Questions tagged [algebraic-manipulation]

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

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0answers
41 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
62 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
76 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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Simplifying expression with Sign [closed]

I am trying to simplify the following expression FullSimplify[Sign[x]^2, x \[Element] Reals] which clearly should be equals to one. Any idea on how to get that ...
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3answers
110 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
204 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
665 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
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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
114 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
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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
38 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
92 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
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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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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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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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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
106 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
41 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
93 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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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
160 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
155 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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How to sum the KroneckerDelta[] in equation?

How to sum the KroneckerDeltas in following equation? k, p1, ...
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2answers
63 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
64 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
123 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
95 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
29 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
86 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
70 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
131 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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2answers
61 views

Collect terms in inverse powers of three variables

I have the following expression ...
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2answers
60 views

Solve for two variables but output second variable in terms of first variable

Here are some equations for illustration: Format[Solve[{4*r1^3 == r2^2*(3*h), t*r2^2*(h - d) == r2^2*(h + d)}, #] & /@ {{h, d}}, InputForm] Here is their ...
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1answer
82 views

RootApproximant for a function

DSolve yield this rather lengthy solution ...
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1answer
71 views

How to convert trigonometric values to AlgebraicNumber

It is known that trigonometric functions evaluated at rational numbers of degrees are algebraic, and Mathematica recognize this: for example ...
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1answer
53 views

TensorExpand, TensorProduct and Distribution over Scalars

Consider: TensorExpand[( b1 x )\[TensorProduct] (b1 x + b2), Assumptions -> x ∈ Reals] (*x^2 b1\[TensorProduct]b1 + x b1\[TensorProduct]b2*) This works as ...
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1answer
89 views

Resolve Error or Mathematica's Bug?

The following code, Resolve[Exists[{n1, n2, n3}, {n1, n2, n3} \[Element] NonNegativeIntegers, 1/2 (1 + n1 + n2 - n3) \[Element] NonPositiveIntegers]] ...
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1answer
84 views

Simple Question: How to simplify what is inside the Sin function like below?

I have this code of Mathematica (1/(2 (fj - fk) π)) Cos[(fj - fk) π T + (fj - fk) π (T + δt)] Sin[(fj - fk) π T - (fj - fk) π (T + δt)] There are a few ...
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2answers
51 views

Solve the system using elimination What are a, b, and c in the quadratic equation, ax^2+bx+c=y given the [closed]

Solve the system using elimination What are a, b, and c in the quadratic equation, ax^2+bx+c=y given the points: (2,17), (-2,9), and (1,6), please solve the question using steps e.g. (step 1, step 2)?
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1answer
38 views

Changing initial conditions in a recursive polynomial family definition. Then, finding the generation function for this family

I'm following a paper trying to find a way to repeat the done computations using Mathematica. I'm beginner using Mathematica and I already read that: I could define functions by recursion; I could ...
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0answers
42 views

Testing Matrix inequalities

I was wondering how one might check whether matrix inequalities are true/false the same way it can be done for scalar variables (like in this post). Say I want to test the obvious inequality A,B are ...
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1answer
67 views

Counting terms in recursive operation

Suppose $X$ is an algebra and $T :X\to X$ is linear function. Let $L:X\to X$ be a function satisfying the following property $$L(a \cdot b)= T(a)\cdot b + a \cdot T(b)+b\cdot T(a)+T(b)\cdot a\tag{*}$$...
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2answers
142 views

Commutation, symmetrizer and duplication matrices

The following 3 matrices are useful when viewing matrices as vectors, known as commutation $K_n$, symmetrizer $N_n$ and duplication $G_n$. They are usually defined by their matrix relations below. $$ \...
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2answers
255 views

How to write a positive function as sum of positive terms only

A multivariate polynomial function can be written in a certain form (x^m (1-x)^n y^k + ... ) if the function is Positive in the whole domain and contains a finite ...
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4answers
333 views

How to generate all combination of multiplication of multiple variables (raised to some powers)

I want to generate all the possible combinations (commutative) of a few variables but also raised to some fixed powers. Lets take the following example: I have three variables ...
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2answers
96 views

How to simplify an equation corresponding to an ellipsoid? [duplicate]

The equation 29/36 - x/2 + x^2/4 + y/9 + y^2/36 - (4 z)/9 + z^2/9 == 1 is equivalent to ...

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