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Mathematica symbols are the ultimate atoms of symbolic data. Every symbol has a unique name, exists in a certain Mathematica context or namespace, and can have a variety of types of values and attributes.

2 votes

Difference between (Names of ) Symbols and Mathematical Objects

$Version "13.2.0 for Mac OS X x86 (64-bit) (November 18, 2022)" Clear["Global`*"] Assigning a value to OverHat[x] OverHat[x] = 3 (* 3 *) OverHat[x]^2 + 3 OverHat[x] + 1 (* 19 *) Clear the value …
Bob Hanlon's user avatar
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4 votes

Can you use superscripts as variable and function names?

ClearAll["Global`*"] Format indexed variables (Format[#[n_]] := Superscript[#, Row[{"(", n, ")"}]]) & /@ {z, w, a, b}; The function definition is z[1][x_, y_, z_] := x*y + z With your specific a …
Bob Hanlon's user avatar
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2 votes

A problem when solving an equation with symbolic variables

Clear["Global`*"] sol[eq_] := Solve[Cases[eq1, c_ *_Dot :> c, Infinity] == 0]; eq1 = (a[3] - a[4]) ψ . ξ + (a[1] + 2 a[2]) ψ . ϕ; sol[eq1] (* {{a[2] -> -(a[1]/2), a[4] -> a[3]}} *) For the o …
Bob Hanlon's user avatar
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0 votes

Using the symbol of the system of equations

eqns = {x + y + z == 1, x - 2 y + 4 z == 2, x + y == 1}; Grid[{ {Style["{", 18*Length@eqns, Gray], First@eqns}, Sequence @@ ({SpanFromAbove, #} & /@ (Rest@eqns))}, Alignment -> {{Right, "=="}, …
Bob Hanlon's user avatar
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4 votes
Accepted

How can i replace the symbols in a list?

Look at the FullForm of a Rule a -> b // FullForm (* Rule[a, b] *) SeedRandom[1234]; b3 = Thread[{a, b, c, d, e} -> RandomInteger[100, 5]] (* {a -> 8, b -> 72, c -> 44, d -> 38, e -> 22} *) b3 /. …
Bob Hanlon's user avatar
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2 votes
Accepted

Programmatically defining variables

Clear["Global`*"] It is much easier to use an indexed variable and use Format to display the variable any way that you want. For example, to display μ as a subscripted variable Format[μ[n_]] := Subsc …
Bob Hanlon's user avatar
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2 votes
Accepted

How to use the SymbolName of variables along with Map and pure function

Enter values as strings and convert to expressions. EDIT: Added Opacity control Manipulate[ A1 = {-1, 0, 1}; A2 = {Cos[α], Sin[2 α], -2}; With[ {polyw = PolyhedronData[poly, "Polyhedron"]}, G …
Bob Hanlon's user avatar
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0 votes
Accepted

Testing Expression over region of values

Clear["Global`*"] expr1 = ((1 - (a*x))^12)*((1 + (a/b))/((1 + (a*x/b))^2)) // Simplify; Evaluating the integral int = Assuming[0 < a <= 1 && 0 < b <= 1, Integrate[expr1, {x, 0, 1}] // Simplify] …
Bob Hanlon's user avatar
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3 votes

Matrix of functions

Recommend that you consider using an indexed variable. labels = {"A", "B", "C"}; If f[x, y] is distinct from f[y, x] ClearAll[f] Format[f[x_, y_]] := Subscript[f, ToString[x] <> ToString[y]] (m …
Bob Hanlon's user avatar
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4 votes
Accepted

Separating variables in an expression

expr = x z Sin[x] Sin[y]; f = Variables[Level[#, {-1}]] &; If the order is not important Times @@@ GatherBy[List @@ expr, f] (* {x Sin[x], z, Sin[y]} *) If you want them ordered by variable …
Bob Hanlon's user avatar
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8 votes

What are the requirements for a well behaved indexed variable? Subscript, ToExpression, Down...

Using DownValues enables you to format the display in the subscripted form without using Notation and Symbolize (Format[#[n_]] := Subscript[#, n]) & /@ {x, σ, a}; kvar[k_] := Through[{x, σ, a}[k]] …
LCarvalho's user avatar
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3 votes

Free symbols in an expression

x = a + b; y = Defer[x*x + g] + 6 x*c + Pi*d + Sin[a*E]; Variables@Level[y, {-1}] (* {a, b, c, d, g} *) Variables@Cases[y, _Symbol, -1] (* {a, b, c, d, g} *) EDIT: y = Defer[x*x] + HoldFor …
Bob Hanlon's user avatar
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3 votes
Accepted

Replace symbols in output without evaluation

expandNCM[(h : NonCommutativeMultiply)[a___, b_Plus, c___]] := Distribute[h[a, b, c], Plus, h, Plus, ExpandNCM[h[##]] &] expandNCM[(h : NonCommutativeMultiply)[a___, b_Times, c___]] := Most[b] Ex …
Bob Hanlon's user avatar
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