Questions tagged [algebraic-manipulation]
The art of manipulating an algebraic expression into the desired form.
740
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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, ...
- 239
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0
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29
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4
votes
3
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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:
$$\frac{4 \sin (2 \pi x)}{\pi }+\frac{4 \sin (6 \pi x)}{3 \pi }+\frac{4 \sin (10 \pi
x)}{5 \pi }+...
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votes
3
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How to factorize $x+y$ in this kind of example?
Consider the following simple polynomial in two variables 5 + 2x + 2y. Suppose I want to simplify it to 5+2(x+y). I have no idea ...
- 481
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5
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How to make ReplaceAll recognize what to be replaced in a situation like this?
I'm a bit confused on how ReplaceAll works. For example
ReplaceAll[2x+2y, x+y -> 1]
just gives ...
- 481
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0
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78
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Output a 24 by 24 Leech lattice
Input a rank-8 $E_8$ lattice,
$$
M_{E_8}=\begin{pmatrix}
2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
-1 & 2 & -1& 0 & 0 & 0 & 0 & 0 \\
0 &...
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1
answer
40
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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,
...
- 513
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 ...
- 1,000
5
votes
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 ...
- 215
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vote
2
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Converting expression to quadratic formula
I want to manipulate and represent the following expression in a more presentable way.
...
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1
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0
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0
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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:
...
- 1
4
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5
answers
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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 ...
- 9,933
1
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3
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114
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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 ...
- 9,933
0
votes
1
answer
59
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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 ...
7
votes
0
answers
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Unexpected behavior of `Exponent`
According to Exponent:
Exponent[expr, form] gives the maximum power with which form appears ...
- 453
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votes
2
answers
67
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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 $...
- 119
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:
...
- 159
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:
...
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1
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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 ...
- 695
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1
answer
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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 $x^6+2x+3$.
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4
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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 ...
- 137k
1
vote
1
answer
29
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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 ...
- 113
0
votes
1
answer
75
views
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 ...
- 1
2
votes
2
answers
85
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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 ...
- 8,135
3
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0
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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 ...
- 1,642
3
votes
2
answers
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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 ...
- 132
1
vote
3
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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 ...
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 ...
- 1,874
2
votes
1
answer
104
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Simplifying expression with many radicals
Are there tools in Mathematica to simplify the following expression further, for $0<x<1$?
...
- 8,135
0
votes
1
answer
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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 ...
- 3
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 $m\times m$
...
- 13
5
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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 ...
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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 ...
- 304
2
votes
2
answers
296
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Is there a Mathematica function that puts a list of numbers in a normalized [1, 10[ scale
I have the following list:
...
0
votes
1
answer
85
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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 ...
1
vote
1
answer
49
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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_{...
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votes
2
answers
176
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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
...
- 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
$\frac{1-\sqrt{3}}{1+\sqrt{3}}$ ...
- 1,470
1
vote
0
answers
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 ...
- 1,642
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:
...
- 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?
...
- 2,905
1
vote
0
answers
59
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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 ...
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3
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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:
...
- 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:
...
- 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 ...
- 660
1
vote
1
answer
86
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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.
...
- 2,905
1
vote
1
answer
111
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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:
...
- 2,905
2
votes
2
answers
125
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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 <...
- 2,905
1
vote
0
answers
52
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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?
...
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