mathics-core/mathics/Autoload/rules/Element.m at 2de1298828ee208393c4ea4e53e903c433586d01 · Mathics3/mathics-core · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
(*Rules for Elements*)


System`Integers::usage="Represents the set of the Integers numbers";
System`Primes::usage="Represents the set of the prime numbers";
System`Rationals::usage="Represents the set of the Rational numbers";
System`Reals::usage="Represents the field of the Real numbers";
System`Complexes::usage="Represents the field of the Complex numbers";
System`Algebraics::usage="Represents the set of the algebraic numbers";
System`Booleans::usage="Represents the set of boolean values";

Begin["internals`elements`"]
Unprotect[Element]


Element[_Integer, Reals]:=True;

(*Booleans*)
Element[True|False, Booleans]:=True;
Element[E|I|EulerGamma|Khinchin|MachinePrecision|Pi, Booleans]:=False;
Element[_Integer|_Rational|_Real|_Complex, Booleans]:=False;


(*Integers*)
Element[True|False|E|I|EulerGamma|Khinchin|MachinePrecision|Pi, Integers]:=False;
Element[_Integer, Integers]:=True;
Element[_Rational|_Complex, Integers]:=False;
Element[x_Real/;(FractionalPart[x]!=0.), Integers]:=False;


(*Rationals*)
Element[True|False|E|I|EulerGamma|Khinchin|MachinePrecision|Pi, Rationals]:=False;
Element[_Integer|_Rational, Rationals]:=True;
Element[_Complex, Rationals]:=False;


(*Reals*)
Element[True|False|I, Reals]:=False;
Element[E|EulerGamma|Khinchin|MachinePrecision|Pi, Reals]:=True;
Element[_Rational, Reals]:=True;
Element[_Real, Reals]:=True;
Element[_Complex, Reals]:=False;


(*Complex*)
Element[True|False, Complexes]:=False;
Element[E|EulerGamma|I|Khinchin|MachinePrecision|Pi, Complexes]:=True;
Element[_Integer|_Rational|_Real|_Complex, Complexes]:=True;


(*Elementary inexact functions*)
Element[f:(Sin[_]|Cos[_]|Tan[_]|Cot[_]|Sec[_]|Cosec[_]|Sinh[_]|Cosh[_]|Tanh[_]|Coth[_]|Sech[_]|Cosech[_]|
	 Log[_]|Exp[_]| ArcSin[_]|ArcCos[_]|ArcTan[_]|ArcCot[_]|ArcSec[_]|ArcCosec[_]|
	 ArcSinh[_]|ArcCosh[_]|ArcTanh[_]|ArcCoth[_]|ArcSech[_]|ArcCosech[_]), domain:Reals|Complexes]:=Element[f[[1]], domain];


(*Primes*)
Element[True|False|E|I|EulerGamma|Khinchin|MachinePrecision|Pi, Primes]:=False;
Element[z_Integer, Primes]:=PrimeQ[z];
Element[_Rational|_Complex, Primes]:=False;
Element[x_Real/;(FractionalPart[x]!=0.), Primes]:=False;
(*TODO: Check this condition. Probably this need to be implemented in Python...*)
Element[x_, Primes]:=If[Element[x, Algebraics]===True, False, HoldForm[Element[x, Primes]]];


(*General Algebraic*)

Element[z:(_Plus|_Times), domain:(Integers|Rationals|Reals|Complexes|Algebraics)]:=Element[Alternatives@@z, domain];
Element[z:(_Plus|_Times), Booleans]:=False;
Element[_Times, Primes]:=False;


Element[z_Power, Algebraics]:=Element[Alternatives@@z, Algebraics];
Element[z:(_Integer|_Rational|_Complex), Algebraics]:=True;
Element[I, Algebraics]:=True;
Element[True|False|E|EulerGamma|Khinchin|MachinePrecision|Pi, Algebraics]:=False;
Element[z_DirectedInfinity, domain:(Booleans|Integers|Rationals|Reals|Complexes)]:=False;
Element[z_Power, Integers]:= (Element[Alternatives@@z, Integers] && z[[2]]>=0);
Element[z_Power/;Element[Alternatives@@z, Integers], Integers]:= (z[[2]]>=0);

Element[z_Power, Complexes]:= Element[z, Algebraics];
Element[Power[b_,p_], Rationals]:=Element[b, Rationals] && Element[p, Integers] ;


Element[Sin[_]|Cos[_]|Tan[_]|Cot[_]|Sec[_]|Cosec[_]|
         Sinh[_]|Cosh[_]|Tanh[_]|Coth[_]|Sech[_]|Cosech[_]|
	 Log[_]|Exp[_]|
	 ArcSin[_]|ArcCos[_]|ArcTan[_]|ArcCot[_]|ArcSec[_]|ArcCosec[_]|
	 ArcSinh[_]|ArcCosh[_]|ArcTanh[_]|ArcCoth[_]|ArcSech[_]|ArcCosech[_]
	 , Integers|Primes|Rationals|Algebraics|Booleans]:=False;


Element[Power[b_Real|b_Rational|b_Integer, _Real|_Rational], Reals]:= (b>=0);
Element[Power[_Real|_Rational|_Integer, p_Integer], Reals]= True;
Element[Power[b_/;(Element[b, Reals]), p_/;Element[p, Reals]], Reals]:=(Element[p, Integers] || b>=0);

Protect[Element]
End[]