Gramschmidt and scalar product

[parisse]

(05-08-2021 12:31 PM)roadrunner Wrote:  gramschmidt([1,1+x],(p,q)->2*p*q)

returns:

[1/sqrt(2),±∞*(-x-1+x+1)/sqrt(2)]

am i doing something wrong? Why is there a ±∞ in there?

-road

1+x is lineary dependent of 1, because your scalar product is defined on R.

If you want to have something more interesting define a scalar product with an integral or by evaluating p and q at some points, like
gramschmidt([1,1+x],(p,q)->subst(p,x=0)*subst(q,x=0)+subst(p,x=1)*subst(q,x=1))