Condense: Difference between revisions
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23<br /> | 23<br /> | ||
<10 20<br /> | <10 20<br /> | ||
10<pn>J</pn>20<br /> | |||
<2 4⍴⍳8<br /> | <2 4⍴⍳8<br /> | ||
1<pn>i</pn>2<pn>j</pn>3<pn>k</pn>4 5<pn>i</pn>6<pn>j</pn>7<pn>k</pn>8<br /> | |||
<2 8⍴(⍳8),⌽⍳8<br /> | <2 8⍴(⍳8),⌽⍳8<br /> | ||
1<pn>i</pn>2<pn>j</pn>3<pn>k</pn>4<pn>l</pn>5<pn>ij</pn>6<pn>jk</pn>7<pn>kl</pn>8 8<pn>i</pn>7<pn>j</pn>6<pn>k</pn>5<pn>l</pn>4<pn>ij</pn>3<pn>jk</pn>2<pn>kl</pn>1<br /> | |||
⍴⎕←<2 3 1⍴⍳6<br /> | ⍴⎕←<2 3 1⍴⍳6<br /> | ||
1 2 3<br /> | 1 2 3<br /> | ||
| Line 35: | Line 35: | ||
2 3<br /> | 2 3<br /> | ||
⍴⎕←<2 3 2⍴(⍳6),⌽⍳6<br /> | ⍴⎕←<2 3 2⍴(⍳6),⌽⍳6<br /> | ||
1<pn>J</pn>2 3<pn>J</pn>4 5<pn>J</pn>6<br /> | |||
6<pn>J</pn>5 4<pn>J</pn>3 2<pn>J</pn>1<br /> | |||
2 3<br /> | 2 3<br /> | ||
⍴⎕←<2 3 4⍴(⍳12),⌽⍳12<br /> | ⍴⎕←<2 3 4⍴(⍳12),⌽⍳12<br /> | ||
1<pn>i</pn>2<pn>j</pn>3<pn>k</pn>4 5<pn>i</pn>6<pn>j</pn>7<pn>k</pn>8 9<pn>i</pn>10<pn>j</pn>11<pn>k</pn>12<br /> | |||
12<pn>i</pn>11<pn>j</pn>10<pn>k</pn>9 8<pn>i</pn>7<pn>j</pn>6<pn>k</pn>5 4<pn>i</pn>3<pn>j</pn>2<pn>k</pn>1<br /> | |||
2 3<br /> | 2 3<br /> | ||
⍴⎕←<2 3 8⍴(⍳24),⌽⍳24<br /> | ⍴⎕←<2 3 8⍴(⍳24),⌽⍳24<br /> | ||
| 1<pn>i</pn>2<pn>j</pn>3<pn>k</pn>4<pn>l</pn>5<pn>ij</pn>6<pn>jk</pn>7<pn>kl</pn>8 9<pn>i</pn>10<pn>j</pn>11<pn>k</pn>12<pn>l</pn>13<pn>ij</pn>14<pn>jk</pn>15<pn>kl</pn>16 17<pn>i</pn>18<pn>j</pn>19<pn>k</pn>20<pn>l</pn>21<pn>ij</pn>22<pn>jk</pn>23<pn>kl</pn>24<br /> | ||
24<pn>i</pn>23<pn>j</pn>22<pn>k</pn>21<pn>l</pn>20<pn>ij</pn>19<pn>jk</pn>18<pn>kl</pn>17 16<pn>i</pn>15<pn>j</pn>14<pn>k</pn>13<pn>l</pn>12<pn>ij</pn>11<pn>jk</pn>10<pn>kl</pn>9 8<pn>i</pn>7<pn>j</pn>6<pn>k</pn>5<pn>l</pn>4<pn>ij</pn>3<pn>jk</pn>2<pn>kl</pn>1<br /> | |||
2 3<br /> | 2 3<br /> | ||
</apll> | </apll> | ||
Revision as of 17:50, 9 April 2017
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| R is an arbitrary Real numeric array (BOOL, INT, FLT, APA, RAT, VFP — otherwise, DOMAIN ERROR) whose number of columns (≢R) is 1, 2, 4, or 8 — otherwise, LENGTH ERROR. | ||||
| Z is the corresponding Real or Hypercomplex array of shape ¯1↓⍴R using the columns of R as the coefficients of the resulting Real or Hypercomplex array. If ≢R is 1, the result is the Real array (¯1↓⍴R)⍴R, if ≢R is 2, the result is a Complex array, if ≢R is 4, the result is a Quaternion array, and if ≢R is 8, the result is an Octonion array. |
For example,
<23
23
<10 20
10J20
<2 4⍴⍳8
1i2j3k4 5i6j7k8
<2 8⍴(⍳8),⌽⍳8
1i2j3k4l5ij6jk7kl8 8i7j6k5l4ij3jk2kl1
⍴⎕←<2 3 1⍴⍳6
1 2 3
4 5 6
2 3
⍴⎕←<2 3 2⍴(⍳6),⌽⍳6
1J2 3J4 5J6
6J5 4J3 2J1
2 3
⍴⎕←<2 3 4⍴(⍳12),⌽⍳12
1i2j3k4 5i6j7k8 9i10j11k12
12i11j10k9 8i7j6k5 4i3j2k1
2 3
⍴⎕←<2 3 8⍴(⍳24),⌽⍳24
1i2j3k4l5ij6jk7kl8 9i10j11k12l13ij14jk15kl16 17i18j19k20l21ij22jk23kl24
24i23j22k21l20ij19jk18kl17 16i15j14k13l12ij11jk10kl9 8i7j6k5l4ij3jk2kl1
2 3
Identities
R ←→ <>R for all R (see Dilate for the definition of monadic Right Caret)
R ←→ ><R for all R with (¯1↑⍴R)∊1 2 4 8
Acknowledgements
This symbol and its name were suggested by David A. Rabenhorst.
