Dilate: Difference between revisions
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| Line 32: | Line 32: | ||
4<br /> | 4<br /> | ||
2 2 1<br /> | 2 2 1<br /> | ||
⍴⎕←>2 | ⍴⎕←>2 2⍴1<pn>J</pn>2 3<pn>J</pn>4 4<pn>J</pn>3 2<pn>J</pn>1<br /> | ||
1 2<br /> | 1 2<br /> | ||
3 4<br /> | 3 4<br /> | ||
| Line 39: | Line 39: | ||
2 1<br /> | 2 1<br /> | ||
2 2 2<br /> | 2 2 2<br /> | ||
⍴⎕←>2 | ⍴⎕←>2 2⍴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 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 /> | ||
1 2 3 4<br /> | 1 2 3 4<br /> | ||
5 6 7 8<br /> | 5 6 7 8<br /> | ||
| Line 46: | Line 46: | ||
4 3 2 1<br /> | 4 3 2 1<br /> | ||
2 2 4 <br /> | 2 2 4 <br /> | ||
⍴⎕←>2 | ⍴⎕←>2 2⍴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 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 /> | ||
1 2 3 4 5 6 7 8<br /> | 1 2 3 4 5 6 7 8<br /> | ||
9 10 11 12 13 14 15 16<br /> | 9 10 11 12 13 14 15 16<br /> | ||
Revision as of 22:59, 9 April 2017
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| R is an arbitrary Real or Hypercomplex numeric array — otherwise, DOMAIN ERROR. | ||||
| Z is the corresponding array of Real numbers of shape (⍴R),=R where =R is the Hypercomplex dimension (1, 2, 4, or 8) of R. |
For example,
⍴⎕←>23
23
1
⍴⎕←>2 2⍴⍳4
1
2
3
4
2 2 1
⍴⎕←>2 2⍴1J2 3J4 4J3 2J1
1 2
3 4
4 3
2 1
2 2 2
⍴⎕←>2 2⍴1i2j3k4 5i6j7k8 8i7j6k5 4i3j2k1
1 2 3 4
5 6 7 8
8 7 6 5
4 3 2 1
2 2 4
⍴⎕←>2 2⍴1i2j3k4l5ij6jk7kl8 9i10j11k12l13ij14jk15kl16 16i15j14k13l12ij11jk10kl9 8i7j6k5l4ij3jk2kl1
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
16 15 14 13 12 11 10 9
8 7 6 5 4 3 2 1
2 2 8
Identities
R ←→ <>R for all R (see Condense for the definition of monadic Left 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.
