# Questions tagged [algebraic-manipulation]

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

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### Factor constants out of multiple dot products

I have expressions of the type (-y A.A).(-y A.A).(A x).(A x) (* Example 1 *) (-y A.A).(-y A.A).(A x) (* Example 2 *) The number of parenthesis factors can vary, ...
29 views

### Simplify argument of Logs

I have the following expression ...
172 views

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### Transform a list of delayed rules with conditions to a new list of delayed rules

I have a list of rules that implement some abstract algebras, for instance, that of the Pauli matrices, ...
431 views

### Present a logarithm in terms of two logarithms

If $\log _8 3=p$ and $\log _3 5=q$ then, in terms of $p$ and $q$, what does $\log _{10} 5$ equal? I tried by my hand, I get the answer is $\dfrac{3pq}{1+3pq}$. How can I tell Mathematica solve ...
202 views

### How to Replace 'delta t' with 'a' in Mathematica Without Affecting Separate Instances of 'delta' or 't'?

In Mathematica, how can I replace instances of delta t in an expression with a, while keeping instances of ...
1 vote
156 views

### Converting expression to quadratic formula

I want to manipulate and represent the following expression in a more presentable way. ...
115 views

### Kernel Crash Using Solve

The following code crashes the Kernel with no error message. ...
43 views

### On MacOs, I cannot use Needs["QDENSITYQdensity"]

I am trying to get Needs["QDENSITYQdensity"] from (https://library.wolfram.com/infocenter/MathSource/5715/), however, it failed and I get this error: ...
329 views

### Most concise code for tangent and normal line of implicit algebraic curve

Can you make the code for tangent line and normal line of implicit algebraic curve cu more concise than mine? The code for tangent line at ...
1 vote
114 views

### Selecting coefficients of multivariable polynomial

We have polynomial in three variables x, y, z. How to list all coefficients of odd powers of z or ...
59 views

### Function to generate analytic solution of StandardDeviation of a list given sublists

Motivation I have the Mean and StandardDeviation of several lists of equal size but I don't know the elements of those lists. I ...
78 views

### Unexpected behavior of Exponent

According to Exponent: Exponent[expr, form] gives the maximum power with which form appears ...
67 views

176 views

### How can expanding trigonometric function retain an expression?

I want to expand this trigonometric function Sin[π/4 + α - β] such that $\alpha - \beta$ is treated as "one" expression, resulting in ...
75 views

Is there an easy way to all remove radicals from a denominator? I would like a function, say RemRadsFromDenom that, e.g., transforms $\frac{1-\sqrt{3}}{1+\sqrt{3}}$ ...
1 vote
80 views

### Why GroebnerBasis fails to reduce a system to one scalar equation, when I can almost do it by hand?

I have a system of five equations (Behn's model of CD4+T/APC interaction). The last four yield rational solutions in x1, so I can plug these in the first equation ...
1 vote
54 views

### How to simplify a long expression by introducing a specific substitution?

I have just started using Mathematica, so I am still familiarising myself with it. Now here is my issue: I have a matrix G, which looks something like: ...
39 views

### How to perform splitting?

Apart[(n + 2)/(n (n + 1) 2^n), n] get the result: 2^(1 - n)/n - 2^-n/(1 + n) How to split the term to this form? ...
1 vote
59 views

### Decide whether a system of polynomial equalities and inequalities is feasible? [closed]

Consider a system of polynomial equations $f_1(x) = ... = f_n(x) = 0$ and polynomial inequalities $g_1(x), ... ,g_m(x) \ge 0$. All polynomials are in rational coefficients, $x = (x_1, ... , x_l)$ is ...
176 views

### How to convert a fractional into an integral equation?

(y1 - 1)/(x1 - 2) + (y2 - 1)/(x2 - 2) == 0 How to convert a fractional equation into an integral equation? to get the result: ...
101 views

### How to optimize the code for deriving the standard equation of the Apollonian circle?

The distance from a moving point in the plane to (0,0) is lambda times the distance from (a, 0). And lambda is not equal to 1. Find the equation The standard equation form for a circle is: ...
264 views

### Extract monomials with a certain structure from a given polynomial

I have a long polynomial such as a x^2+ bx^2y+cx^2y^2 +d x^3y^4+e x^4y^3+f y^2+g xy^2 Consider an example problem as follows: I want to output the monomials (along ...
1 vote
86 views

### How to automatically move roots with coefficients to the right of the equation?

How can I move one term with Sqrt to the right side of equation? The root of the previous problem does not have a coefficient in front of it, so using the previous code for this problem has no effect. ...
1 vote
111 views

### How can I move one term with Sqrt to the right side of equation?

How can I automatically identify the term containing a radical (Sqrt[x^2 + (2 + y)^2]) in an equation and move it to the right side: ...