Dynamic input for Complex, Determinant output problems

Question

I'm having trouble using Complex with Dynamic real and imaginary inputs. The inputs come from a matrix of popup menus:

InitA = {
    {PopupMenu[Dynamic[a11re], Range[-5,5]] + PopupMenu[Dynamic[a11im], Range[-5,5]] Style["i", Italic], PopupMenu[Dynamic[a12re], Range[-5,5]] + PopupMenu[Dynamic[a12im], Range[-5,5]] Style["i", Italic]},
    {PopupMenu[Dynamic[a21re], Range[-5,5]] + PopupMenu[Dynamic[a21im], Range[-5,5]] Style["i", Italic], PopupMenu[Dynamic[a22re], Range[-5,5]] + PopupMenu[Dynamic[a22im], Range[-5,5]] Style["i", Italic]}
        };

Using those dynamic inputs, I set the parts of a new matrix equal to those dynamic inputs.

a11 = Complex[Dynamic[a11re], Dynamic[a11im]];
a12 = Complex[Dynamic[a12re], Dynamic[a12im]];
a21 = Complex[Dynamic[a21re], Dynamic[a21im]];
a22 = Complex[Dynamic[a22re], Dynamic[a22im]];
A = {{a11, a12},
    {a21, a22}};

For some reason, the matrix A isn't read as 4 complex numbers, but just four inputs of the form Complex[Re, Im]. If I remove the Dynamic[] around the variables when using Complex[], A displays 4 complex numbers in TraditionalForm. Does anyone know about the behavior of Complex that restricts it from using dynamic inputs?

EDIT

Later in the application, Det[A] must be found. Using JM's suggestion for creating the complex numbers in A, with initial inputs of A as:

a11re = 2; a11im = -4; a12re = 2; a12im = 0;
a21re = 3; a21im = 0; a22re = 5; a22im = -3;
a11 = Dynamic[a11re + I*a11im];
a12 = Dynamic[a12re + I*a12im];
a21 = Dynamic[a21re + I*a21im];
a22 = Dynamic[a22re + I*a22im];

Det[A]//TraditionalForm outputs "2-4i5-3i-23", which is (2-4i)(5-3i)-(2)(3) without the parenthesis. Why would it not evaluate the determinant fully? That just doesn't make sense to me.

Use an explicit construction instead: Dynamic[a11re + I a11im]. Complex requires explicit numbers (i.e. satisfies NumberQ[]). — J. M.'s missing motivation, Jun 20 '16 at 16:16
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Condensing into a comment: 1 is a number and can be used everywhere where a number is expected. Dynamic[1] is not a number and cannot be used in such places. Dynamic[expr] is a way to display expr and automatically recompute it any time a subpart changes. Things wrapped in Dynamic cannot be used for computation. If it's a determinant you want to display and update dynamically, Dynamic must appear once, wrapping Det. — Szabolcs, Jun 20 '16 at 18:02
Thank you Szabolcs! That did the trick! Also thanks to J.M. for his initial response! — J_Nat, Jun 20 '16 at 18:15

score 1 · Answer 1 · answered Jun 20 '16 at 18:23

Thanks to J.M. and Szabolcs for addressing my questions clearly. Here's what they came up with:

I was using Dynamic incorrectly, wrapping variables that weren't being displayed.

The new code is now this

InitA = {
    {PopupMenu[Dynamic[a11re], Range[-5,5]] + PopupMenu[Dynamic[a11im], Range[-5,5]] Style["i", Italic], PopupMenu[Dynamic[a12re], Range[-5,5]] + PopupMenu[Dynamic[a12im], Range[-5,5]] Style["i", Italic]},
    {PopupMenu[Dynamic[a21re], Range[-5,5]] + PopupMenu[Dynamic[a21im], Range[-5,5]] Style["i", Italic], PopupMenu[Dynamic[a22re], Range[-5,5]] + PopupMenu[Dynamic[a22im], Range[-5,5]] Style["i", Italic]}
        };

a11 = a11re + I a11im;
a12 = a12re + I a12im;
a21 = a21re + I a21im;
a22 = a22re + I a22im;
A = {{a11, a12},
    {a21, a22}};

Dynamic[Det[A]]

Dynamic input for Complex, Determinant output problems

1 Answers1