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2017-07-01 03:03:26 +0200	commented question	quadratic form def function(Q): #(Sylvester theorem to obtain a diagonalizing base) n=Q.dim() D=Q.rational_diagonal_form(return_matrix=True)[0] M=Q.rational_diagonal_form(return_matrix=True)[1] base=[M.column(i) for i in range(0,n)] BASEpos=[] BASEneg=[] BASEnull=[] for i in range(0,n): if D[i,i]>0: BASEpos=BASEpos+[1/sqrt(D[i,i])base[i]] if D[i,i]<0: BASEneg=BASEneg+[1/sqrt(-D[i,i])base[i]] if D[i,i]==0: BASEnull=BASEnull+[base[i]] Base1= BASEpos+BASEneg #(base without radical's vector to generate W) Base2= BASEpos+BASEneg+BASEnull W=span(SR,B1) return W When i give as input a quadratic form Q such as Q=QuadraticForm(SR,4,[0,0,0,1,0,-1,0,0,0,0]) W=function(Q) the program give me a lot of errors
2017-06-30 16:07:04 +0200	received badge	● Editor (source)
2017-06-30 13:53:01 +0200	commented question	quadratic form i'm a sage beginner, i know what to do but i don't know how to implement it.. the idea is that i want to give in input a symmetrical nontrivial matrix A associated to the bilinear form B respect to the canonical base in R^n..then i want to obtain a subspace W⊆ R^n of maximal dimension such that the restriction B\|wxw has max rank, in other words the matrix associated to this restriction has maximum rank and this condition occurs if kerW=[0].So i have to : 1. Give in input a matrix, 2. Declare the canonical basis of R^n and R 3. If B is the bilinear form and ei elements of the canonical base of R^n, i say that B(ei,ej)= A(i,j) with A(i,j) the i,j element of A 4. Obtain a subspace W ... (more)
2017-06-30 03:03:09 +0200	asked a question	quadratic form Write a function in Sage that accepts as input a symmetrical bilinear (not trivial) form B [caracterized by the associated matrix respect to the canonical base in R^n] and gives in output a vector subspace W ⊆ R^n such that: - Dim W is maximal - the restriction B\|wxw has maximum rank
2017-06-30 03:03:09 +0200	asked a question	Bilinear form Write a function in Sage that accepts as input a symmetrical bilinear (not trivial) form B [caracterized by the associated matrix respect to the canonical base in R^n] and gives in output a vector subspace W ⊆ R^n such that: - Dim W=n - the restriction of B to WxW has maximum rank