Hi,
I was wondering why Sage expands products of sums in an unexpected
order:
var('a0,a1,b0,b1,b2,c0,c1,c2,c3,d0,d1,d2,d3,d4')
expand((a0+a1)*(b0+b1))
a1*b1 + a0*b1 + a1*b0 + a0*b0
expand((a0+a1)*(b0+b1+b2)*(c0+c1+c2+c3)*(d0+d1+d2+d3+d4))
a1*b2*c3*d4 + a0*b2*c3*d4 + a1*b1*c3*d4 + a0*b1*c3*d4 + a1*b0*c3*d4 +
a0*b0*c3*d4 + a1*b2*c2*d4 + a0*b2*c2*d4 + a1*b1*c2*d4 + a0*b1*c2*d4 +
a1*b0*c2*d4 + a0*b0*c2*d4 + a1*b2*c1*d4 + a0*b2*c1*d4 + a1*b1*c1*d4 +
a0*b1*c1*d4 + a1*b0*c1*d4 + a0*b0*c1*d4 + a1*b2*c0*d4 + a0*b2*c0*d4 +
a1*b1*c0*d4 + a0*b1*c0*d4 + a1*b0*c0*d4 + a0*b0*c0*d4 + a1*b2*c3*d3 +
a0*b2*c3*d3 + a1*b1*c3*d3 + a0*b1*c3*d3 + a1*b0*c3*d3 + a0*b0*c3*d3 +
a1*b2*c2*d3 + a0*b2*c2*d3 + a1*b1*c2*d3 + a0*b1*c2*d3 + a1*b0*c2*d3 +
a0*b0*c2*d3 + a1*b2*c1*d3 + a0*b2*c1*d3 + a1*b1*c1*d3 + a0*b1*c1*d3 +
a1*b0*c1*d3 + a0*b0*c1*d3 + a1*b2*c0*d3 + a0*b2*c0*d3 + a1*b1*c0*d3 +
a0*b1*c0*d3 + a1*b0*c0*d3 + a0*b0*c0*d3 + a1*b2*c3*d2 + a0*b2*c3*d2 +
a1*b1*c3*d2 + a0*b1*c3*d2 + a1*b0*c3*d2 + a0*b0*c3*d2 + a1*b2*c2*d2 +
a0*b2*c2*d2 + a1*b1*c2*d2 + a0*b1*c2*d2 + a1*b0*c2*d2 + a0*b0*c2*d2 +
a1*b2*c1*d2 + a0*b2*c1*d2 + a1*b1*c1*d2 + a0*b1*c1*d2 + a1*b0*c1*d2 +
a0*b0*c1*d2 + a1*b2*c0*d2 + a0*b2*c0*d2 + a1*b1*c0*d2 + a0*b1*c0*d2 +
a1*b0*c0*d2 + a0*b0*c0*d2 + a1*b2*c3*d1 + a0*b2*c3*d1 + a1*b1*c3*d1 +
a0*b1*c3*d1 + a1*b0*c3*d1 + a0*b0*c3*d1 + a1*b2*c2*d1 + a0*b2*c2*d1 +
a1*b1*c2*d1 + a0*b1*c2*d1 + a1*b0*c2*d1 + a0*b0*c2*d1 + a1*b2*c1*d1 +
a0*b2*c1*d1 + a1*b1*c1*d1 + a0*b1*c1*d1 + a1*b0*c1*d1 + a0*b0*c1*d1 +
a1*b2*c0*d1 + a0*b2*c0*d1 + a1*b1*c0*d1 + a0*b1*c0*d1 + a1*b0*c0*d1 +
a0*b0*c0*d1 + a1*b2*c3*d0 + a0*b2*c3*d0 + a1*b1*c3*d0 + a0*b1*c3*d0 +
a1*b0*c3*d0 + a0*b0*c3*d0 + a1*b2*c2*d0 + a0*b2*c2*d0 + a1*b1*c2*d0 +
a0*b1*c2*d0 + a1*b0*c2*d0 + a0*b0*c2*d0 + a1*b2*c1*d0 + a0*b2*c1*d0 +
a1*b1*c1*d0 + a0*b1*c1*d0 + a1*b0*c1*d0 + a0*b0*c1*d0 + a1*b2*c0*d0 +
a0*b2*c0*d0 + a1*b1*c0*d0 + a0*b1*c0*d0 + a1*b0*c0*d0 + a0*b0*c0*d0
This ordering makes it extremely difficult to do index association
from the j-th term of the expansion back into constituent indices of
each sum (i0,i1,i2,i3); for example, (0,1,2,3) corresponds to
a0*b1*c2*d3 and is associated with j=33. A more intuitive left to
right product expansion would have been simpler and more useful when
working with these expansions. Also, other math packages expand these
products in a different order than what's seen in Sage. In the
simpler case (a0+a1)*(b0+b1) I would expect the accepted FOIL ordering
of terms. What was the rationale?
Given j, how would you calculate (i0,i1,i2,i3,...,ik) considering
Sage's expansion order?
Your help is appreciated,
philabuster
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