.14159 I
-
-    #> N[Log[10], 30]
-     = 2.30258509299404568401799145468
     """
 
     summary_text = "logarithm function"
@@ -316,9 +298,6 @@ class LogisticSigmoid(Builtin):
 
     >> LogisticSigmoid[{-0.2, 0.1, 0.3}]
      = {0.450166, 0.524979, 0.574443}
-
-    #> LogisticSigmoid[I Pi]
-     = LogisticSigmoid[I Pi]
     """
 
     summary_text = "logistic function"