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(kill(all), 'done);
'done$
(load("vector_rebuild"), 'done);
'done;
[1,2]+t*[3,4], vector_simp;
[3*t+1,4*t+2]$
vector_rebuild([3*t+1,4*t+2], [t]);
t*[3,4]+[1,2]$
vector_rebuild([1,2]+t*[3,4]+[5,6]+(t/2-1)*[7,8], [t]);
t*[13/2,8]+[-1,0]$
covect([1/2,1/3,1/4]), vector_factor;
(1/12)*matrix([6],[4],[3])$
/*
`vector_factor' returns
((MTIMES SIMP) -1 ((MTIMESQ SIMP) 2 ((MLIST SIMP) 1 2))) */
block([vector_factor_minus:true],
args(vector_factor([-2,-4])));
[2*[1, 2]]$
extract_equations([1,2]+t*[3,4] = [4,3]+s*[2,1]);
[3*t+1 = 2*s+4,4*t+2 = s+3]$
[1,0,0]~[0,1,0];
[0,0,1]$
block([v: covect([1,2])], 1/|v|*v);
(1/sqrt(5))*matrix([1],[2])$
(v([args]):= covect(args), 'done);
done$
block([plane1, plane2, veq, sys, so, params],
plane1: v(1,2,3)+p*v(4,5,6)+q*v(7,8,9),
plane2: v(3,2,1)+r*v(6,5,4)+s*v(9,8,7),
veq: plane1 = plane2,
sys: extract_equations(veq),
so: algsys(sys,[p,q,r,s]),
params: subst([%rnum_list[1]=u, %rnum_list[2]=v], so),
vector_rebuild(subst(params, plane2), [u, v]));
v*matrix([7],[8],[9])+u*matrix([4],[5],[6])+matrix([1],[2],[3])$
block([n, a, plane],
n: [1,2,3], a: [2,0,1],
plane: x.n = a.n,
plane: vector_simp(plane),
plane: subst(x=[x1,x2,x3], plane),
vector_simp(plane));
3*x3+2*x2+x1 = 5$
block([n],
n: v(1,2,3),
1/|n|*n);
(1/sqrt(14))*matrix([1],[2],[3])$
block([n, a, plane],
n: v(1,2,3),
a: v(2,0,1),
plane: x.n = a.n,
vector_simp(plane));
x . matrix([1],[2],[3]) = 5$
block([point, a, n, en],
point: v(0,1,2),
a: v(2,0,1),
n: v(1,2,3),
en: 1/|n|*n,
|(point-a)*en|);
sqrt(17)/sqrt(14)$
block([a, n, en],
a: v(2,0,1),
n: v(1,2,3),
en: 1/|n|*n,
[vector_simp(a+t*en), vector_factor(vector_rebuild(a+t*en, [t]))]);
[matrix([t/sqrt(14)+2],[(2*t)/sqrt(14)],[(3*t)/sqrt(14)+1]),
(t/sqrt(14))*matrix([1],[2],[3])+matrix([2],[0],[1])]$
args(vector_factor(v(-2,-4)));
[2,matrix([-1],[-2])]$
block([vector_factor_minus:true], args(vector_factor(v(-2,-4))));
[2*matrix([1],[2])]$
block([vector_factor: true, M, M_1],
M: matrix([1,2],[3,-1]),
M_1: M^^-1,
vector_simp(M.M_1));
matrix([1,0],[0,1])$
(kill(v), reset(listarith,doallmxops,domxmxops,dotexptsimp), 'done);
'done$
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