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Define and solve formula syntax problem

Karl S

Posted 4 years ago

POSTED BY: Karl S

7 Replies

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 4 years ago

I am getting no errors: Kramer[Z_, \[Lambda]_, T_, x_] := 10810^-4Z* Log[Konst[\[Lambda]]]/((T/100)^(3/ 2)\[Lambda]^2)((electrondensity[x, Z, Avog])/(electrondensitycrit[\[Lambda]]))^2; Integrate[Kramer[Z, \[Lambda], T, x], x]

I am getting no errors:

Kramer[Z_, \[Lambda]_, T_, x_] := 
  108*10^-4*Z*
   Log[Konst[\[Lambda]]]/((T/100)^(3/
         2)*\[Lambda]^2)*((electrondensity[x, Z, 
        Avog])/(electrondensitycrit[\[Lambda]]))^2;
Integrate[Kramer[Z, \[Lambda], T, x], x]

POSTED BY: Gianluca Gorni

Karl S

Posted 4 years ago

Kramer[Z_, \[Lambda]_, T_, x_] := 10810^-4Z* Log[Konst[\[Lambda]]]/((T/100)^(3/ 2)\[Lambda]^2)((electrondensity[x, Z, Avog])/(electrondensitycrit[\[Lambda]]))^2; Plot[Integrate[Kramer[12, 10.6, 30, x], x], {x, 0, 40}] I get SetDelayed::write: Tag Times in (5.2061710^-6 [Lambda]^2 Log[6.5737410^25 [Lambda]] Z)[Z,[Lambda],T,x_] is Protected. and the plot is empty

Kramer[Z_, \[Lambda]_, T_, x_] := 
      108*10^-4*Z*
       Log[Konst[\[Lambda]]]/((T/100)^(3/
             2)*\[Lambda]^2)*((electrondensity[x, Z, 
            Avog])/(electrondensitycrit[\[Lambda]]))^2;
    Plot[Integrate[Kramer[12, 10.6, 30, x], x], {x, 0, 40}]

I get

SetDelayed::write: Tag Times in (5.20617*10^-6 [Lambda]^2 Log[6.57374*10^25 [Lambda]] Z)[Z,[Lambda],T,x_] is Protected.

and the plot is empty

POSTED BY: Karl S

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 4 years ago

You must give a numerical value `Avog` and decide what function is `Konst`. Also, you must wrap Integrate in `Evaluate`, to avoid the trap of the order of evaluation: electrondensity[x_, Z_, Avog_] := (7AvogZ)/(118)(1/x)^3; electrondensitycrit[\[Lambda]_] := 1.1 10^21/\[Lambda]^2; Kramer[Z_, \[Lambda]_, T_, x_] := 10810^-4Z Log[Konst[\[Lambda]]]/((T/100)^(3/ 2)\[Lambda]^2)((electrondensity[x, Z, Avog])/(electrondensitycrit[\[Lambda]]))^2; Block[{Konst = Identity, Avog = Quantity[1, "AvogadroConstant"] // QuantityMagnitude}, Plot[Evaluate[Integrate[Kramer[12, 10.6, 30, x], x]], {x, 0, 40}]]

You must give a numerical value Avog and decide what function is Konst. Also, you must wrap Integrate in Evaluate, to avoid the trap of the order of evaluation:

electrondensity[x_, Z_, Avog_] := (7*Avog*Z)/(118)*(1/x)^3;
electrondensitycrit[\[Lambda]_] := 1.1 10^21/\[Lambda]^2;
Kramer[Z_, \[Lambda]_, T_, x_] := 
  108*10^-4*Z*
   Log[Konst[\[Lambda]]]/((T/100)^(3/
         2)*\[Lambda]^2)*((electrondensity[x, Z, 
        Avog])/(electrondensitycrit[\[Lambda]]))^2;
Block[{Konst = Identity, 
  Avog = Quantity[1, "AvogadroConstant"] // QuantityMagnitude}, 
 Plot[Evaluate[Integrate[Kramer[12, 10.6, 30, x], x]], {x, 0, 40}]]

POSTED BY: Gianluca Gorni

Rohit Namjoshi

Posted 4 years ago

Probably because of preexisting conflicting definitions. Quit the kernel and start over. Integrate[Kramer[12, 10.6, 30, x], x] (* -((7.4229110^-42 Avog^2 (50.0099 + Log[T]))/x^5) ) `Avog` and `T` do not have numeric values so a `Plot` cannot be generated.

POSTED BY: Rohit Namjoshi

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 4 years ago

Also, beware of the expression `4T/100 \[Lambda]2 \[Pi]`. Mathematica reads it as `4(T/100) \[Lambda]2 \[Pi]`, which may not be what you have in mind.

POSTED BY: Gianluca Gorni

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 4 years ago

This works well enough for me: electrondensity[x_, Z_, Avog_] := (7AvogZ)/(118)*(1/x)^3 electrondensitycrit[\[Lambda]_] := 1.1 10^21/\[Lambda]^2; Solve[electrondensity[x, 12, Avog] == electrondensitycrit[10.6], x, Reals] It is somewhat tricky, because Mathematica may interpret the cubic root in the complex sense, while you may expect real values only. As for indicating the variables, it depends on what you want to do with the formula. Do you need only to display it, or for actual calculation?

POSTED BY: Gianluca Gorni

Karl S

Posted 4 years ago

Ok this works for me also now. electrondensity[x_, Z_, Avog_] := (7AvogZ)/(118) * (1/x)^3 electrondensitycrit[\[Lambda]_] := 1.1 10^21/\[Lambda]^2 Konst[\[Lambda]_] := 4T/(100 \[Lambda]2 \[Pi])/(0.5776.62610^-34 310^8) I want to integrate the following formula for x: Kramer[Z_, \[Lambda]_, T_, x_] := 10810^-4 Z Log[Konst[\[Lambda]]]/((T/100)^(3/ 2)\[Lambda]^2 ) ((electrondensity[ x])/(electrondensitycrit[\[Lambda]]))^2 However, with defining this equation, the error: SetDelayed::write: Tag Times in (5.2061710^-6 [Lambda]^2 Log[6.5737410^25 [Lambda]] Z)[Z,[Lambda],T,x_] is Protected. occurs with the output: $Failed

Ok this works for me also now.

electrondensity[x_, Z_, Avog_] := (7*Avog*Z)/(118) * (1/x)^3
electrondensitycrit[\[Lambda]_] := 1.1 10^21/\[Lambda]^2
Konst[\[Lambda]_] := 
 4*T/(100 *\[Lambda]*2 \[Pi])/(0.577*6.626*10^-34 *3*10^8)

I want to integrate the following formula for x:

Kramer[Z_, \[Lambda]_, T_, x_] := 
 108*10^-4 *Z * 
  Log[Konst[\[Lambda]]]/((T/100)^(3/
        2)*\[Lambda]^2 ) *((electrondensity[
       x])/(electrondensitycrit[\[Lambda]]))^2

However, with defining this equation, the error:

SetDelayed::write: Tag Times in (5.20617*10^-6 [Lambda]^2 Log[6.57374*10^25 [Lambda]] Z)[Z,[Lambda],T,x_] is Protected.

occurs with the output: $Failed

POSTED BY: Karl S

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