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1.82 kBtext/coffeescriptView Raw
1test_polar = ->
2 run_test [
3 "polar(1+i)",
4 "2^(1/2)*exp(1/4*i*pi)",
5
6 "polar(-1+i)",
7 "2^(1/2)*exp(3/4*i*pi)",
8
9 "polar(-1-i)",
10 "2^(1/2)*exp(-3/4*i*pi)",
11
12 "polar(1-i)",
13 "2^(1/2)*exp(-1/4*i*pi)",
14
15 "rect(polar(3+4*i))",
16 "3+4*i",
17
18 "rect(polar(-3+4*i))",
19 "-3+4*i",
20
21 "rect(polar(3-4*i))",
22 "3-4*i",
23
24 "rect(polar(-3-4*i))",
25 "-3-4*i",
26
27 "rect(polar((-1)^(1/2)))",
28 "i",
29
30 "rect(polar((-1)^(-5/6)))",
31 "-1/2*i-1/2*3^(1/2)",
32
33 "rect(polar((-1)^(-5/a)))",
34 "cos(5*pi/a)-i*sin(5*pi/a)",
35
36 "rect(polar((-1)^(a)))",
37 "cos(a*pi)+i*sin(a*pi)",
38
39 "-i*(-2*rect(polar((-1)^(1/6)))/rect(polar((3^(1/2))))+2*rect(polar((-1)^(5/6)))/rect(polar((3^(1/2)))))^(1/4)*(2*rect(polar((-1)^(1/6)))/rect(polar((3^(1/2))))-2*rect(polar((-1)^(5/6)))/rect(polar((3^(1/2)))))^(1/4)/(2^(1/2))",
40 #"-(-1)^(3/4)",
41 "1/2^(1/2)-i/(2^(1/2))",
42
43 # this is also "-(-1)^(3/4)" but we get to that after the simplification after
44 # this test
45 "-i*(-2*polar((-1)^(1/6))/polar((3^(1/2)))+2*polar((-1)^(5/6))/polar((3^(1/2))))^(1/4)*(2*polar((-1)^(1/6))/polar((3^(1/2)))-2*polar((-1)^(5/6))/polar((3^(1/2))))^(1/4)/(2^(1/2))",
46 "-i*(-2*exp(1/6*i*pi)/(3^(1/2))+2*exp(5/6*i*pi)/(3^(1/2)))^(1/4)*(2*exp(1/6*i*pi)/(3^(1/2))-2*exp(5/6*i*pi)/(3^(1/2)))^(1/4)/(2^(1/2))",
47
48 "simplify",
49 "(1-i)/(2^(1/2))",
50
51 "-i*(-2*rect(exp(1/6*i*pi))/(3^(1/2))+2*rect(exp(5/6*i*pi))/(3^(1/2)))^(1/4)*(2*rect(exp(1/6*i*pi))/(3^(1/2))-2*rect(exp(5/6*i*pi))/(3^(1/2)))^(1/4)/(2^(1/2))",
52 #"-(-1)^(3/4)",
53 "1/2^(1/2)-i/(2^(1/2))",
54
55 "polar(-(-1)^(3/4))",
56 "exp(-1/4*i*pi)",
57
58 "polar(-i*(-2*(-1)^(1/6)/(3^(1/2))+2*(-1)^(5/6)/(3^(1/2)))^(1/4)*(2*(-1)^(1/6)/(3^(1/2))-2*(-1)^(5/6)/(3^(1/2)))^(1/4)/(2^(1/2)))",
59 "exp(-1/4*i*pi)",
60
61 # nothing to do for polar since we end
62 # up with a real
63 "polar((-1)^(1/6) - (-1)^(5/6))",
64 "3^(1/2)",
65
66 ]