|Bill Allombert on Sat, 09 Sep 2017 00:20:09 +0200|
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
|Re: Symbolic verification of determinant identities|
On Fri, Sep 08, 2017 at 09:56:52PM +0000, Jacques Gélinas wrote: > Compound determinants such as D3 in > D1 = matdet([ a, b; b, c ]); D2 = matdet([ a, c; b, d ]); > D3 = matdet([ a, 2*b; D1, D2 ]); > are manipulated to prove that D3>0. > > How can PARI/GP be used to verify the formal equivalence of such expressions ? > Of course, I would prefer not to have to write the determinants twice > in original and in final form, if possible. > > Now I run into problems in verifying, for example, the simple identity > D1 == matdet([ a, b + L*a; b + L*a, c + 2*L*b + L^2*a ]) > by using substitutions > > D1 == subst(subst(D1,b,b+L*a),c,c+2*L*b+L^2*a) \\ seems to work ? > D1 == subst(subst(D1,c,c+2*L*b+L^2*a),b,b+L*a) \\ oups !!! Nope! You should use substvec if you need to do simultaneous substitutions. ? D1 == substvec(D1,[b,c],[b+L*a,c+2*L*b+L^2*a]) %3 = 1 Cheers, Bill.