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, ...
Ben's user avatar
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Simplify argument of Logs

I have the following expression ...
BabaYaga's user avatar
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4 votes
3 answers
172 views

Automatically extract a factor from a sum of terms and rewrite the sum

I would like to automatically extract the same factor of each term, and thus write a sum such as: $$\frac{4 \sin (2 \pi x)}{\pi }+\frac{4 \sin (6 \pi x)}{3 \pi }+\frac{4 \sin (10 \pi x)}{5 \pi }+...
David G. Stork's user avatar
2 votes
3 answers
84 views

How to factorize $x+y$ in this kind of example?

Consider the following simple polynomial in two variables 5 + 2x + 2y. Suppose I want to simplify it to 5+2(x+y). I have no idea ...
user1620696's user avatar
4 votes
5 answers
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How to make ReplaceAll recognize what to be replaced in a situation like this?

I'm a bit confused on how ReplaceAll works. For example ReplaceAll[2x+2y, x+y -> 1] just gives ...
user1620696's user avatar
0 votes
0 answers
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Output a 24 by 24 Leech lattice

Input a rank-8 $E_8$ lattice, $$ M_{E_8}=\begin{pmatrix} 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\ -1 & 2 & -1& 0 & 0 & 0 & 0 & 0 \\ 0 &...
zeta's user avatar
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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, ...
Lelouch's user avatar
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5 votes
1 answer
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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 ...
Laurenso's user avatar
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1 answer
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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 ...
Tokubara's user avatar
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1 vote
2 answers
156 views

Converting expression to quadratic formula

I want to manipulate and represent the following expression in a more presentable way. ...
Dotman's user avatar
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1 answer
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Kernel Crash Using Solve

The following code crashes the Kernel with no error message. ...
Just Some Old Man's user avatar
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On MacOs, I cannot use Needs["QDENSITY`Qdensity`"]

I am trying to get Needs["QDENSITY`Qdensity`"] from (https://library.wolfram.com/infocenter/MathSource/5715/), however, it failed and I get this error: ...
Xui Lao's user avatar
4 votes
5 answers
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 ...
azerbajdzan's user avatar
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1 vote
3 answers
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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 ...
azerbajdzan's user avatar
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1 answer
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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 ...
IntroductionToProbability's user avatar
7 votes
0 answers
78 views

Unexpected behavior of `Exponent`

According to Exponent: Exponent[expr, form] gives the maximum power with which form appears ...
user688486's user avatar
0 votes
2 answers
67 views

How to define an infinite dimensional algebra with a known basis and multiplication rule?

My goal is to do symbolic calculations in the noncommutative associative algebra generated by two elements $x,y$ satisfying the relation $x.y=q~y.x$. This infinite dimensional algebra has the basis $...
Lagrenge's user avatar
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2 votes
1 answer
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Creating a boolean expression of assumptions between variables

I'm trying to create a boolean expression from a list of lists of variables such that the elements of one list are not equal to the elements of all other lists. I thought this might work: ...
David's user avatar
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2 votes
2 answers
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How to approximate the distance from {x,y} to a hyperbola?

I can get a good approximation, but making this into a MMA algorithm is getting complicated. Consider this example: ...
Ted Ersek's user avatar
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How to factor a quartic equation whose coefficient has unknown parameters?

i'm trying to see if a quartic equation I obtained can be factored into simpler forms, such as the product of two quadratics. The problem is that their coefficients are some complex expressions in ...
larry's user avatar
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4 votes
1 answer
218 views

Working in Mathematica over a cyclotomic ring [closed]

How can I simplify expressions in $\mathbb Q[x]/(x^7-1)$ in Mathematica, i.e. make Mathematica transform $x^{20}+x^8+x+3$ into $x^6+2x+3$.
Adam's user avatar
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17 votes
4 answers
776 views

What is Mathematica's equivalent to Maple's collect with distributed option?

Given a polynomial in $x,y$, I want to collect on $x,y$ and any products of these also. As given using Maple's collect with the distributed option. Currently Mathematica will collect on $x$ then ...
Nasser's user avatar
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1 vote
1 answer
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Validate equalities among Square roots for a simple expression

I am trying to validate this property: $\sqrt{1-z}=\sqrt{-(-1+z)}=(\text{}\pm i) \sqrt{-1+z}$ FullSimplify[Sqrt[1 - z] == I Sqrt[(-1 + z)]] I have seen how we need ...
Jmtz's user avatar
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1 answer
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How to obtain approximate form for a calculation using Mathematica with specific approximations?

I am currently working on a calculation in Mathematica that involves various parameters, including Nb, k, and Ns. I want to obtain an approximate form of the calculation by considering the following ...
Sagar's user avatar
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2 votes
2 answers
85 views

Grouping expressions by their $O(..)$ rate of growth around 0

Given a list of expressions like $3 x^2,\frac{\sqrt{x}}{\sqrt{2}},\frac{2 \sqrt{x}}{\pi },\frac{9 x^3}{2},x,$, how could I group them based on their rates of growth around 0? IE, $2x$ and $3x$ are ...
Yaroslav Bulatov's user avatar
3 votes
0 answers
44 views

Can we ask Mathematica if a reduction of a system to one scalar equation in one variable+ rational representations of the other variables exists?

Nonlinear determined systems have typically several solutions involving square or higher order roots. Instead of solving them, it may be more profitable to reduce them to smaller systems with fewer ...
florin's user avatar
  • 1,642
3 votes
2 answers
183 views

Decoupling a system of four linear $1$-st order ODEs

I have a system of four $1$-st order ODEs. $$ \dot{p_1} = -2\beta^2 q_1 - \gamma p_1 + \Delta p_2 $$ $$ \dot{p_2} = -2\beta^2 q_2 - \gamma p_2 + \Delta p_1 $$ $$ \dot{q_1} = 2\alpha^2 p_1 + \gamma q_1 ...
Kazi Abu Rousan's user avatar
1 vote
3 answers
143 views

Expanding a complex number

How does one get Mma to expand (1/2 + I/2)/Sqrt[2] into 1/(2 Sqrt[2]) + I/(2 Sqrt[2]) Even evaluating this second expression ...
Mariano Suárez-Álvarez's user avatar
1 vote
1 answer
48 views

Factoring without need to guess the extension

To provide a simple example (but I need more complicated ones): I want to factor x^2-6x*y+y^2. After solving x^2-6x*y+y^2==0 I ...
მამუკა ჯიბლაძე's user avatar
2 votes
1 answer
104 views

Simplifying expression with many radicals

Are there tools in Mathematica to simplify the following expression further, for $0<x<1$? ...
Yaroslav Bulatov's user avatar
0 votes
1 answer
55 views

What's a good way to do specific algebraic operations on an expression?

This is the first time I've submitted a question so please forgive my inexperience. I want to simplify the following expression Cos[ArcTan[Xt/Rt]] which is ...
Pat Lane's user avatar
1 vote
1 answer
90 views

How can I solve/verify the following matrix?

Given $ZFZ’ = C$, I have the following set of symbolic matrices: $Z$ of order $m\times q$ $Z’$ is the transpose of matrix $Z$ of order $q\times m$ $F$ of order $q\times q$ $C$ of order $m\times m$ ...
EVC's user avatar
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5 votes
0 answers
134 views

How to highlight internal symmetries while simplifying a symbolic expression?

Context I would like to have a function which symmetrizes and simplifies a symbolic expression to highlight its internal symmetries. I believe such a function would be extremely useful for post ...
chris's user avatar
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2 votes
1 answer
49 views

Replace coefficients with RootApproximant of themselves

I have an expression, not necessarily a polynomial, and want to take all the coefficients on whatever terms there are and replace them with the RootApproximant ...
D. Brown's user avatar
  • 304
2 votes
2 answers
296 views

Is there a Mathematica function that puts a list of numbers in a normalized [1, 10[ scale

I have the following list: ...
Granger Obliviate's user avatar
0 votes
1 answer
85 views

Simplifying expression and arranging terms in power of exponent

I have lots of expressions like below which I want to simplify but I am not sure how to do it in Mathematica. I am looking to simplify them in the form of $\Sigma _i A_i e^{y_i}$ where $A_i$ will be ...
Navneet M's user avatar
1 vote
1 answer
49 views

A problem with the evaluation of expressions using assumptions through Mathematica

I want to evaluate the expression below, $((2 (a_{01}+2 ya_{02}+x a_{11})^2+(b_{01}+2 y b_{02}+x b_{11})^2) (2 (a_{10}+y a_{11}+2 x a_{20})^2+(b_{10}+y b_{11}+2 x b_{20})^2))$, at $x=-((2 (2 a_{02}a_{...
VH84's user avatar
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3 votes
2 answers
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 ...
csn899's user avatar
  • 2,905
2 votes
1 answer
75 views

Removing radicals from denominator

Is there an easy way to all remove radicals from a denominator? I would like a function, say RemRadsFromDenom that, e.g., transforms $\frac{1-\sqrt{3}}{1+\sqrt{3}}$ ...
Gert's user avatar
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1 vote
0 answers
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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 ...
florin's user avatar
  • 1,642
1 vote
1 answer
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: ...
Q.Ask's user avatar
  • 15
0 votes
1 answer
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? ...
csn899's user avatar
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1 vote
0 answers
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 ...
giulio bullsaver's user avatar
2 votes
3 answers
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: ...
csn899's user avatar
  • 2,905
0 votes
2 answers
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: ...
csn899's user avatar
  • 2,905
4 votes
4 answers
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 ...
cleanplay's user avatar
  • 660
1 vote
1 answer
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. ...
csn899's user avatar
  • 2,905
1 vote
1 answer
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: ...
csn899's user avatar
  • 2,905
2 votes
2 answers
125 views

How can I automatically identify the type of free term in an equation and shift it?

How can I automatically identify the type of term in an equation and shift it to the left of the equal sign in this equation? The quadratic terms containing x and <...
csn899's user avatar
  • 2,905
1 vote
0 answers
52 views

Mathematica reacts to a wrong condition in a weird way

With apologies, I evaluated the eigenvalues of a matrix under a condition which included wrongly some Falses. The weird result was a failure to obtain the eigenvalues? ...
florin's user avatar
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