Questions tagged [algebraic-manipulation]
The art of manipulating an algebraic expression into the desired form.
574
questions
1
vote
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 ...
1
vote
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....
5
votes
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 ...
0
votes
0answers
15 views
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 ...
2
votes
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
...
3
votes
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.
...
4
votes
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
...
6
votes
3answers
302 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
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, ...
4
votes
1answer
77 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
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 ...
0
votes
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 ...
2
votes
0answers
112 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
24 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
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 ...
1
vote
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 ...
1
vote
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 ...
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
38 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
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
$$ \dfrac{{\cal U}}{{\cal T}}\dfrac{\partial u}{\partial t}+\dfrac{{\cal U}^{2}}{{\cal L}}u\dfrac{\...
5
votes
3answers
155 views
Verify that given expr is a general solution to a given ODE
As in the title, for example:
eq = y''[x] + 4 y[x] == 7;
sol = DSolveValue[{eq}, y[x], x]
7/4 + C[1] Cos[2 x] + C[2] Sin[2 x]
...
2
votes
0answers
75 views
How to sum the KroneckerDelta[] in equation?
How to sum the KroneckerDeltas in following equation?
k, p1, ...
1
vote
2answers
63 views
How to efficiently simplify using PowerExpand
I am tying to simplify the following expression using Simplify, FullSimplify, Expand and <...
0
votes
0answers
29 views
Simplifying Expressions in a Different Way
Let's say I have the following code,
f[x_]:=(b-x)/(b-a)
(b-a)*f[x]^2
Is there a way to get Mathematica to output (b-x)*f[x] ...
0
votes
1answer
64 views
Taking absolute square of the following term
I have this equation and I wanted to find the absolute square of this term in Mathematica
$$ H_1 = \left | 1 + j\; \left(\frac{ 2 \pi}{1-e^\lambda}\right) \right|^2 $$
I did this in mathematica
<...
3
votes
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 (...
4
votes
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:
...
0
votes
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 ...
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
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 <...
1
vote
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?
3
votes
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'...
1
vote
2answers
61 views
2
votes
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 ...
3
votes
1answer
82 views
1
vote
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
...
3
votes
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 ...
2
votes
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]]
...
0
votes
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 ...
0
votes
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)?
1
vote
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 ...
0
votes
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 ...
3
votes
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
$$L(a \cdot b)= T(a)\cdot b + a \cdot T(b)+b\cdot T(a)+T(b)\cdot a\tag{*}$$...
4
votes
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.
$$
\...
3
votes
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 ...
5
votes
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 ...
1
vote
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
...
