Function: qfbil
Section: linear_algebra
C-Name: qfbil
Prototype: GGDG
Help: qfbil(x,y,{q}): evaluate the bilinear form q (symmetric matrix)
 at (x,y); if q omitted, use the standard Euclidean scalar product.
Doc: evaluate the bilinear form $q$ (symmetric matrix)
 at the vectors $(x,y)$; if $q$ omitted, use the standard Euclidean scalar
 product, corresponding to the identity matrix.

 Roughly equivalent to \kbd{x\til * q * y}, but a little faster and
 more convenient (does not distinguish between column and row vectors):
 \bprog
 ? x = [1,2,3]~; y = [-1,0,1]~; qfbil(x,y)
 %1 = 2
 ? q = [1,2,3;2,2,-1;3,-1,0]; qfbil(x,y, q)
 %2 = -13
 ? for(i=1,10^6, qfbil(x,y,q))
 %3 = 568ms
 ? for(i=1,10^6, x~*q*y)
 %4 = 717ms
 @eprog\noindent The associated quadratic form is also available, as
 \tet{qfnorm}, slightly faster:
 \bprog
 ? for(i=1,10^6, qfnorm(x,q))
 time = 444ms
 ? for(i=1,10^6, qfnorm(x))
 time = 176 ms.
 ? for(i=1,10^6, qfbil(x,y))
 time = 208 ms.
 @eprog