'''	\"  eqn file | troff -mm [-Tdevname] | ...
.PH "'EQN:  File(\n(.F)''Device(\*(.T)'"
.P
.B Knuth
(Vol. 2, p. 317):
.DS CB
.EQ 
Q sub n (x sub 1 ,x sub 2 , ... ,x sub n ) ~=~ left {
matrix {
lcol { 1, above x sub 1 , above 
x sub 1 Q sub n-1 (x sub 2 , ... ,x sub n ) +
Q sub n-2 (x sub 3 , ... ,x sub n ) }
lcol {  if above  if above  if }
lcol { n=0; above n=1; above n>1. }
}
.EN
.DE
.sp 0.5i
.B Knuth
(Vol. 2, p. 426):
.sp
.in +0.25i
.P
When zero occurs, the determinant is even easier to compute;
for example, if
.DS CB
.EQ
x sub 11 =0 
.EN
.DE
but
.DS CB
.EQ
x sub 21  != 0,
.EN
.DE
we have
.DS CB
.EQ
det ~
left [ 
matrix {
col { 0 above x sub 21 above x sub 31 above ...  above x sub n1 }
col { x sub 12 above x sub 22 above x sub 32 above ~ above x sub n2 }
col { ...  above ...  above ...  above ~ above ...  }
col { x sub 1n above x sub 2n above x sub 3n above ~ above x sub nn }
}
right ]
.EN
.DE
.sp .5
.DS CB
.EQ (8)
=~-x sub 21 det
left [
matrix {
col { 
x sub 12 above x sub 32 -(x sub 31 /x sub 21 )x sub 22
above ...  above x sub n2 -(x sub n1 /x sub 21 )x sub 22 }
col { ...  above ...  above ~ above ...  }
col {
x sub 1n above x sub 3n -(x sub 31 /x sub 21 )x sub 2n
above ...  above x sub nn -(x sub n1 /x sub 21 )x sub 2n
   }
}
right ]
~~.
.EN
.DE
