Questions tagged [algebraic-manipulation]
The art of manipulating an algebraic expression into the desired form.
762
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Putting a polynomial into a multilinear form
Consider the polynomials in $x$ with positive-integer parameters $a,b,c$
...
- 181
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0
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40
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Factoring Custom Tensor Products
I have now made a post on the Computer Science stack exchange that talks about the general problems from an algorithmnic perspective here.
I have defined a custom tensor product function ...
- 101
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2
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45
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How to impose distributivity over custom tensor product
I have written a custom tensor-like product called "TProduct[a,b]"
...
- 101
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0
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38
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Simplifying fractional powers and collecting coefficient list from it
Problem
I want to generalize a solution I already have for a simpler situation. In my case I need to collect coefficients from a variable assuming fractional powers and on. First I'll present some ...
- 175
2
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1
answer
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How to use Sum properly to avoid problems when the summating limits are undefined?
I'm struggling in the use of Sum.
I want to define something like that:
...
- 175
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0
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82
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Is there an easy way to understand how to manipulate summations?
I'm working in a very very long calculation that could be done by hand but it might be tedious. Moreover, when doing by hand that amount of calculations I'm subject to errors, of course. Then I ...
- 175
2
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3
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Converting an algebric expression into a matrix form
Consider the following expression:
a1 b1 c1 + a4 b2 c1 + a7 b3 c1 + a2 b1 c2 + a5 b2 c2 + a8 b3 c2 +
a3 b1 c3 + a6 b2 c3 + a9 b3 c3
Can Mathematica convert it ...
- 575
0
votes
1
answer
74
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Separable decomposition $F(r,\theta) = A(r) + B(\theta)$ [closed]
Is it possible in Mathematica to take a function $F(r, \theta)$ and ask it to rewrite it as $F(r,\theta) = A(r) + B(\theta)$? In particular, I have the expression:
$$ \frac{g^{2} (r) f^{2} (r) \sin^{2}...
- 157
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2
answers
103
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Multiple replacements in a long expression
Why does the replace /. not work on the second argument in the following expression:
...
- 575
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1
answer
108
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How to write an expression as a ratio of polynomials [closed]
I have the following Mathematica expression as a result of some calculations:
...
- 347
1
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0
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77
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Function to express Piecewise as UnitStep functions
Is there a documentation for the function Simplify`PWToUnitStep? This is a function which can be used to express a Piecewise ...
- 405
4
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1
answer
169
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What's the reverse operation of TransferFunctionExpand?
Given a transfer funtion
TransferFunctionModel[1/(s + I) + 1/(s - I) + 1/(s + 1) + 1/(s - 2)^2,s]
we can obtain the polinomial form by using TransferFunctionExpand
...
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1
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Is it possible to express $\text{Li}_2(-\frac18(-i+\sqrt{15})+\text{Li}_2(\frac18 (i+\sqrt{15})$ as an explicit real expression (not numeric)? [closed]
I obtain this expression in my calculations, and numerically I am sure that it is a real number.
...
- 195
0
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1
answer
57
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Convergent Taylor series unrecognized by Sum
I am trying to understand why Sum does not recognize a particular Taylor series as convergent. I have defined a function 'series' like this, that computes the Taylor series of a function 'f' at 'x', ...
- 196
10
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4
answers
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Visualizing Wicks' contractions using brackets
Given a string like MMMM, what is the easiest way to draw all Wicks contractions similar to the diagram below (from Ch. 2 of Eynard paper)? Example below is for (MMMM), but I need it to work for other ...
- 8,041
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Separate exponentials [duplicate]
Good afternoon,
I have an expression
Exp[2 I (t - tau) + a] + 2 Exp[2 I t + b] + 3 Exp[-I t + b]
And I want to write it as a summation of powers of Exp[I t]. So,
<...
- 41
2
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0
answers
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Equivalent of `MomentConvert` for free moments/free cumulants? [closed]
I'm looking for Mathematica implementation of conversion between free moments and free cumulants.
For instance, for traditional moments we have from ...
- 8,041
3
votes
2
answers
104
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Closed-Form Solution for k-ary Tree Traversal Order
I was reading this blog post (https://research.swtch.com/treenum) that proposes a new base-k ordering for k-ary trees - I found myself wondering: is it possible to use Mathematica to solve a ...
- 153
5
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1
answer
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Quantum Field Regularization: Choice between ExpIntegralE and Gamma for Casimir Effect
For the Casimir effect with exponential regularization, we compute the vacuum energy between the plates (somewhat simplified) with:
$$\omega = c\ \sqrt{q^2+k_z^2}$$
$$ E = \sum_{k_z=n\pi/a} 2 \int\...
- 307
2
votes
1
answer
198
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How can I get stronger simplification than FullSimplify?
Short description: Is there a simplification that can for a>1 simplify
...
- 307
4
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2
answers
213
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Putting a term under the square root
I want to put a term under the square root (but with Mathematica), such that
$$(1+t)^2\sqrt{1+\frac{t^3}{(1+t)^3}}$$
is transformed to
$$\sqrt{(1+t)^4+(1+t)t^3}.$$
I've tried all the forms of ...
- 1,894
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4
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365
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Getting formulas like $E[\operatorname{Tr}(A^3 (A^T)^3]=n^4+10n^2+4n$
Suppose $A$ is an random $n\times n$ matrix with standard normal entries.
A user was able to obtain the following formula by enumerating all diagrams by hand:
$$E[\operatorname{Tr}(A^3 (A^T)^3]=n^4+...
- 8,041
0
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1
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56
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How to factorize high-order polynomials that have only complex roots?
I have polynomials like this:
...
- 215
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1
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68
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Algebraic replacement [duplicate]
How do I replace an algebraic expression with a symbol? I'm trying to replace repeated terms such as $(a+b)$ with c, for example, so that $x(4a + 4b) + x^2(6a + 6b)$ becomes $x4c + x^26c$ .
3
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Expressing equation in terms of a ratio between two variables
I have
x = (-2 h^2 k - 2 h k^2 - k^3 - Sqrt[8 h^4 k^2 + 16 h^3 k^3 +
14 h^2 k^4 + 6 h k^5 + k^6])/(2 h^2 + 2 h k + k^2)
which has ...
- 61
3
votes
1
answer
108
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Factor constants out of multiple dot products
I have expressions of the type
(-y A.A).(-y A.A).(A x).(A x) (* Example 1 *)
(-y A.A).(-y A.A).(A x) (* Example 2 *)
The number of parenthesis factors can vary, ...
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45
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4
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3
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Automatically extract a factor from a sum of terms and rewrite the sum
I would like to automatically extract the same factor of each term, and thus write a sum such as:
$$\frac{4 \sin (2 \pi x)}{\pi }+\frac{4 \sin (6 \pi x)}{3 \pi }+\frac{4 \sin (10 \pi
x)}{5 \pi }+...
- 42.1k
2
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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 ...
- 553
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6
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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 ...
- 553
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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
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51
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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,
...
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5
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1
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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 ...
- 1,088
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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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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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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
votes
5
answers
340
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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 ...
- 20.9k
1
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3
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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 ...
- 20.9k
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1
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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
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1
answer
105
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Unexpected behavior of `Exponent`
Fixed in Version 14.0
According to Exponent:
Exponent[expr, form] gives the maximum power with which ...
- 505
0
votes
2
answers
78
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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
57
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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:
...
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2
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2
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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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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 ...
- 735
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1
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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 ...
- 149k
1
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1
answer
35
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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
1
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1
answer
126
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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 ...
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