3
Making use of the observation that the OP is asking for a Vandermonde determinant:
With[{n = 5},
Product[a[i]-a[j], {i, 0, n - 1}, {j, 0, i - 1}] /. a[0] -> x]
(* (-x+a[1])(-x+a[2])(-a[1]+a[2])(-x+a[3])(-a[1]+a[3])(-a[2]+a[3])(-x+a[4])(-a[1]+a[4])(-a[2]+a[4])(-a[3]+a[4]) *)
This method is exponentially faster than actually building the matrix ...
3
Does this do what you want?
expr=(1/(2 (fj - fk) π)) Cos[(fj - fk) π T + (fj -
fk) π (T + δt)] Sin[(fj - fk) π T - (fj -
fk) π (T + δt)];
expr /. (f : Cos | Sin)[a_] :> f[Simplify[a]]
This applies Simplify only to the arguments of Sin and Cos
Alternatively,
Simplify[expr,Trig->False]
(This prevents Mathematica from applying Trig ...
3
Solve[Table[
a*x^2 + b*x + c == y /.
Thread[{x, y} -> i], {i, {{2, 17}, {-2, 9}, {1, 6}}}], {a, b, c}]
(* {{a -> 3, b -> 2, c -> 1}} *)
3
Adding the domain Reals allows Solve to work:
Solve[maxrowsum[mat] == 1, a, Reals]
{{a -> 0}, {a -> 2/7}}
3
Alternatively set it up as a univariate minimization and use calculus to solve exactly. We use the usual sqrt(x^2) to form abs(x) and insist that the product of squared differences of rownorms from 1 be zero. Since this is a product of squares we use calculus to find candidate minima.
mat = {{1 - 2 a + 3 a^2, 2 a^2}, {2 a^2, 1 - 4 a + 12 a^2}};
rownorms = ...
3
You can set it up almost like a LP problem.
mat = {{1 - 2 a + 3 a^2, 2 a^2}, {2 a^2, 1 - 4 a + 12 a^2}};
dims = Dimensions[mat];
vars = Array[x, dims];
c1 = Flatten[
Table[{vars[[i, j]] >= mat[[i, j]],
vars[[i, j]] >= -mat[[i, j]]}, {i, dims[[1]]}, {j, dims[[2]]}]];
c2 = Table[Total[vars[[i]]] <= 1, {i, dims[[1]]}];
c3 = Append[Thread[max &...
2
Are this equations linear ? If so you can try to transform the equations.
If you have a nearly linear dependent basis for your equations, it may help, first to search for a new orthogonalized basis, write the equation in this basis and then solve the equations.
As an example we solve a 3D problem: Given a not orthogonal badly conditioned basis: bas and a ...
1
Answer to question 2.:
Newer version of AceGen includes function SMSEigensystem, which calculates eigenvalues and corresponding eigenvectors. Updating AceGen package to latest release is the solution.
1
Clear["`*"];
n = 5;
v = Table[Subscript[a, i], {i, 0, n - 1}] /. Subscript[a, 0] -> x
m = Outer[Power, v, Range[0, n - 1]];
m // MatrixForm
m // Det // Simplify
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