# Questions tagged [algebraic-manipulation]

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

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59 views

### Redundancy in Solve

Solve[{ a a == a a, a^2 == a^2, a a == a a, a^2 == a^2 }] returns ...
1 vote
58 views

106 views

### A remarkable elimination involving the basic reproduction number R0

I have a polynomial pol of third order, whose coefficients depend on 5 parameters, and whose free coefficient is proportional to R0-1, where R0 is a certain rational function of the parameters (the ...
87 views

### Implementing einsum in Mathematica

I've been using Carl Woll's einsum function, but it's missing the ability to handle repeated indices. For instance np.einsum('i,i->i',w, w) will perform a ...
35 views

### Spotting and condensing expressions in output

I am running some symbolic scripts to generate a model problem. One of my outputs is This is generated by the Mathematica code or, in Mathematica format (owing to the fancy lettering and formatting ...
87 views

### Speeding up ComplexExpand

I have a code where I have to take the dot product of two lists, that contain some symbols, and then use ComplexExpand. For a long list it take a very long time and ...
127 views

### Fully expanding and distributing a symbolic sum

I have quite a large expression I want to simplify. For example, this can be generated by a recursive definition: ...
58 views

### Expand tensor expressions with matrix powers and outer products

I would like to have TensorExpand distribute across repeated matrices involving outer products. This question notes that ...
203 views

### Stability analysis of coupled ODE's

I'd like to reproduce Panel A of Figure 7 (red curve) of this paper, which represents the steady-state solutions of four coupled ODE's, and verify this claim that the diagonal branch in the Z-shape ... 125 views

### Solving a system of differential-algebraic equations

I am trying to solve a coupled system of differential-algebraic equations as follows. First define a list of 6 equations ...
1 vote
77 views

### How to help Eliminate simplify simultaneous equations

I have a set of three moderately simple simultaneous equations that I'd like to simplify and eliminate a set of variables for (this is a simple example of a more general class of problem - but I'd ...
78 views

### Compute real and imaginary part of parametrized complex rational expression

I would like to compute the real and imaginary part of a complex valued rational function $Z_b=\frac{1}{\frac{1}{\frac{1}{C_1 \text{i$\omega $}}+L \text{i$\omega $}+R}+C_2 \text{i$\omega $}}$ that ...
72 views

I am trying to manipulate a Hamiltonian with non-commutative operators, $a_j,a_j^\dagger$. After some algebra using NCAlgebra package in Mathematica, I have an expression like, $$H = C_1 (b**a) + C_2 (... 1 vote 1 answer 73 views ### Wrong limit appears [closed] Consider the following limit$$ \lim_{x\to-\infty}x-\sqrt{x^2+7x} $$Going through some algebra leads to$$\begin{align} \lim_{x\to-\infty}x-\sqrt{x^2+7x}&=\lim_{x\to-\infty}\frac{(x-\sqrt{x^2+7x})...
I have the following expansions: $\frac{a+b-\sqrt{a^2-b^2}}{\sqrt{a+b}}$ and $a>b>0$ Obviously we can simplify it further by hand $\sqrt{a+b}-\sqrt{a-b}$, but Mathematica doesn't know how to ...