Imaginary base numbers: Difference between revisions

=={{header|J}}==

Implementation:

<lang J>

ibdec=: {{

0j2 ibdec y

:

digits=. 0,".,~&'36b'@> tolower y -.'. '

(x #. digits) % x^#(}.~ 1+i.&'.')y-.' '

}}"1

ibenc=: {{

0j2 ibenc y

:

if.0=y do.,'0' return.end.

sq=:*:x

step=: }.,~(1,|sq) +^:(0>{:@]) (0,sq) #: {.

seq=: step^:(0~:{.)^:_

raw=: ,hfd(}.~0 i.~0=]),|:seq"0 (1,|x)*+.y

trimfrac=. (#!.'.'~ 1 j. 2|.#{.1:)`}:@.((1<#)*'0'={:)

trimfrac raw

}}"0 </lang>

This ibdec can handle decoded numbers in complex bases up to 0j6, but this ibenc can only represent digits in complex bases up to 0j4.

Examples:

<lang J>

(ibenc i:16),.' ',.ibenc j.i:16

1030000 102000

1030001 102000.2

1030002 103030

1030003 103030.2

300 103020

301 103020.2

302 103010

303 103010.2

200 103000

201 103000.2

202 30

203 30.2

100 20

101 20.2

102 10

103 10.2

0 0

1 2.

2 1030

3 1030.2

10300 1020

10301 1020.2

10302 1010

10303 1010.2

10200 1000

10201 1000.2

10202 2030

10203 2030.2

10100 2020

10101 2020.2

10102 2010

10103 2010.2

10000 2000

(ibdec ibenc i:16),: ibdec ibenc j.i:16

_16 _15 _14 _13 _12 _11 _10 _9 _8 _7 _6 _5 _4 _3 _2 _1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0j16 0j15 0j14 0j13 0j12 0j11 0j10 0j9 0j8 0j7 0j6 0j5 0j4 0j3 0j2 0j1 0 2 0j_2 0j_3 0j_4 0j_5 0j_6 0j_7 0j_8 0j_9 0j_10 0j_11 0j_12 0j_13 0j_14 0j_15 0j_16

0j4 ibenc 42

10e0a

0j4 ibdec 0j4 ibenc 42

42

</lang>