System Function DC: Difference between revisions

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{{BoxLine |<apll>R</apll> is a numeric array.}}
{{BoxLine |<apll>R</apll> is a numeric array.}}
{{BoxEnd  |
{{BoxEnd  |
<ul><li>For simple numeric (a.k.a. Hypercomplex 1-dimensional &mdash; BOOL, INT, APA, FLOAT, RAT, or VFP) <apll>R</apll> where the number of columns of <apll>R</apll> (call that <apll>NC</apll>) is <apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>, <apll>Z</apll> is the corresponding Hypercomplex array whose Hypercomplex dimension is the same as the number of columns of <apll>R</apll>, and whose shape is <apll>¯1↓⍴R</apll>.  That is, the values in the last coordinate of <apll>R</apll> are treated as the coefficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number.</li>
<ul><li>For simple numeric (a.k.a. Hypercomplex 1-dimensional &mdash; BOOL, INT, APA, FLOAT, RAT, or VFP) <apll>R</apll>, where the number of columns of <apll>R</apll> (call that <apll>NC</apll>) is <apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>, <apll>Z</apll> is the corresponding Hypercomplex array whose Hypercomplex dimension is the same as the number of columns of <apll>R</apll>, and whose shape is <apll>¯1↓⍴R</apll>.  That is, the values in the last coordinate of <apll>R</apll> are treated as the coefficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number. '''This capability has been replaced by the [[Condense]] function (<apll>&lt;R</apll>).'''</li>
<li>For Hypercomplex 2-, 4-, or 8-dimensional <apll>R</apll>, <apll>Z</apll> is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new coordinate on the right consisting of the coefficients of the Hypercomplex numbers in <apll>R</apll>, and whose shape is <apll>(⍴R),NC</apll>.  That is, <apll>Z</apll> contains the coefficients of the Hypercomplex number <apll>R</apll>.</li></ul>}}
<li>For Hypercomplex 2-, 4-, or 8-dimensional <apll>R</apll>, <apll>Z</apll> is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new coordinate on the right consisting of the coefficients of the Hypercomplex numbers in <apll>R</apll>, and whose shape is <apll>(⍴R),NC</apll>.  That is, <apll>Z</apll> contains the coefficients of the Hypercomplex number <apll>R</apll>. '''This capability has been replaced by the [[Dilate]] function (<apll>&gt;R</apll>).'''</li></ul>}}
<br />
<br />
<br />
<br />
<p>For example,</p>
<p>For example,</p>
<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⎕←a←⎕DC 4 2⍴1 0 ¯1 0 0 1 0 ¯1<br />1 ¯1 0<pn>i</pn>1 0<pn>i</pn>¯1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⍝ </apll>The four units for Complex numbers<br />
<apll><pre>
<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⎕DC a<br />
      ⎕←a←⎕DC 4 2⍴1 0 ¯1 0 0 1 0 ¯1
&nbsp;1&nbsp; 0<br />
1 ¯1 0<hc>i</hc>1 0<hc>i</hc>¯1     ⍝ The four units for Complex numbers  
¯1&nbsp; 0<br />
      ⎕DC a  
&nbsp;0&nbsp; 1<br />
1 0  
&nbsp;0 ¯1</apll>
¯1 0  
<br /><br />
0 1  
0 ¯1</pre></apll>


==Dyadic Function==
==Dyadic Function==
Line 22: Line 23:
|converts the coefficients of <apll>R</apll> to the datatype indicated by <apll>L</apll>.}}
|converts the coefficients of <apll>R</apll> to the datatype indicated by <apll>L</apll>.}}
{{BoxLine|<apll>R</apll> is a numeric array.}}
{{BoxLine|<apll>R</apll> is a numeric array.}}
{{BoxLine|<apll>L</apll> is a character scalar or one-element vector datatype (<apll>'I'</apll>, <apll>'F'</apll>, <apll>'R'</apll>, or <apll>'V'</apll>) indicating the datatype to which the coefficients should be converted.}}
{{BoxLine|If <apll>L</apll> is a character scalar or one-element vector whose value is one of (<apll>'I'</apll>, <apll>'F'</apll>, <apll>'R'</apll>, or <apll>'V'</apll>), this value indicates the datatype to which the coefficients of <apll>R</apll> should be converted.}}
{{BoxLine|If <apll>L</apll> is a numeric scalar or one-element vector, then its datatype is the datatype to which the coefficients of <apll>R</apll> should be converted.}}
{{BoxEnd|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.
{{BoxEnd|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.
The shape of <apll>Z</apll> is the same as that of <apll>R</apll>.}}
The shape of <apll>Z</apll> is the same as that of <apll>R</apll>.}}
<br /><p>For example,</p><apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'R' ⎕DC 1.5<pn>i</pn>3<br />3<pn>r</pn>2<pn>i</pn>3<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'R' ⎕DC 1.1<pn>i</pn>3<br />2476979795053773<pn>r</pn>2251799813685248<pn>i</pn>3<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'F' ⎕DC 3<pn>r</pn>2 2476979795053773<pn>r</pn>2251799813685248<br />1.5 1.1</apll>
<br />
 
For example,
 
<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'R' ⎕DC 1.5<_i/>3
3<_r/>2<_i/>3
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'R' ⎕DC 1.1<_i/>3
2476979795053773<_r/>2251799813685248<_i/>3
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'F' ⎕DC 3<_r/>2 2476979795053773<_r/>2251799813685248
1.5 1.1
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;0 ⎕DR ⎕←0<_x/> ⎕DC 2<_i/>1
2<_i/>1  
Complex Rational (1416):  arbitrary precision numerator and denominator
</apll>
<br/>
<br/>
{{SFDM|DC}}
{{SFDM|DC}}

Latest revision as of 09:49, 9 November 2023

This function is available in both monadic and dyadic forms.

Monadic Function

Z←⎕DC R converts R between the coefficients of a Hypercomplex number and the corresponding Hypercomplex number.
R is a numeric array.
  • For simple numeric (a.k.a. Hypercomplex 1-dimensional — BOOL, INT, APA, FLOAT, RAT, or VFP) R, where the number of columns of R (call that NC) is 1, 2, 4, or 8, Z is the corresponding Hypercomplex array whose Hypercomplex dimension is the same as the number of columns of R, and whose shape is ¯1↓⍴R. That is, the values in the last coordinate of R are treated as the coefficients of a Hypercomplex number and Z is the corresponding Hypercomplex number. This capability has been replaced by the Condense function (<R).
  • For Hypercomplex 2-, 4-, or 8-dimensional R, Z is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new coordinate on the right consisting of the coefficients of the Hypercomplex numbers in R, and whose shape is (⍴R),NC. That is, Z contains the coefficients of the Hypercomplex number R. This capability has been replaced by the Dilate function (>R).



For example,

      ⎕←a←⎕DC 4 2⍴1 0 ¯1 0 0 1 0 ¯1
1 ¯1 0i1 0i¯1      ⍝  The four units for Complex numbers 
      ⎕DC a 
 1  0 
¯1  0 
 0  1 
 0 ¯1

Dyadic Function

Z←L ⎕DC R converts the coefficients of R to the datatype indicated by L.
R is a numeric array.
If L is a character scalar or one-element vector whose value is one of ('I', 'F', 'R', or 'V'), this value indicates the datatype to which the coefficients of R should be converted.
If L is a numeric scalar or one-element vector, then its datatype is the datatype to which the coefficients of R should be converted.
Z is R where all of the coefficients of each of the values are converted to the datatype indicated by L. The shape of Z is the same as that of R.


For example,

      'R' ⎕DC 1.5i3 3r2i3       'R' ⎕DC 1.1i3 2476979795053773r2251799813685248i3       'F' ⎕DC 3r2 2476979795053773r2251799813685248 1.5 1.1       0 ⎕DR ⎕←0x ⎕DC 2i1 2i1 Complex Rational (1416): arbitrary precision numerator and denominator

Note: ⎕DC is available as both a monadic and dyadic form system function, you cannot assign a value to it.

System Variables (A value may be assigned to these except for ⎕DM)
⎕ALX ⎕CT ⎕DM ⎕DT ⎕ELX ⎕FC ⎕FEATURE ⎕FPC ⎕IC ⎕IO
⎕LR ⎕LX ⎕PP ⎕PR ⎕PW ⎕RL ⎕SA ⎕WSID
Niladic System Functions (a value cannot be assigned to these)
⎕A ⎕AV ⎕EM ⎕ET ⎕LC ⎕NNAMES ⎕NNUMS ⎕SI ⎕SYSID ⎕SYSVER
⎕T ⎕TC ⎕TCBEL ⎕TCBS ⎕TCESC ⎕TCFF ⎕TCHT ⎕TCLF ⎕TCNL ⎕TCNUL
⎕TS ⎕WA
Monadic or dyadic system functions (a value cannot be assigned to these)
⎕AT ⎕CR ⎕DC ⎕DFT ⎕DL ⎕DR ⎕EA ⎕EC ⎕ERROR ⎕ES
⎕EX ⎕FMT ⎕FX ⎕MF ⎕NAPPEND ⎕NC ⎕NCREATE ⎕NERASE ⎕NINFO ⎕NL
⎕NLOCK ⎕NREAD ⎕NRENAME ⎕NREPLACE ⎕NRESIZE ⎕NSIZE ⎕NTIE ⎕NUNTIE ⎕STOP ⎕TF
⎕TRACE ⎕UCS ⎕VR
Note that quad functions and variables (except for the ⎕A family of functions) are case insensitive


See Also
System Commands System Variables and Functions Operators


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