Table of contents

Some beginner tips for using Mathematica.

Expression to a string for inputting

Convert an expression to a string: TextString[expression] // InputForm where expression denotes the expression to convert. See

• Converting between Expressions & Strings—Wolfram Language Documentation [visited 2024-04-27T00:16:03Z]
• TextString—Wolfram Language Documentation [visited 2024-04-27T00:16:11Z]

Remark (2024-06-01): Better use ToString[InputForm[expression]]? TextString[RootApproximant[1.41421356237, 2]] // InputForm returns "1.41421" while ToString[InputForm[RootApproximant[1.41421356237, 2]]] yields the expected "Sqrt[2]".

Create a matrix of subscripted elements

Array[Subscript[a, #1, #2] &, {3, 3}] // MatrixForm

Code taken from Subscript: Place a character below the baseline—Wolfram Documentation [visited 2024-04-27T00:04:48Z]. See also

• Create a Matrix—Wolfram Language Documentation [visited 2024-04-27T00:16:25Z]
• MatrixForm—Wolfram Language Documentation [visited 2024-04-27T00:16:33Z]

Semidefinite Optimization

If you copy the code of the first example of SemidefiniteOptimization—Wolfram Language Documentation [visited 2024-04-26T22:42:27Z], you get

Subscript[a, 0] = ({
   {0, 1},
   {1, 0}
  }); Subscript[a, 1] = ({
   {1, 0},
   {0, 0}
  }); Subscript[a, 2] = \!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"0", "0"},
{"0", "1"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]}, 
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]}, 
Offset[0.2]}, "RowsIndexed" -> {}}], "", ")"}],
Function[BoxForm`e$, 
MatrixForm[BoxForm`e$]]]\);
res = SemidefiniteOptimization[2 Subscript[x, 1] + 3 Subscript[x, 2], 
  Subscript[a, 0] + Subscript[a, 1] Subscript[x, 1] + 
    Subscript[a, 2] Subscript[x, 2] 
\!\(\*UnderscriptBox[\(\[VectorGreaterEqual]\), 
TemplateBox[{"2"},
"SemidefiniteConeList"]]\) 0, {Subscript[x, 1], Subscript[x, 2]}]

This code is confusing to read, and in particular gives barely any hint how to create the relation for a matrix being semidefinite (\(\underset{S^2_+}{\succeq}\)).

The following code considerably simplifies this example:

a0 = {{0, 1}, {1, 0}}; a1 = {{1, 0}, {0, 0}}; a2 = {{0, 0}, {0, 1}};
res = SemidefiniteOptimization[2 x1 + 3 x2, 
  VectorGreaterEqual[{a0 + a1 x1 + a2   x2, 0}, {"SemidefiniteCone", 2}], 
  {x1, x2}]

Note that you can also use Minimize if you want an exact result:

a0 = {{0, 1}, {1, 0}}; a1 = {{1, 0}, {0, 0}}; a2 = {{0, 0}, {0, 1}};
res = Minimize[2 x1 + 3 x2, 
  VectorGreaterEqual[{a0 + a1 x1 + a2 x2, 0}, {"SemidefiniteCone", 2}], 
  {x1, x2}]

Concerning creating the semidefinite partial ordering via VectorGreaterEqual, see VectorGreaterEqual—Wolfram Language Documentation [visited 2024-04-27T00:22:25Z].`