## # Tablature

### # Postponed operators

Hands on! We evaluate `a*{c}b` superpower stars by putting postponed operations `+*{s}t` right on top. The prefixed plus sign postpones the right superstar operation until the same number of stars occur on the left. This enhanced system has a better resolution, useful for comparisons.

Define how postponed superstars work. Use `{k}` RepExp to repeat signs, so that for example `2*{4}3` `= 2****3` whose reduction train is shown in the left column of the table below.
The underscore `_` signifies an arbitrary part, not changed by the operation.

• a^..b ^:c = a*..b *:c1 = a*{c1}b = a,{c2}b
• _a*{c1}b1 = _a*{c1}b+*{c}a
• _a*{c1}b1+*{s}t = _a*{c1}b+*{c}a+*{s}t
• _+*{c}a+*{s}t = _+*{c}a*{s}t
• _a*{c}1+_ = _a+_

Postponed addition in `a*{c>1}b++t` benefits from an extra plus sign, to distinguish it from `a*b+t` which works like ordinary addition (in the table below).
Expressions of the first row of Btrix (abbreviated to Bx in the table head) is translated to postponed superstars format in the column left.
An alternative system By is presented in the right columns, its iterator entries are counted down to `1` (instead of `0`) and By can be read as a row of up-arrow operations.

Calculation of ```11,,,,,111 = 1.. :65536```
** Bx to ,0 ^ By to ,1
1 2****3 2,,,,,3 2^^^3 2,3,1,1,1,1,2
2 2****2+***2 2,2,,,,2 2^^2^^2 2,1,1,1,1,4,1
2,2,1,1,1,3
3 2****1+***2***2
2+***2***2
2,,,,2,1
4 2+***2***1+**2
2+***2+**2
2,2,,,1,1 2^^(2^2) 2,2,1,1,2,2
5 2+***2**2 2,,,2,,1
6 2+***2**1+*2
2+***2+*2
2,2,,1,,1 2^^(2*2) 2,2,1,2,1,2
7 2+***2*2 2,,2,,,1
8 2+***2*1+2
2+***2+2
2,2,1,,,1 2^^(2+2) 2,2,2,1,1,2
9 2+***4 2,4,,,,1 2^^4 2,4,1,1,1,2
10 2***4 2,,,,4,
11 2***3+**2 2,2,,,3, 2^2^2^2 2,1,1,1,5,1
2,2,1,1,4
12 2***2+**2**2 2,,,2,2,
13 2***2+**2**1+*2
2***2+**2+*2
2,2,,1,2, 2^2^(2*2) 2,2,1,2,3
14 2***2+**2*2 2,,2,,2,
15 2***2+**2*1+2
2***2+**2+2
2,2,1,,2, 2^2^(2+2) 2,2,2,1,3
16 2***2+**4 2,4,,,2, 2^2^4 2,4,1,1,3
17 2***1+**2**4
2+**2**4
2,,,4,1,
18 2+**2**3+*2 2,2,,3,1, 2^(2*2*2*2) 2,2,1,4,2
19 2+**2**2+*2*2 2,,2,2,1,
20 2+**2**2+*2*1+2
2+**2**2+*2+2
2,2,1,2,1, 2^(2*2*(2+2)) 2,2,2,3,2
21 2+**2**2+*4 2,4,,2,1, 2^(2*2*4) 2,4,1,3,2
22 2+**2**1+*2*4
2+**2+*2*4
2,,4,1,1,
23 2+**2+*2*3+2 2,2,3,1,1, 2^(2*(2+2+2+2)) 2,2,4,2,2
24 2+**2+*2*2+4 2,4,2,1,1, 2^(2*(2+2+4)) 2,4,3,2,2
25 2+**2+*2*1+6
2+**2+*2+6
2,6,1,1,1, 2^(2*(2+6)) 2,6,2,2,2
26 2+**2+*8 2,8,,1,1, 2^(2*8) 2,8,1,2,2
27 2+**2*8 2,,8,,1,
28 2+**2*7+2 2,2,7,,1, 2^(.2+..2) :7 2,2,8,1,2
29 2+**2*6+4 2,4,6,,1, 2^(.2+..4) :6 2,4,7,1,2
30 2+**2*5+6 2,6,5,,1, 2^(.2+..6) :5 2,6,6,1,2
31 2+**2*4+8 2,8,4,,1, 2^(.2+..8) :4 2,8,5,1,2
32 2+**2*3+10 2,10,3,,1, 2^(2+2+2+10) 2,10,4,1,2
33 2+**2*2+12 2,12,2,,1, 2^(2+2+12) 2,12,3,1,2
34 2+**2*1+14
2+**2+14
2,14,1,,1, 2^(2+14) 2,14,2,1,2
35 2+**16 2,16,,,1, 2^16 2,16,1,1,2
36 2**16 2,,,16,,
37 2**15+*2 2,2,,15,, 2*..2 :15
2*..2*2 :14
2,1,1,17,1
2,2,1,16
38 2**14+*2*2 2,,2,14,,
39 2**14+*2*1+2
2**14+*2+2
2,2,1,14,, 2*..(2+2) :14 2,2,2,15
40 2**14+*4 2,4,,14,, 2*..4 :14
2*..2*4 :13
2,4,1,15
41 2**13+*2*4 2,,4,13,,
42 2**13+*2*3+2 2,2,3,13,, 2*..(2+2+2+2) :13 2,2,4,14
43 2**13+*2*2+4 2,4,2,13,, 2*..(2+2+4) :13 2,4,3,14
44 2**13+*2*1+6
2**13+*2+6
2,6,1,13,, 2*..(2+6) :13 2,6,2,14
45 2**13+*8 2,8,,13,, 2*..8 :13
2*..2*8 :12
2,8,1,14
46 2**12+*2*8 2,,8,12,,
47 2**12+*2*7+2 2,2,7,12,, (2*){12}((2+){7}2) 2,2,8,13
48 2**12+*2*6+4 2,4,6,12,, (2*){12}((2+){6}4) 2,4,7,13
49 2**12+*2*5+6 2,6,5,12,, (2*){12}((2+){5}6) 2,6,6,13
50 2**12+*2*4+8 2,8,4,12,, (2*){12}((2+){4}8) 2,8,5,13
51 2**12+*2*3+10 2,10,3,12,, (2*){12}(2+2+2+10) 2,10,4,13
52 2**12+*2*2+12 2,12,2,12,, (2*){12}(2+2+12) 2,12,3,13
53 2**12+*2*1+14
2**12+*2+14
2,14,1,12,, (2*){12}(2+14) 2,14,2,13
54 2**12+*16 2,16,,12,, 2*..16 :12
2*..2*16 :11
2,16,1,13
55 2**11+*2*16 2,,16,11,,
56 2**11+*2*15+2 2,2,15,11,, (2*){11}((2+){15}2) 2,2,16,12
57 2**11+*2*14+4 2,4,14,11,, (2*){11}((2+){14}4) 2,4,15,12
58 2**11+*2*13+6 2,6,13,11,, (2*){11}((2+){13}6) 2,6,14,12

68 2**11+*2*3+26 2,26,3,11,, (2*){11}((2+){3}26) 2,26,4,12
69 2**11+*2*2+28 2,28,2,11,, (2*){11}((2+){2}28) 2,28,3,12
70 2**11+*2*1+30
2**11+*2+30
2,30,1,11,, (2*){11}((2+){1}30)
(2*){11}(2+30)
2,30,2,12
71 2**11+*32 2,32,,11,, 2*..32 :11
2*..2*32 :10
2,32,1,12
72 2**10+*2*32 2,,32,10,,
73 2**10+*2*31+2 2,2,31,10,, (2*){10}((2+){31}2) 2,2,32,11
74 2**10+*2*30+4 2,4,30,10,, (2*){10}((2+){30}4) 2,4,31,11

102 2**10+*2*2+60 2,60,2,10,, (2*){10}((2+){2}60) 2,60,3,11
103 2**10+*2*1+62
2**10+*2+62
2,62,1,10,, (2*){10}(2+62) 2,62,2,11
104 2**10+*64 2,64,,10,, 2*..64 :10
2*..2*64 :9
2,64,1,11
105 2**9+*2*64 2,,64,9,,
106 2**9+*2*63+2 2,2,63,9,, (2*){9}((2+){63}2) 2,2,64,10

168 2**9+*2+126 2,126,1,9,, (2*){9}(2+126) 2,126,2,10
169 2**9+*128 2,128,,9,, 2*..128 :9 2,128,1,10
170 2**8+*2*128 2,,128,8,,

298 2**8+*256 2,256,,8,, 2*..256 :8 2,256,1,9

555 2**7+*512 2,512,,7,, 2*..512 :7 2,512,1,8

1068 2**6+*1024 2,1024,,6,, 2*..1024 :6 2,1024,1,7

2093 2**5+*2048 2,2048,,5,, 2*..2048 :5 2,2048,1,6

4142 2**4+*4096 2,4096,,4,, 2*..4096 :4 2,4096,1,5

8239 2**3+*8192 2,8192,,3,, 2*..8192 :3 2,8192,1,4

16432 2**2+*16384 2,16384,,2,, 2*..16384 :2 2,16384,1,3

32817 2**1+*32768
2+*32768
2,32768,,1,, 2*..32768 :1
2*32768
2,32768,1,2
32818 2*32768 2,,32768,,,
32819 2*32767+2 2,2,32767,,, 2+..2 :32767 2,0,32769,1
2,2,32768
32820 2*32766+4 2,4,32766,,, 2+..4 :32766 2,4,32767

65584 2*2+65532 2,65532,2,,, 2+..65532 :2 2,65532,3
65585 2*1+65534
2+65534
2,65534,1,,, 2+65534 2,65534,2
65586 65536 2,65536,,,, 65536 2,65536,1
2,65536
65587 65536 65536

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