Questions tagged [algebraic-manipulation]

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

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0answers
57 views

derivative like operator

assuming I have a derivative operator $\partial$, and a function $f$ and $g$ I want $\partial$ to stick to whatever is in front of it and don't need to do anything else after the computation, the ...
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5answers
804 views

Simplify radical expression (a + b - Sqrt[a^2 - b^2])/Sqrt[a + b]

I have the following expansions: $\frac{a+b-\sqrt{a^2-b^2}}{\sqrt{a+b}}$ and $a>b>0$ Obviously we can simplify it further by hand $\sqrt{a+b}-\sqrt{a-b}$, but Mathematica doesn't know how to ...
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1answer
77 views

Ordinary differential equation with variable (polynomial) coefficients -form of solution

If you have a differential equation with polynomial coefficients then quite remarkably Mathematica can find a solution. For example for the second order differential equation $ y''(t)+b y'(t)+\left(\...
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2answers
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1answer
39 views

Trigonometric simplification .Correct syntax? [closed]

I cannot simplify this expression any further, which should result in 7. Could you please provide me with the correct syntax, I have tried several without success. $$Assumptions[A + B + C == 0 , ...
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1answer
89 views

Rewrite a variable in terms of another variable

I have two variables t = 1/Sqrt[2] (Sqrt[1 + Cos[a]] + Sqrt[1 - Cos[a]] + Sqrt[1 + Cos[b]] + Sqrt[1 - Cos[b]] + Sqrt[1 + Cos[c]] + Sqrt[1 - Cos[c]]) and <...
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1answer
50 views

Grouping together same exponent terms in a multivariate monomial

This is a rather simple question but for some reason, I am spending too much time on this. Suppose I have a monomial in 4 variables, each raised to some linear combination of 3 exponent variables: <...
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0answers
58 views

What is the ComplexityFunction used by FullSimplify in Mathematica 12? [duplicate]

I was surprised to see FullSimplify make my expressions numerically unstable. The result can be summarized below: ...
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2answers
266 views

Telling Mathematica to treat square roots as real valued

I often deal with problems which I know are real-valued, but Mathematica skips some simplifications because it doesn't know which branch of Sqrt to take. Is there ...
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1answer
101 views

Simplifying quantum operators (ladder operators with multiple modes)

Similar to this question, I am interested in working with an implementation of quantum ladder operators. I've been trying to use this "Quantum Mathematica Package" to solve some lengthy ...
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2answers
65 views

Formal substitution of exponential factors in an expression

Assume that we have some complex algebraic expression, like Exp[(a t + b s)/w] ( t Exp[ q t] w + q Exp[q s] Exp[-2 s] + a^2 Exp[3 s] + s t + 1 ) Now, this is just ...
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Commutator of QFT Operators $[\hat{a}_p, \hat{a}^\dagger_k]$ and 4-Momentum Integrals

I just recently started looking into CAS (i.e. i have very little experience in Mathematica), specifically for doing basic calculations in Quantum Field Theory. For that i would like to define $\hat{a}...
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28 views

Issues in expanding expressions with formal sums

I have a very long expression involving formal sums to infinity, unfixed functions and several variables. In this very long expression, I need a typical term, like $\frac{6 A \sigma \sum _{n=0}^{\...
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0answers
23 views

How to rearrange terms in an expression to a particular form (e.g. A/w-> A*(1/w)

I have a huge expression for which the numerators are a big mess, involving numbers, variables, formal sums and unevaluted function, let's call the numerators Ai, with i=1,2,...n This "beast"...
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1answer
54 views

Expression should vanish under assumptions. How can I use Mathematica to simplify this type of of expression (and similar)?

This is maybe the worst type of question because it is super specific, but I am hoping that some Mathematica function or rule exists (built-in or custom) that can be helpful for simplifying a somewhat ...
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1answer
53 views

How to simplify for a ratio of two variables

Say I have an equation like $$2 z \ln[\frac{a v_{2}^{2}}{b_{2}}]+(v_{1}-2v_{2}) - z \ln[\frac{a v_{1}^{2}}{b_{1}}]\geq0$$ ...
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0answers
69 views

Inner polygon approximation

Suppose you want to perform an inner approximation of a planar semialgebraic set by a finite set of polygons. The following is a quick way to yield an approximation but I am not convinced that it is ...
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1answer
83 views

Reduce/Resolve without roots/radicals

Is there a way to convince Mathematica to perform quantifier elimination on a semialgebraic set and yield a resulting semialgebraic set whose representation does not involve any roots or radicals, i.e....
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1answer
107 views

DChange fails to change variables for 1D Schrödinger equation

I have a PDE (1D Schrödinger equation) as follows: Applying the following transformations to the PDE, we get the following ODE: I am trying to use @Kuba 's ...
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3answers
115 views

How to collect a polynomial with a specific power

Suppose I have got this polynomial u=x^12-3x^8-x^4+3 Now, I am trying to collect this polynomial with x^4 terms. I need to write it like this: (-1+x^4) (-3 + x^4) (1 + x^4) To evaluate it, I used ...
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3answers
214 views

How to solve these algebraic identities?

I need help in finding/solving these types of algebraic equations using Mathematica. here is the problem/code. I tried using 'With' command but no use. Thanks in advance. ...
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2answers
674 views

Where I am wrong?

I have an ODE: ( I want to write a code for Manuel solution algorithm) ...(Eq.4) STEP 1: Assume that the solution of ODE can be expressed by ...
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3answers
319 views

Express MeijerG as integral

For definite integrals MMA gives identities in terms of Meijer G-functions, e.g. $\begin{align}\sqrt{\pi}\int_0^\infty \textrm{e}^{-4x/t^2-t}\ \textrm{d}t &= G_{0,\,3}^{3,\,0} \left( x\left. \...
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3answers
119 views

How can I more quickly get the interchangeable variables in a function?

Let's say I have an expression like a b + c d e. This is equal to: a b + c d e, a b + c e d, ...
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1answer
83 views

To find the combinational coefficients of vectors in polynomials

Simply put, I have a few vectors of polynomials $\{d_i\}$ and I know one of their combinations gives $x$, which is also a vector of polynomials. How do I find the combinational coefficients $a_i$, ...
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1answer
45 views

Solving from previous results

I require in this program to use only all the value of “p” form “solution 1” in “solution 2”. Instead of copy and paste each value of “p” individually in solution 2, I am trying to write a function to ...
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3answers
106 views

Simplification with User defined rules and assumptions

The results of DSolve are usually expressions that can be further simplified. For instance, consider the following expression for a co-ordinate of a particle in ...
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0answers
124 views

What is Wolfram's equivalent of Maple's algsubs?

Maple has two primary substitution functions. subs - which is similar to ReplaceAll in WL. algsubs - which does replacement but takes into account the algebraic ...
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0answers
27 views

Reconcile FullSimplify vs Reduce on Simple Problem

Can FullSimplify be coerced to give an answer here? If not, is it easy to say why? ...
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0answers
31 views

Custom multiplication operation between variables

I am constructing polynomial expressions in the variables $s[0],s[1],...,s[n]$ and I'm trying to define a new operation to simplify the expression: ...
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0answers
34 views

How can I implement a function that is a homomorphism?

I want to do the follow: Write a function $f$ such that if I evaluate $f(ax+by)$, it returns $f(a)f(x)+f(b)f(y)$. How can I do that? I tried to look in the help for "homomorphism" but didn't ...
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2answers
110 views

Quick way to numerically cancel exponentials

I have a problem with exponentials and the use of the commands N and Collect. I am trying to write a code that generates a very ...
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1answer
45 views

Idiomatic way to express a polynomial in terms of a shifted variable

I have a polynomial of known degree, $f(x) = \sum_{n = 0}^N a_n x^n$ and I' d like to express it in terms of a shifted variable $x - x_ 0$, so that $f(x) = \sum_{n = 0}^N b_n (x - x_ 0)^n$. I can do ...
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1answer
94 views

How to properly attempt to express a function in terms of new variables

I have a specific problem in mind, but I am more interested in how to "properly" convey to Mathematica the result that I want. To start with, I have a function $G$ that can be represented ...
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1answer
28 views

Call part of a replaced list

I have what I believe to be a very simple problem. I want to use an equation which depends on the values inside a list, but to be able to evaluate that equation with different lists. So: ...
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1answer
45 views
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41 views

How to find out rational exponent

I am trying to check whether an expression has any rational exponent or not. I am using the following boolean to check that and a combination of Exponent, ...
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1answer
165 views

Easy way to extract coefficients of functions in an ODE/PDE? [closed]

Suppose I have an ODE like $$ \epsilon y''(x)y(x) + xy'(x) + \epsilon^2 y(x)=0$$ or a PDE like $$ \dfrac{{\cal U}}{{\cal T}}\dfrac{\partial u}{\partial t}+\dfrac{{\cal U}^{2}}{{\cal L}}u\dfrac{\...
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3answers
158 views

Verify that given expr is a general solution to a given ODE

As in the title, for example: eq = y''[x] + 4 y[x] == 7; sol = DSolveValue[{eq}, y[x], x] 7/4 + C[1] Cos[2 x] + C[2] Sin[2 x] ...
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0answers
76 views

How to sum the KroneckerDelta[] in equation?

How to sum the KroneckerDeltas in following equation? k, p1, ...
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2answers
88 views

How to efficiently simplify using PowerExpand

I am tying to simplify the following expression using Simplify, FullSimplify, Expand and <...
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0answers
29 views

Simplifying Expressions in a Different Way

Let's say I have the following code, f[x_]:=(b-x)/(b-a) (b-a)*f[x]^2 Is there a way to get Mathematica to output (b-x)*f[x] ...
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1answer
66 views

Taking absolute square of the following term

I have this equation and I wanted to find the absolute square of this term in Mathematica $$ H_1 = \left | 1 + j\; \left(\frac{ 2 \pi}{1-e^\lambda}\right) \right|^2 $$ I did this in mathematica <...
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2answers
485 views

Is it possible to ask Mathematica to separate all the terms containing $x$ and $y$ in the given function?

I have a 6-variable function like this $ f(x,y,z,t,w,v)= 8 t^6 e^{i (3 t v+2 t w-x+2 y)}+t^6 e^{i (2 t v-x+y)}-2 t^5 e^{i t (v+3 w)}+2 t^5 e^{4 i t w}+3 t^4 e^{i t (v+w)}+2 t^4 e^{2 i t w}+2 e^{i (t (...
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2answers
96 views

Computing the sign of an expression

Can you please help with the following. I would like to compute the sign of an expression: ...
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1answer
30 views

Perform Eliminate, Solve and Format at once in Mathematica

I have a series of equations where I use eliminate to get a new equation with desired variables. This equation is then solved for a specific variable and then the result is presented in a specific ...
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1answer
61 views

Extracting coefficients from equation [closed]

I am looking for a Mathematica code that finds the coefficients from an equation. So for example, when I have the equation $ax^2+bx+c$ I want to the code to spit out: ...
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4answers
87 views

numerical values of coefficients

Consider the following output: x= (Sqrt[3/(2 (1 + Sqrt[11]/4))] b[0, π/3] - (1 + Sqrt[7/3]) b[(2 π)/3, (2 π)/3])/(4 Sqrt[2] 7^(1/4) Sqrt[1 + Sqrt[7]/4]) If i do <...
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1answer
80 views

Mathematica Partial Fraction Decomposition full steps [closed]

I hope to get full steps instead of getting the result. Any ways to do so?
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2answers
138 views

How to factor a polynomial expression with variable coefficients (and imaginary values)

How can I factor terms with variable coefficients? For example for the expression: $x^2 + a$ I know that I can factor this to: $(x+i\sqrt{a})(x -i\sqrt{a})$ How do I do this in mathematica? I would'...

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