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1test_rect = ->
2 run_test [
3
4 # check when not assuming real variables ----------
5 "assumeRealVariables = 0",
6 "",
7
8 "rect(a)",
9 "rect(a)",
10
11 # same as rect(a) + i*rect(b)
12 # where rect(b) is abs(b)*(cos(arg(b)) + i*sin(arg(b)))
13 "rect(a+i*b)",
14 "rect(a)-abs(b)*sin(arg(b))+i*abs(b)*cos(arg(b))",
15
16 "assumeRealVariables = 1",
17 "",
18 # --------------------------------------------------
19
20 "rect(a)",
21 "a",
22
23 "rect(a+i*b)",
24 "a+i*b",
25
26 "rect(exp(a+i*b))",
27 "i*exp(a)*sin(b)+exp(a)*cos(b)",
28
29 "rect(1+exp(i*pi/3))",
30 "3/2+1/2*i*3^(1/2)",
31
32 "z=(a+b*i)/(c+d*i)",
33 "",
34
35 "rect(z)-real(z)-i*imag(z)",
36 "0",
37
38 "z=quote(z)",
39 "",
40
41 "rect((-1)^(2/3))",
42 "-1/2+1/2*i*3^(1/2)",
43
44 "rect(exp(-3/4*i*pi))",
45 "-1/2*2^(1/2)-1/2*i*2^(1/2)",
46
47 "rect(exp(-1/4*i*pi))",
48 "1/2*2^(1/2)-1/2*i*2^(1/2)",
49
50 "rect(exp(-2/4*i*pi))",
51 "-i",
52
53 "rect(exp(-3/4*i*pi))",
54 "-1/2*2^(1/2)-1/2*i*2^(1/2)",
55
56 "rect(exp(-4/4*i*pi))",
57 "-1",
58
59 "rect(((-1)^(1/2)/(3^(1/2)))^(1/2))",
60 "i*2^(1/2)/(2*3^(1/4))+2^(1/2)/(2*3^(1/4))",
61
62 "rect((-1)^(1/6) - (-1)^(5/6))",
63 "3^(1/2)",
64
65 ]