apl>" <-APL2-------------------- sam287.txt ---------------------------->
apl>F`1'sine of ' t ' degrees = ' (1OO(t#30)%180)
sine of 30 degrees = .5
apl>F`1'cosine of ' t ' degrees = ' (2OO(t#45)%180)
cosine of 45 degrees = .707107
apl>F`1'arcsine of ' t ' = ' ((-1Ot#.5)X180%O1) ' degrees'
arcsine of .5 = 30 degrees
apl>F`1'arctan of ' t ' = ' ((-3Ot#1)X180%O1) ' degrees'
arctan of 1 = 45 degrees
apl>" <----------------------------------------------------------------->
apl>Gz#k circle r;a;b;c;d;e;f
[1] b#arctanh arccosh arcsinh arctan arccos arcsin sin cos tan sinh cosh tanh
[2] c#1 2 3 5 6 7 9 10 11 13 14 15
[3] z#I0 " Initialize result.
[4] loop:$doneXI0=R,k
[5] a#1Yk
[6] k#1Uk
[7] $(c=a+8)/b
[8] z#'bad selection = ',Fk
[9] $0
[10] arctanh: z#z,`ZaOr " -7
[11] $loop
[12] arccosh: z#z,`ZaOr " -6
[13] $loop
[14] arcsinh: z#z,`ZaOr " -5
[15] $loop
[16] arctan: d#aOr " -3
[17] (e/,d)#(O1)+(e#1>9O,d)/,d " Add pitimes(1) where real(d) < 1.
[18] z#z,`Zd
[19] $loop
[20] arccos: d#aOr " -2
[21] (e/,d)#(O2)+(e#0K11O,r)/,d " e is 1 where imag(r) >= 0.
[22] " if (*(r+1)>0)
[23] " *d+=pitimes(2);
[24] (f/,d)#_(f#~e)/,d " else { *d=-*d; *(d+1)=-*(d+1); }
[25] z#z,`Zd
[26] $loop
[27] arcsin: d#aOr " -1
[28] (e/,d)#(O1)_(e#0K11O,r)/,d " e is 1 where imag(r) -ge 0.
[29] " if (*(r+1)>0) {
[30] " *d=pitimes(1)-*d;
[31] " *(d+1)=-*(d+1);
[32] " }
[33] (f/,d)#(O2)+(f#(~e)&0>9O,r)/,d " f is 1 where imag(r)<0 && real(r)<0.
[34] " if (*r<0 && *(r+1)<0)
[35] " *d+=pitimes(2);
[36] z#z,`Zd
[37] $loop
[38] sin: z#z,`ZaOr " 1
[39] $loop
[40] cos: z#z,`ZaOr " 2
[41] $loop
[42] tan: z#z,`ZaOr " 3
[43] $loop
[44] sinh: z#z,`ZaOr " 5
[45] $loop
[46] cosh: z#z,`ZaOr " 6
[47] $loop
[48] tanh: z#z,`ZaOr " 7
[49] $loop
[50] done:$I0
[51] G
apl>Lpp#4
apl>c#Rn#'sin' 'cos' 'tan' 'sinh' 'cosh' 'tanh'
apl>b# 1 2 3 5 6 7
apl>(n,(c,(Ru))Ru),[2]((c,e#Rt)Ru#F`1t),F`1a#bJ.Ow#tJ.+0j1Xt#I5
sin 1 2 3 4 5
1 1.30j.63 3.17j1.96 8.47j5.41 23.0j14.7 62.4j40.1
2 1.4j-0.489 3.42j-1.51 9.15j-4.17 24.8j-11.4 67.5j-30.9
3 .2178j-1.16 .53j-3.59 1.42j-9.9 3.85j-27 10.5j-73.5
4 -1.17j-0.77 -2.85j-2.37 -7.62j-6.55 -20.7j-17.8 -56.2j-48.5
5 -1.48j.3334 -3.6j1.03 -9.7j2.84 -26.2j7.74 -71.2j21
cos 1 2 3 4 5
1 .83j-0.99 2.03j-3.05 5.44j-8.43 14.8j-23.0 40.1j-62.4
2 -0.64j-1.07 -1.57j-3.30 -4.19j-9.11 -11.4j-24.8 -30.9j-67.5
3 -1.53j-0.1658 -3.72j-0.51 -10.0j-1.41 -27j-3.85 -73.5j-10.5
4 -1j.89 -2.46j2.74 -6.58j7.58 -17.8j20.7 -48.5j56.2
5 .4377j1.13 1.07j3.48 2.86j9.6 7.75j26.2 21j71.2
tan 1 2 3 4 5
1 .2718j1.08 .0338j1.01 .0045j1 .0006j1 0j1
2 -0.2435j1.17 -0.0284j1.02 -0.0038j1 -0.0005j1 0j1
3 -0.0592j.77 -0.0099j.97 -0.0014j1.00 -0.0002j1 0j1
4 .2736j1 .0364j1 .0049j1 .0007j1 0j1
5 -0.1861j1.24 -0.0206j1.03 -0.0027j1 -0.0004j1 0j1
sinh 1 2 3 4 5
1 .63j1.30 -0.489j1.4 -1.16j.2178 -0.77j-1.17 .3334j-1.48
2 1.96j3.17 -1.51j3.42 -3.59j.53 -2.37j-2.85 1.03j-3.6
3 5.41j8.47 -4.17j9.15 -9.9j1.42 -6.55j-7.62 2.84j-9.7
4 14.7j23.0 -11.4j24.8 -27j3.85 -17.8j-20.7 7.74j-26.2
5 40.1j62.4 -30.9j67.5 -73.5j10.5 -48.5j-56.2 21j-71.2
cosh 1 2 3 4 5
1 .83j.99 -0.64j1.07 -1.53j.1658 -1j-0.89 .4377j-1.13
2 2.03j3.05 -1.57j3.30 -3.72j.51 -2.46j-2.74 1.07j-3.48
3 5.44j8.43 -4.19j9.11 -10.0j1.41 -6.58j-7.58 2.86j-9.6
4 14.8j23.0 -11.4j24.8 -27j3.85 -17.8j-20.7 7.75j-26.2
5 40.1j62.4 -30.9j67.5 -73.5j10.5 -48.5j-56.2 21j-71.2
tanh 1 2 3 4 5
1 1.08j.2718 1.17j-0.2435 .77j-0.0592 1j.2736 1.24j-0.1861
2 1.01j.0338 1.02j-0.0284 .97j-0.0099 1j.0364 1.03j-0.0206
3 1j.0045 1j-0.0038 1.00j-0.0014 1j.0049 1j-0.0027
4 1j.0006 1j-0.0005 1j-0.0002 1j.0007 1j-0.0004
5 1 1 1 1 1
apl>((m#'a',`1n),(c,(Ru))Ru),[2]((c,Rt)Ru),F`1f#((Ra)R`X(`Ze e)J.R_b)Oa
asin 1 2 3 4 5
1 1j1 1j2 1j3 1j4 1j5
2 1.14j-1 1.14j-2 1.14j-3 1.14j-4 1.14j-5
3 .1416j-1 .1416j-2 .1416j-3 .1416j-4 .1416j-5
4 -0.86j-1 -0.86j-2 -0.86j-3 -0.86j-4 -0.86j-5
5 -1.28j1 -1.28j2 -1.28j3 -1.28j4 -1.28j5
acos 1 2 3 4 5
1 -1j-1 -1j-2 -1j-3 -1j-4 -1j-5
2 -2j-1 -2j-2 -2j-3 -2j-4 -2j-5
3 -3j-1 -3j-2 -3j-3 -3j-4 -3j-5
4 -2.28j1 -2.28j2 -2.28j3 -2.28j4 -2.28j5
5 -1.28j1 -1.28j2 -1.28j3 -1.28j4 -1.28j5
atan 1 2 3 4 5
1 1j1 1j2 1j3 1j4 1j5
2 -1.14j1 -1.14j2 -1.14j3 -1.14j4 -1.14j5
3 -0.1416j1 -0.1416j2 -0.1416j3 -0.1416j4 -0.1416j5
4 .86j1 .86j2 .86j3 .86j4 .86j5
5 -1.28j1 -1.28j2 -1.28j3 -1.28j4 -1.28j5
asinh 1 2 3 4 5
1 1j1 -1j1.14 -1j.1416 -1j-0.86 1j-1.28
2 2j1 -2j1.14 -2j.1416 -2j-0.86 2j-1.28
3 3j1 -3j1.14 -3j.1416 -3j-0.86 3j-1.28
4 4j1 -4j1.14 -4j.1416 -4j-0.86 4j-1.28
5 5j1 -5j1.14 -5j.1416 -5j-0.86 5j-1.28
acosh 1 2 3 4 5
1 1j1 -1j-2 -1j-3 -1j2.28 1j-1.28
2 2j1 -2j-2 -2j-3 -2j2.28 2j-1.28
3 3j1 -3j-2 -3j-3 -3j2.28 3j-1.28
4 4j1 -4j-2 -4j-3 -4j2.28 4j-1.28
5 5j1 -5j-2 -5j-3 -5j2.28 5j-1.28
atanh 1 2 3 4 5
1 1j1 1j-1.14 1j-0.1416 1j.86 1j-1.28
2 2j1 2j-1.14 2j-0.1416 2j.86 2j-1.28
3 3j1 3j-1.14 3j-0.1416 3j.86 3j-1.28
4 4j1 4j-1.14 4j-0.1416 4j.86 4j-1.28
5 5j1 5j-1.14 5j-0.1416 5j.86 5j-1.28
apl>a[3;;]
0.2718j1.08 0.0338j1.01 0.0045j1.00 0.0006j1 0j1
-0.2435j1.17 -0.0284j1.02 -0.0038j1.00 -0.0005j1 0j1
-0.0592j.77 -0.0099j.97 -0.0014j1.00 -0.0002j1 0j1
0.2736j1.00 0.0364j1.00 0.0049j1.00 0.0007j1 0j1
-0.1861j1.24 -0.0206j1.03 -0.0027j1.00 -0.0004j1 0j1
apl>f[3;;]
1.000j1 1.000j2 1.000j3 1.000j4 1.000j5
-1.142j1 -1.142j2 -1.142j3 -1.142j4 -1.142j5
-0.142j1 -0.142j2 -0.142j3 -0.142j4 -0.142j5
0.858j1 0.858j2 0.858j3 0.858j4 0.858j5
-1.283j1 -1.283j2 -1.283j3 -1.283j4 -1.283j5
apl>Lfx 'z#atan r' 'z#-3Or'
atan
apl>atan a[3;;]
1.000j1 1.000j2 1.000j3 1.000j4 1.000j5
-1.142j1 -1.142j2 -1.142j3 -1.142j4 -1.142j5
-0.142j1 -0.142j2 -0.142j3 -0.142j4 -0.142j5
0.858j1 0.858j2 0.858j3 0.858j4 0.858j5
-1.283j1 -1.283j2 -1.283j3 -1.283j4 -1.283j5
apl>-3 circle a[3;;]
1.00j1 1.00j2 1.00j3 1.00j4 1.00j5
2.00j1 2.00j2 2.00j3 2.00j4 2.00j5
3.00j1 3.00j2 3.00j3 3.00j4 3.00j5
4.00j1 4.00j2 4.00j3 4.00j4 4.00j5
1.86j1 1.86j2 1.86j3 1.86j4 1.86j5
apl>Lex 'demo'
1
apl>Gz#m demo n;s;t;u;v;w;x;y;a;b;c
[1] v#s,u#(a#n[1])Os#t 1R(m_+/(St%2)Xy)+x#(It#n[2])Xy#1%n[3]
[2] z#v,w,(w+O1),(w#(_a)Ou)+O2
[3] c#(F_a),'O',b#(Fa),'Oin'
[4] z#'in' b c ('(',c,')+O1') ('(',c,')+O2'),[1]z
[5] G
apl>(0j1_8XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
-6.48j1 -0.3066j1.15 -0.2j1 2.94j1 6.08j1
-6.38j1 -0.154j1.17 -0.1j1 3.04j1 6.18j1
-6.28j1 0j1.18 0j1 3.14j1 6.28j1
-6.18j1 .154j1.17 .1j1 3.24j1 6.38j1
-6.08j1 .3066j1.15 .2j1 3.34j1 6.48j1
-5.98j1 .456j1.12 .3j1 3.44j1 6.58j1
apl>(0j1_7XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
-5.70j1 .85j.98 .59j1 3.73j1 6.87j1
-5.60j1 .98j.91 .69j1 3.83j1 6.97j1
-5.50j1 1.09j.83 .79j1 3.93j1 7.07j1
-5.40j1 1.19j.74 .89j1 4.03j1 7.17j1
-5.30j1 1.29j.65 .99j1 4.13j1 7.27j1
-5.20j1 1.36j.55 1.09j1 4.23j1 7.37j1
apl>(0j1_6XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
-4.91j1 1.51j.2335 1.37j1 4.51j1 7.65j1
-4.81j1 1.54j.1173 1.47j1 4.61j1 7.75j1
-4.71j1 1.54 1.57j-1 4.71j-1 7.85j-1
-4.61j1 1.54j-0.1173 1.47j-1 4.61j-1 7.75j-1
-4.51j1 1.51j-0.2335 1.37j-1 4.51j-1 7.65j-1
-4.41j1 1.47j-0.3473 1.27j-1 4.41j-1 7.55j-1
apl>(0j1_5XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
-4.13j1 1.29j-0.65 .99j-1 4.13j-1 7.27j-1
-4.03j1 1.19j-0.74 .89j-1 4.03j-1 7.17j-1
-3.93j1 1.09j-0.83 .79j-1 3.93j-1 7.07j-1
-3.83j1 .98j-0.91 .69j-1 3.83j-1 6.97j-1
-3.73j1 .85j-0.98 .59j-1 3.73j-1 6.87j-1
-3.63j1 .72j-1.04 .4854j-1 3.63j-1 6.77j-1
apl>(0j1_4XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
-3.34j1 .3066j-1.15 .2j-1 3.34j-1 6.48j-1
-3.24j1 .154j-1.17 .1j-1 3.24j-1 6.38j-1
-3.14j1 0j-1.18 0j-1 3.14j-1 6.28j-1
-3.04j1 -0.154j-1.17 -0.1j-1 3.04j-1 6.18j-1
-2.94j1 -0.3066j-1.15 -0.2j-1 2.94j-1 6.08j-1
-2.84j1 -0.456j-1.12 -0.3j-1 2.84j-1 5.98j-1
apl>(0j1_3XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
-2.56j1 -0.85j-0.98 -0.59j-1 2.56j-1 5.70j-1
-2.46j1 -0.98j-0.91 -0.69j-1 2.46j-1 5.60j-1
-2.36j1 -1.09j-0.83 -0.79j-1 2.36j-1 5.50j-1
-2.26j1 -1.19j-0.74 -0.89j-1 2.26j-1 5.40j-1
-2.16j1 -1.29j-0.65 -0.99j-1 2.16j-1 5.30j-1
-2.06j1 -1.36j-0.55 -1.09j-1 2.06j-1 5.20j-1
apl>(0j1_2XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
-1.77j1 -1.51j-0.2335 -1.37j-1 1.77j-1 4.91j-1
-1.67j1 -1.54j-0.1173 -1.47j-1 1.67j-1 4.81j-1
-1.57j1 -1.54 -1.57j1 1.57j1 4.71j1
-1.47j1 -1.54j.1173 -1.47j1 1.67j1 4.81j1
-1.37j1 -1.51j.2335 -1.37j1 1.77j1 4.91j1
-1.27j1 -1.47j.3473 -1.27j1 1.87j1 5.01j1
apl>(0j1_1XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
-0.99j1 -1.29j.65 -0.99j1 2.16j1 5.30j1
-0.89j1 -1.19j.74 -0.89j1 2.26j1 5.40j1
-0.79j1 -1.09j.83 -0.79j1 2.36j1 5.50j1
-0.69j1 -0.98j.91 -0.69j1 2.46j1 5.60j1
-0.59j1 -0.85j.98 -0.59j1 2.56j1 5.70j1
-0.4854j1 -0.72j1.04 -0.4854j1 2.66j1 5.80j1
apl>(0j1+0XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
-0.2j1 -0.3066j1.15 -0.2j1 2.94j1 6.08j1
-0.1j1 -0.154j1.17 -0.1j1 3.04j1 6.18j1
0j1 0j1.18 0j1 3.14j1 6.28j1
.1j1 .154j1.17 .1j1 3.24j1 6.38j1
.2j1 .3066j1.15 .2j1 3.34j1 6.48j1
.3j1 .456j1.12 .3j1 3.44j1 6.58j1
apl>(0j1+1XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
.59j1 .85j.98 .59j1 3.73j1 6.87j1
.69j1 .98j.91 .69j1 3.83j1 6.97j1
.79j1 1.09j.83 .79j1 3.93j1 7.07j1
.89j1 1.19j.74 .89j1 4.03j1 7.17j1
.99j1 1.29j.65 .99j1 4.13j1 7.27j1
1.09j1 1.36j.55 1.09j1 4.23j1 7.37j1
apl>(0j1+2XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
1.37j1 1.51j.2335 1.37j1 4.51j1 7.65j1
1.47j1 1.54j.1173 1.47j1 4.61j1 7.75j1
1.57j1 1.54 1.57j1 4.71j1 7.85j1
1.67j1 1.54j-0.1173 1.47j-1 4.61j-1 7.75j-1
1.77j1 1.51j-0.2335 1.37j-1 4.51j-1 7.65j-1
1.87j1 1.47j-0.3473 1.27j-1 4.41j-1 7.55j-1
apl>(0j1+3XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
2.16j1 1.29j-0.65 .99j-1 4.13j-1 7.27j-1
2.26j1 1.19j-0.74 .89j-1 4.03j-1 7.17j-1
2.36j1 1.09j-0.83 .79j-1 3.93j-1 7.07j-1
2.46j1 .98j-0.91 .69j-1 3.83j-1 6.97j-1
2.56j1 .85j-0.98 .59j-1 3.73j-1 6.87j-1
2.66j1 .72j-1.04 .4854j-1 3.63j-1 6.77j-1
apl>(0j1+4XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
2.94j1 .3066j-1.15 .2j-1 3.34j-1 6.48j-1
3.04j1 .154j-1.17 .1j-1 3.24j-1 6.38j-1
3.14j1 0j-1.18 0j-1 3.14j-1 6.28j-1
3.24j1 -0.154j-1.17 -0.1j-1 3.04j-1 6.18j-1
3.34j1 -0.3066j-1.15 -0.2j-1 2.94j-1 6.08j-1
3.44j1 -0.456j-1.12 -0.3j-1 2.84j-1 5.98j-1
apl>(0j1+5XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
3.73j1 -0.85j-0.98 -0.59j-1 2.56j-1 5.70j-1
3.83j1 -0.98j-0.91 -0.69j-1 2.46j-1 5.60j-1
3.93j1 -1.09j-0.83 -0.79j-1 2.36j-1 5.50j-1
4.03j1 -1.19j-0.74 -0.89j-1 2.26j-1 5.40j-1
4.13j1 -1.29j-0.65 -0.99j-1 2.16j-1 5.30j-1
4.23j1 -1.36j-0.55 -1.09j-1 2.06j-1 5.20j-1
apl>(0j1+6XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
4.51j1 -1.51j-0.2335 -1.37j-1 1.77j-1 4.91j-1
4.61j1 -1.54j-0.1173 -1.47j-1 1.67j-1 4.81j-1
4.71j1 -1.54 -1.57j-1 1.57j-1 4.71j-1
4.81j1 -1.54j.1173 -1.47j1 1.67j1 4.81j1
4.91j1 -1.51j.2335 -1.37j1 1.77j1 4.91j1
5.01j1 -1.47j.3473 -1.27j1 1.87j1 5.01j1
apl>(0j1+7XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
5.30j1 -1.29j.65 -0.99j1 2.16j1 5.30j1
5.40j1 -1.19j.74 -0.89j1 2.26j1 5.40j1
5.50j1 -1.09j.83 -0.79j1 2.36j1 5.50j1
5.60j1 -0.98j.91 -0.69j1 2.46j1 5.60j1
5.70j1 -0.85j.98 -0.59j1 2.56j1 5.70j1
5.80j1 -0.72j1.04 -0.4854j1 2.66j1 5.80j1
apl>(0j1+8XO1%4) demo 1,6,10
in 1Oin -1O1Oin (-1O1Oin)+O1 (-1O1Oin)+O2
6.08j1 -0.3066j1.15 -0.2j1 2.94j1 6.08j1
6.18j1 -0.154j1.17 -0.1j1 3.04j1 6.18j1
6.28j1 0j1.18 0j1 3.14j1 6.28j1
6.38j1 .154j1.17 .1j1 3.24j1 6.38j1
6.48j1 .3066j1.15 .2j1 3.34j1 6.48j1
6.58j1 .456j1.12 .3j1 3.44j1 6.58j1
apl>(0j1_8XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
-6.48j1 -0.0832j.77 -0.2j1 2.94j1 6.08j1
-6.38j1 -0.0419j.76 -0.1j1 3.04j1 6.18j1
-6.28j1 0j.76 0j1 3.14j1 6.28j1
-6.18j1 .0419j.76 .1j1 3.24j1 6.38j1
-6.08j1 .0832j.77 .2j1 3.34j1 6.48j1
-5.98j1 .123j.79 .3j1 3.44j1 6.58j1
apl>(0j1_7XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
-5.70j1 .2219j.87 .59j1 3.73j1 6.87j1
-5.60j1 .2474j.92 .69j1 3.83j1 6.97j1
-5.50j1 .2658j.96 .79j1 3.93j1 7.07j1
-5.40j1 .275j1.02 .89j1 4.03j1 7.17j1
-5.30j1 .273j1.08 .99j1 4.13j1 7.27j1
-5.20j1 .2581j1.13 1.09j1 4.23j1 7.37j1
apl>(0j1_6XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
-4.91j1 .137j1.28 1.37j1 4.51j1 7.65j1
-4.81j1 .0714j1.3 1.47j1 4.61j1 7.75j1
-4.71j1 0j1.31 -1.57j1 1.57j1 4.71j1
-4.61j1 -0.0714j1.3 -1.47j1 1.67j1 4.81j1
-4.51j1 -0.137j1.28 -1.37j1 1.77j1 4.91j1
-4.41j1 -0.1923j1.23 -1.27j1 1.87j1 5.01j1
apl>(0j1_5XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
-4.13j1 -0.273j1.08 -0.99j1 2.16j1 5.30j1
-4.03j1 -0.275j1.02 -0.89j1 2.26j1 5.40j1
-3.93j1 -0.2658j.96 -0.79j1 2.36j1 5.50j1
-3.83j1 -0.2474j.92 -0.69j1 2.46j1 5.60j1
-3.73j1 -0.2219j.87 -0.59j1 2.56j1 5.70j1
-3.63j1 -0.1907j.84 -0.4854j1 2.66j1 5.80j1
apl>(0j1_4XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
-3.34j1 -0.0832j.77 -0.2j1 2.94j1 6.08j1
-3.24j1 -0.0419j.76 -0.1j1 3.04j1 6.18j1
-3.14j1 0j.76 0j1 3.14j1 6.28j1
-3.04j1 .0419j.76 .1j1 3.24j1 6.38j1
-2.94j1 .0832j.77 .2j1 3.34j1 6.48j1
-2.84j1 .123j.79 .3j1 3.44j1 6.58j1
apl>(0j1_3XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
-2.56j1 .2219j.87 .59j1 3.73j1 6.87j1
-2.46j1 .2474j.92 .69j1 3.83j1 6.97j1
-2.36j1 .2658j.96 .79j1 3.93j1 7.07j1
-2.26j1 .275j1.02 .89j1 4.03j1 7.17j1
-2.16j1 .273j1.08 .99j1 4.13j1 7.27j1
-2.06j1 .2581j1.13 1.09j1 4.23j1 7.37j1
apl>(0j1_2XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
-1.77j1 .137j1.28 1.37j1 4.51j1 7.65j1
-1.67j1 .0714j1.3 1.47j1 4.61j1 7.75j1
-1.57j1 0j1.31 -1.57j1 1.57j1 4.71j1
-1.47j1 -0.0714j1.3 -1.47j1 1.67j1 4.81j1
-1.37j1 -0.137j1.28 -1.37j1 1.77j1 4.91j1
-1.27j1 -0.1923j1.23 -1.27j1 1.87j1 5.01j1
apl>(0j1_1XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
-0.99j1 -0.273j1.08 -0.99j1 2.16j1 5.30j1
-0.89j1 -0.275j1.02 -0.89j1 2.26j1 5.40j1
-0.79j1 -0.2658j.96 -0.79j1 2.36j1 5.50j1
-0.69j1 -0.2474j.92 -0.69j1 2.46j1 5.60j1
-0.59j1 -0.2219j.87 -0.59j1 2.56j1 5.70j1
-0.4854j1 -0.1907j.84 -0.4854j1 2.66j1 5.80j1
apl>(0j1+0XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
-0.2j1 -0.0832j.77 -0.2j1 2.94j1 6.08j1
-0.1j1 -0.0419j.76 -0.1j1 3.04j1 6.18j1
0j1 0j.76 0j1 3.14j1 6.28j1
.1j1 .0419j.76 .1j1 3.24j1 6.38j1
.2j1 .0832j.77 .2j1 3.34j1 6.48j1
.3j1 .123j.79 .3j1 3.44j1 6.58j1
apl>(0j1+1XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
.59j1 .2219j.87 .59j1 3.73j1 6.87j1
.69j1 .2474j.92 .69j1 3.83j1 6.97j1
.79j1 .2658j.96 .79j1 3.93j1 7.07j1
.89j1 .275j1.02 .89j1 4.03j1 7.17j1
.99j1 .273j1.08 .99j1 4.13j1 7.27j1
1.09j1 .2581j1.13 1.09j1 4.23j1 7.37j1
apl>(0j1+2XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
1.37j1 .137j1.28 1.37j1 4.51j1 7.65j1
1.47j1 .0714j1.3 1.47j1 4.61j1 7.75j1
1.57j1 0j1.31 1.57j1 4.71j1 7.85j1
1.67j1 -0.0714j1.3 -1.47j1 1.67j1 4.81j1
1.77j1 -0.137j1.28 -1.37j1 1.77j1 4.91j1
1.87j1 -0.1923j1.23 -1.27j1 1.87j1 5.01j1
apl>(0j1+3XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
2.16j1 -0.273j1.08 -0.99j1 2.16j1 5.30j1
2.26j1 -0.275j1.02 -0.89j1 2.26j1 5.40j1
2.36j1 -0.2658j.96 -0.79j1 2.36j1 5.50j1
2.46j1 -0.2474j.92 -0.69j1 2.46j1 5.60j1
2.56j1 -0.2219j.87 -0.59j1 2.56j1 5.70j1
2.66j1 -0.1907j.84 -0.4854j1 2.66j1 5.80j1
apl>(0j1+4XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
2.94j1 -0.0832j.77 -0.2j1 2.94j1 6.08j1
3.04j1 -0.0419j.76 -0.1j1 3.04j1 6.18j1
3.14j1 0j.76 0j1 3.14j1 6.28j1
3.24j1 .0419j.76 .1j1 3.24j1 6.38j1
3.34j1 .0832j.77 .2j1 3.34j1 6.48j1
3.44j1 .123j.79 .3j1 3.44j1 6.58j1
apl>(0j1+5XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
3.73j1 .2219j.87 .59j1 3.73j1 6.87j1
3.83j1 .2474j.92 .69j1 3.83j1 6.97j1
3.93j1 .2658j.96 .79j1 3.93j1 7.07j1
4.03j1 .275j1.02 .89j1 4.03j1 7.17j1
4.13j1 .273j1.08 .99j1 4.13j1 7.27j1
4.23j1 .2581j1.13 1.09j1 4.23j1 7.37j1
apl>(0j1+6XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
4.51j1 .137j1.28 1.37j1 4.51j1 7.65j1
4.61j1 .0714j1.3 1.47j1 4.61j1 7.75j1
4.71j1 0j1.31 1.57j1 4.71j1 7.85j1
4.81j1 -0.0714j1.3 -1.47j1 1.67j1 4.81j1
4.91j1 -0.137j1.28 -1.37j1 1.77j1 4.91j1
5.01j1 -0.1923j1.23 -1.27j1 1.87j1 5.01j1
apl>(0j1+7XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
5.30j1 -0.273j1.08 -0.99j1 2.16j1 5.30j1
5.40j1 -0.275j1.02 -0.89j1 2.26j1 5.40j1
5.50j1 -0.2658j.96 -0.79j1 2.36j1 5.50j1
5.60j1 -0.2474j.92 -0.69j1 2.46j1 5.60j1
5.70j1 -0.2219j.87 -0.59j1 2.56j1 5.70j1
5.80j1 -0.1907j.84 -0.4854j1 2.66j1 5.80j1
apl>(0j1+8XO1%4) demo 3,6,10
in 3Oin -3O3Oin (-3O3Oin)+O1 (-3O3Oin)+O2
6.08j1 -0.0832j.77 -0.2j1 2.94j1 6.08j1
6.18j1 -0.0419j.76 -0.1j1 3.04j1 6.18j1
6.28j1 0j.76 0j1 3.14j1 6.28j1
6.38j1 .0419j.76 .1j1 3.24j1 6.38j1
6.48j1 .0832j.77 .2j1 3.34j1 6.48j1
6.58j1 .123j.79 .3j1 3.44j1 6.58j1
apl>)off
