Questions tagged [algebraic-manipulation]
The art of manipulating an algebraic expression into the desired form.
589
questions
1
vote
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 ...
10
votes
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 ...
1
vote
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(\...
1
vote
2answers
112 views
0
votes
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 ,
...
1
vote
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
<...
1
vote
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: <...
3
votes
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:
...
7
votes
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 ...
0
votes
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 ...
2
votes
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 ...
3
votes
0answers
78 views
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}...
0
votes
0answers
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}^{\...
0
votes
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"...
3
votes
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 ...
0
votes
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$$
...
2
votes
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 ...
1
vote
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....
5
votes
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 ...
2
votes
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
...
3
votes
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.
...
4
votes
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
...
6
votes
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.
\...
1
vote
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, ...
4
votes
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$, ...
0
votes
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 ...
0
votes
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 ...
2
votes
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 ...
1
vote
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?
...
1
vote
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:
...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
1
vote
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 ...
1
vote
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:
...
0
votes
1answer
45 views
0
votes
0answers
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, ...
2
votes
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{\...
5
votes
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]
...
2
votes
0answers
76 views
How to sum the KroneckerDelta[] in equation?
How to sum the KroneckerDeltas in following equation?
k, p1, ...
1
vote
2answers
88 views
How to efficiently simplify using PowerExpand
I am tying to simplify the following expression using Simplify, FullSimplify, Expand and <...
0
votes
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] ...
0
votes
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
<...
3
votes
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 (...
4
votes
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:
...
0
votes
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 ...
2
votes
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: ...
1
vote
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 <...
1
vote
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?
3
votes
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'...