# Tagged Questions

The art of manipulating an algebraic expression into the desired form.

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### Unexpected result from InverseFunction [closed]

Given the following two equivalent inverse functions, why does one simplify (using inverse functions that are acceptable to me) and the other doesn't? Is there an assumption or setting I can give ...
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### Making multi-linear polynomial change of variables (simplifications) by updating replacementFunction

This is an evolution of one of my previous questions; I've got a partial answer to that question and now have a much cleaner question to ask: Question: What changes to ...
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### Replacing patterns (determinants) in a rational multivariate function and/or getting replacementFunction to work on a multi-linear expression

Given a rational multivariate function known to contain determinants, what is the best way to rewrite the function in terms of the determinants? A simple example: ...
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### How do I use “Factor” to get this form

Here is the default answer. However, I want to get the result which looks like this Here is the Mathematica code: ...
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### how to use Expand command efficiently

Recently I got in a problem and I will try to explain with a simple example. I have an expression which reads : y = (10 + 2*x )/x; Now I want to substitute 1/x ->...
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### Partial fraction decomposition of $1/(e^x-1)$

This link has discussion on finding partial fraction decomposition of $1/(e^x-1)$, so I experimented with Mathematica to see if M can do it, but looks like not. Similar is the case with one more CAS I ...
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### generating random algebraic matrix using elementary operations

I generate several algebraic matrices of 12x12 where each element is a combination no repeat of the variables x, y, z and operations +, -, *, /, power, establishment (square root), any of them or any ...
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### RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
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### build absolute value equations know solution [closed]

We have absolute value equations with unknown coefficients: |x + a| = b and we know solutions: x = 11 and x = 5 We need ...
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### Lagrangian to Hamiltonian

I want to go from Lagrangian description to Hamiltonian one. Using the example given by Mathematica I do something like: ...
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### Expand power of a polynomial

I'm very new to Mathematica, so excuse my innocence. I have the following expression: $$\left( \sum_{n=0}^r \frac{(-1)^n}{n!} y^n \right)^f$$ I would like Mathematica to expand out the expression ...
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Suppose I have a quadratic polynomial in two variables x and y in which the squares with respect to ...
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### ApartSquareFree function

I have a doubt concerning the ApartSquareFree function in Mathematica. Roughly speaking, it is supposed to compute the partial fraction decomposition of a rational function $h/g$ with the denominators ...
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### Function inversion [closed]

I have an expression of this kind ...
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### Replace pattern for exponentials

Ultimately, I want to replace every Exp[(const) w[i,j]] to T[i,j] and Exp[-(const) w[i,j]] to 1/T[i,j] in the following expression ...
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### Pertubation series of given equations

I would like to define a function that does the following. If I have an equation, for example: $$f(x)+[1-f^2(x)]+f^{\prime\prime}(x)+f(x)\ f^\prime(x)=0$$ and I am given a value for $f$ to expand ...
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### Dividing out any constant factor from expression [closed]

How do I divide out any constants from an expression? Let's say: $2A+4B+2C+6 \rightarrow A+2B+C+3$ What's the right command for this? I have been using ...
### Forcing Mathematica to Output $1/\sqrt2$ as $\sqrt2/2$
I am trying to force Mathematica to output $\frac{1}{\sqrt2}$ as $\frac{\sqrt2}{2}$. I tried: {1, Sqrt[2]}*Sqrt[2] Which outputs: ...