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<table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""> <tr> <td> <table border="0" cellpadding="5" cellspacing="0" summary=""> <tr> <td valign="top"><apll>Zβ>R</apll> or <apll>Zβ>[X] R</apll></td> <td></td> <td></td> <td>extracts from <apll>R</apll> its Hypercomplex coefficients.</td> </tr> </table> </td> </tr> <tr> <td><apll>X</apll> is an optional numeric singleton axis with <apll>Xββ³1+β΄β΄R</apll>. If <apll>[X]</apll> is omitted, the operation applies to the last axis plus one.</td> </tr> <tr> <td><apll>R</apll> is an arbitrary Real or Hypercomplex numeric array — otherwise, <apll>DOMAIN ERROR</apll>.</td> </tr> <tr> <td><apll>Z</apll> is the corresponding array of Real numbers of shape <apll>((=R),β΄R)[ββXβ β³1+β΄β΄R]</apll> where <apll>=R</apll> is the Hypercomplex dimension of <apll>R</apll> as in <apll>(=R)β1 2 4 8</apll>.</td> </tr> </table> <br /> <p>For example,</p> <apll><pre> β΄ββ>23 23 1 β΄ββ>[1] 23 23 1 β΄ββ>2 2β΄β³4 1 2 3 4 2 2 1 β΄ββ>2 2β΄1<hc>J</hc>2 3<hc>J</hc>4 4<hc>J</hc>3 2<hc>J</hc>1 1 2 3 4 4 3 2 1 2 2 2 β΄ββ>[1] 2 2β΄1<hc>J</hc>2 3<hc>J</hc>4 4<hc>J</hc>3 2<hc>J</hc>1 1 3 4 2 2 4 3 1 2 2 2 β΄ββ>2 2β΄1<hc>i</hc>2<hc>j</hc>3<hc>k</hc>4 5<hc>i</hc>6<hc>j</hc>7<hc>k</hc>8 8<hc>i</hc>7<hc>j</hc>6<hc>k</hc>5 4<hc>i</hc>3<hc>j</hc>2<hc>k</hc>1 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 2 2 4 β΄ββ>2 2β΄1<hc>i</hc>2<hc>j</hc>3<hc>k</hc>4<hc>l</hc>5<hc>ij</hc>6<hc>jk</hc>7<hc>kl</hc>8 9<hc>i</hc>10<hc>j</hc>11<hc>k</hc>12<hc>l</hc>13<hc>ij</hc>14<hc>jk</hc>15<hc>kl</hc>16 16<hc>i</hc>15<hc>j</hc>14<hc>k</hc>13<hc>l</hc>12<hc>ij</hc>11<hc>jk</hc>10<hc>kl</hc>9 8<hc>i</hc>7<hc>j</hc>6<hc>k</hc>5<hc>l</hc>4<hc>ij</hc>3<hc>jk</hc>2<hc>kl</hc>1 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 </pre></apll> ==Identities== <apll> R ββ < > R</apll> for all <apll>R</apll> (see [[Condense]] for the definition of monadic Left Caret)<br /> <apll> R ββ <[X] >[X] R</apll> for all <apll>R</apll><br /> <apll> R ββ > < R</apll> for all <apll>R</apll> with <apll>(Β―1ββ΄ R)β1 2 4 8</apll><br /> <apll>1/R ββ > < R</apll> for all <apll>R</apll> with <apll>(Β―1ββ΄1/R)β1 2 4 8</apll><br /> <apll> R ββ >[X] <[X] R</apll> for all non-scalar <apll>R</apll> with <apll>(β΄R)[X]β1 2 4 8</apll> == Acknowledgements== <p>This symbol and its name were suggested by David A. Rabenhorst.</p>
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