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Questions tagged [algebraic-manipulation]

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

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0answers
29 views

Factoring explicit quantities

I'm wondering if there is a way I can explicitly factor an equation into separate chunks. For example, if I have ...
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3answers
22 views

Storing solution of equation and performing operation

I have the following equations which I solve to find a and b. ...
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1answer
34 views

Changing variables to obtain derivatives of new variables [duplicate]

Let's say that I have some symbolic expression of a function $x(t)$, and would like to obtain its derivative $x'(t)$. However, I also have the following two identities, $\xi = \omega t$, and $\eta = ...
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1answer
30 views

Neglect terms of order $1/n$

I have expressions like the following $A+B/n+C/n^2+\cdots,Z/n^p$. I'd like to keep just the first two terms, i.e., $A+B/n,$ however it seems that using the command O[1/n^2] is not working. The ...
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2answers
40 views

Collect term in a distributive way

Consider P = x (a2 b2 v^a2-1+a3 b3 v^a3-1+d1+d2-2 y)-(y-d1)(y-d2)-x I would like to collect terms in (x,y,z) in a distributive way, that is to get an expression ...
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1answer
124 views

How to implement split-complex numbers?

For those who do not know, the split-complex numbers are an analogue to the complex numbers where J is defined such that $J^2=1$ but $J\ne\pm1$, so they are all of the form $a+bJ$. By using ...
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1answer
71 views

How to distribute rules?

For example i want to have following equation : Det[A B C]=Det[A] Det[B] Det[C] What is the simplest way to distribute automatically?
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5answers
302 views

Reconstructing a polynomial from its coefficient array

A polynomial coefficient matrix: mat = CoefficientList[3 + 5 x^3 + 4 y^3 + 2 x + 6 x^2 y + 7 x y^2 + 8 x y, {x, y}]; \begin{equation} \left( \begin{array}{...
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1answer
54 views

Computing the seven roots of a polynomial

This question was originally asked by @fsrong70 six months ago. The OP deleted it shortly after posting and has not returned to this site since. I had just figured it out when it was deleted. I ...
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0answers
45 views

Commutator of differential operators

Let $P_x = \frac{\hbar}{i}\frac{d}{dx}$, after specifying the commutator relation symbolically $[X, P_x] = i\hbar$, I can ask Mathematica to calculate commutator algebra. My question: is there a way ...
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1answer
32 views

Solving an equation

I need to solve the following equation (expr = 0) for "A", but looks like Solve and Reduce struggle. All parameters are positive, and "expr" is given below. (I suspect the issue might be due to powers ...
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1answer
49 views

Compare algebraic equivalence (regardless of term order) without having to simplify? [closed]

I know that in order to find the equivalence of say $ a+b $ and $ b+a $, then: FullSimplify[a + b == b + a] is sufficient. However, suppose I want to compare ...
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1answer
62 views

List from algebraic expression?

Consider an algebraic expression exp = a x^2 -b x +c I want to create a list from its element: list = {a x^2, -b x, c} Is ...
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0answers
76 views

Surprising result using operator form of FoldList [closed]

I was trying to implement some Graph related functions in Functional form and came accross this result which I found surprising. I want a function that does various operations on a graph. The ...
3
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2answers
106 views

Replace $ z z^* $ by $ |z|^2 $

I have a long expression involving different complex numbers. I want to force Mathematica to replace z Conjugate[z] by Abs[z]^2 ...
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1answer
41 views

Extracting parts of symbolic expressions

I've searched around and found things that could help me only in cases that are simpler than the one I had in mind. I would like to extract polynomials from expressions that schematically look like $$...
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0answers
31 views

Manipulating Equations: Substracting two equations

I was wondering why I fail to substract two equations using thread, while it works properly, as described here for additions. Example: Let a system of equations be given: ...
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1answer
37 views

Output of Apart as a list?

I have a rational funtion of one variable that I know will always have a simple partial fraction decomposition of the form $$\sum_{n=1}^N\frac{\alpha_n}{z- \beta_n},$$ but I do not know the values ...
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3answers
83 views

Finding the integer terms of a binomial expansion [closed]

What functions can I use to find how many integer terms the following expression has? $$\left (\sqrt[19]{19}+\sqrt[95]{95}\right )^{1995}$$ Edit 1 In the development of that binomial, at some point ...
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3answers
52 views

Eliminating radicals from denominator or numerator of an expression

I need to find the limit when r2 tends to r1 of the following expression: ...
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0answers
20 views

Pauli matrix dot momentum in _feyncalc_

So I want to perform a dot product of a Pauli matrix (vector form) and momentum (also a vector) in feyncalc. How would I do that?. And next question is: Can feyncalc show gamma matrices in terms of ...
3
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1answer
93 views

rational parameterization of a plane curve

Say one has a plane curve defined by a polynomial equation $$P(x,y)=0$$ and one knows that the curve has genus 0. Is there an implementation in Mathematica of a (proper) rational parameterization, i.e....
2
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1answer
46 views

FindInstance for all real values satisfying a condition

I seek at least one instance of positive fractions $p,q,r$ where $p,q,r \in \mathbb{Q}^+$, for which $$\frac12 (a - 2 b + c)^2 \ge pa^2 + qb^2 + rc^2\quad \forall\ a,b,c \in \mathbb{R}.$$ I used this ...
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1answer
36 views

Proofs and exponents to the N power

I'm still a beginner at Mathematica and I'd like to understand how to use it for proofs. Here is a simple one on exponent properties (a*b)^n == a^n*b^n I tried ...
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2answers
786 views

Mathematica can't simplify some logarithmic expressions

When I simplify some logarithmic expressions in Mathematica, it just returns the expression ...
3
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2answers
111 views

Rewrite $ x\sqrt{1-y^2/x^2} = \text{sgn}(x)\sqrt{x^2-y^2} $

I'm trying to coax Mathematica into rewriting $ x\sqrt{1-y^2/x^2} = \text{sgn}(x)\sqrt{x^2-y^2} $ for $ x $ and $ y $ real. I have tried all combinations of ...
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1answer
41 views

Separating positive and negative terms in an algebraic expression

I want to isolate positive and negative terms in this algebraic expression, for example. I have looked at the FullForm and tried many functions like ...
2
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1answer
74 views

Symmetrize a polynomial forgetting the commutativity property of multiplication

I need a script to authomatically symmetrize a given polynomial. For example, if the input is xy the output should be ...
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2answers
82 views

Relation between variables

I have the following two equations: ...
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2answers
42 views

Manipulation system of equation

I apologize for the banality of my question... Suppose we have two equations: b=a*x+l; y=3x+2 How can I have b as a function of y?
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1answer
187 views

Tag Times in Null is Protected [closed]

I've some problems with the error mentioned in the title. Unfortunately, my code is full of subscripts so I'll show it in a photo. In this code the central aspect is to assign a scalar value to an ...
1
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1answer
38 views

Strange thing about simplification between product and productory [closed]

Good morning, I have this strange problem. I have to divide a product of 5 variables by 4 of the 5 variables : $C x_1 * x_2* x_3 *x_4 / (x_1 * x_2* x_3 *x_4)$. Now if I do this I don't obtain only $C$...
2
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3answers
104 views

Noncommutative Expand into power series

I am new to Mathematica and am trying to apply it to quantum mechanics problems. The practice project I am dealing with now is considering quantum harmonic oscillator and ladder operator algebra ...
5
votes
3answers
301 views

Selecting parts of algebraic expressions?

(a1 q1^2 + b1 p1^2 + c1 q1 + d1 p1 + e1) E^(a2 q1^2 + b2 p1^2 + c2 q1 + d2 p1 + e2) Is there a command to select factor polynomial ...
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0answers
42 views

Defining commutations rules over arbitrary matrix

I'm working with spin connections with Dirac gamma matrix commutator (I know, mathematica has specific ways to work with it), and I need to define the following rules; $[\gamma_{0},\gamma_{i}]= 2 \...
2
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2answers
57 views

Maximizing number of positive elements in formatted output

The following code $Assumptions = {0 < x < 1, 0 < y < 1, z > 1}; myexpr = Expand[(1 - x) (1 - y) (z - 1)]; TraditionalForm[Simplify[myexpr]] ...
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0answers
17 views

ClearAttributes in ParallelDo

The following code ClearAttributes[Times, Orderless]; temp = b*a; Do[ Print[temp];, {i, 1} ] will print b*a However, the ...
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2answers
43 views

Solving for a variable [closed]

I have 2 equations that I want to equate to each other and solve for a certain variable in one of the equations. (1/a)-(b*e^-2a)/a= -(e^-2a*V0)/a I want to ...
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0answers
137 views

Non-determinstic kernel crash when manipulating large expressions in Mathematica 11.3

I have a encountered a very weird behavior of Mathematica 11.3 when collecting and factoring large expressions. To be more precise, such operations often lead to an abrupt kernel crash, but the ...
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1answer
70 views

Simplifying algebraic expressions with fractions in exponential

When letting Mathematica simplify (a^(-5) b (a^2 c^3)^3)/((a b^2 )^(-2) c^7) it returns the 'correct' answer a^3 b^5 c^2 ...
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0answers
85 views

How to find “nice” partial fraction decompositions

This is similar to one of my previous questions How to factorize polynomials into "shortest possible" pieces -- unfortunately I do not have any rigorous formulations of what I want to ...
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0answers
53 views

Simultaneous solving of three equations with nested, complicated expressions

I have the following variables s1, s2, and r1 defined as ...
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1answer
94 views

Indefinite order of differential operator

In the latest version of Mathematica, D can compute derivatives of symbolic order, that is, the $n^{\text{th}}$ (partial) derivative, returning an expression ...
4
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3answers
500 views

Writing System of Equations == 0

I have a system of equations and would like to retrieve the Jacobain w.r.t. to some variables. Now I see that this would be best done if I wrote the equations in a form == 0. Is there an easy way to ...
3
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4answers
182 views

How to separate integers and radicals from a term?

If I have a variable such as r = 1 + Sqrt[2] + Sqrt[13] how can I separate that into two separate variables with the rational and irrational parts? i.e. ...
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1answer
24 views

Keeping terms separate without combining it especially with multiplied random numbers

Suppose I have an expression where random numbers in exponentials are multiplied and this expression will keep on iterating such that more of such terms will occur. But I need to keep those terms as ...
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1answer
31 views

Threading Functions Specifying the Head and Level

I'm trying to thread a function only on the second level of an expression. For example Thread[(a * b) ** (c * d),Times] gives (a ** c) * (b ** d) However Thread[2(a * b) ** (c * d),Times] ...
4
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1answer
72 views

Distribute NonCommutativeMultiply over Times

Is there a method to transform (a1 * a2) ** (b1 * b2) into (a1 ** b1) * (a2 ** b2) I am trying to transform non-...
1
vote
1answer
40 views

How to force Refine to use a specific form

I have an assumption relating three variables and Simplify (and all functions that use assumptions) seem to take preference on one of these variables. For example: ...