$title piped projection and counts to 1,2,3 dimensions (PIPE5,SEQ=115)

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Contributor: Alex Meeraus
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$version 137 goto OK
$clearError
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$label OK

set i / 1*5 /; alias(i,i1,i2,i3,i4);

parameter a4(i1,i2,i3,i4);

a4(i1,i2,i3,i4)$(uniform(0,1) > .9) = uniform(1,2);

parameters three123(i1,i2,i3)
           three432(i4,i3,i2)
           three312(i3,i1,i2)
           two12(i1,i2)
           two34(i3,i4)
           two41(i4,i1)
           two23(i2,i3)
           two24(i2,i4)
           one1(i1)
           one2(i2)
           one3(i3)
           one4(i4);

option one1 < a4
       one2 < a4
       one3 < a4
       one4 < a4 ;

abort$sum(i1, one1(i1) <> sum((   i2,i3,i4)$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum(i2, one2(i2) <> sum((i1,   i3,i4)$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum(i3, one3(i3) <> sum((i1,i2,   i4)$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum(i4, one4(i4) <> sum((i1,i2,i3   )$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';


option two12 < a4
       two34 < a4
       two41 < a4
       two23 < a4
       two24 < a4

abort$sum((i1,i2), two12(i1,i2) <> sum((      i3,i4)$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum((i3,i4), two34(i3,i4) <> sum((i1,i2      )$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum((i4,i1), two41(i4,i1) <> sum((   i2,i3   )$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum((i2,i3), two23(i2,i3) <> sum((i1      ,i4)$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum((i2,i4), two24(i2,i4) <> sum((i1   ,i3   )$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';

option three123 < a4
       three432 < a4
       three312 < a4;

abort$sum((i1,i2,i3), three123(i1,i2,i3) <> sum(i4$a4(i1,i2,i3,i4), 1)) 'bad sort';
abort$sum((i4,i3,i2), three432(i4,i3,i2) <> sum(i1$a4(i1,i2,i3,i4), 1)) 'bad sort';
abort$sum((i3,i1,i2), three312(i3,i1,i2) <> sum(i4$a4(i1,i2,i3,i4), 1)) 'bad sort';