Questions tagged [algebraic-manipulation]
The art of manipulating an algebraic expression into the desired form.
538
questions
0
votes
1answer
70 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
42 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
32 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
35 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
60 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
87 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.
$$
\...
3
votes
2answers
243 views
How to write a positive function as sum of positive terms only
A multivariate polynomial function can be written in a certain form (x^m (1-x)^n y^k + ... ) if the function is Positive in the whole domain and contains a finite ...
5
votes
4answers
291 views
How to generate all combination of multiplication of multiple variables (raised to some powers)
I want to generate all the possible combinations (commutative) of a few variables but also raised to some fixed powers.
Lets take the following example:
I have three variables ...
1
vote
2answers
85 views
How to simplify an equation corresponding to an ellipsoid? [duplicate]
The equation
29/36 - x/2 + x^2/4 + y/9 + y^2/36 - (4 z)/9 + z^2/9 == 1
is equivalent to
...
0
votes
2answers
57 views
Inverse function and Integral: How to simplify this DSolve output?
I'm trying to DSolve these equations with each other:
...
0
votes
1answer
41 views
How to compute the factors in Bezout's Identity
If I have two polynomials $p(x),q(x)$, PolynomialGCD[p,q,x] can give me their greatest common divisor. But how to compute the polynomials $a(x),b(x)$ such that $d(x)...
0
votes
1answer
50 views
How do you convert an ordinary equation into a parametric equation? [duplicate]
It's a 3D linear equation
{P1: 2x-y-3z+2=0,P1: x+2y-z-6=0}
Are there any methods that can convert this linear equation to its parametric form.
Ps:the parametric form is {x=7t, y=-t+14/5, z=5t}
1
vote
1answer
50 views
How to use Collect to group negative terms?
For example, I have: $-d^2-k^{d+1}+d k^d+d+k-1$.
I want to get: $-\left(d^2+k^{d+1}+1\right)+d k^d+d+k$.
0
votes
1answer
69 views
Solving a coupled system of ODEs
I have two coupled ODEs for $T(x)$ and $t(x)$:
$$\frac{d^2 T}{d x^2}-\beta (T-t)+K=0 \tag 1$$
$$\frac{d t}{dx}-\alpha(T-t)=0 \tag 2$$
$\alpha, \beta$ and $K$ are constants $>0$. Also, it is known ...
2
votes
1answer
57 views
How to get the result in terms of a previously defined expression?
Say I have a vector
X[n_] := Table[Subscript[x, i], {i, 1, n}]
and a matrix of connections:
...
4
votes
2answers
75 views
Trouble verifying a solution to a differential equation
I am reading a physics book which has discussed one approach towards solving the differential equation
$$
\frac{d^2 x(t)}{dt^2} = Cx(t)
$$
as follows:
Using Mathematica to solve the equation. I tried ...
2
votes
1answer
94 views
Numerical integration of MeijerG function with variables
I applied the integration, How to solve the function which is mentioned below.
here, 'theta' is the only variable.
q13, q1,q2,p,qi1 are all variables will take value from the loop ranges from 0 to 2, ...
3
votes
0answers
29 views
Symbolic Set Difference
Suppose I have two symbolic set containing 2-points like
A={(m,n)| for m,n belonging to whole numbers}. So m,n=0,1,2,...
and I have another set containing 2-points ...
5
votes
1answer
138 views
Derivative of real antisymmetric matrix in mathematica
Is it possible to find the derivative of components of a real antisymmetric matrix using index notation? Eg: I have a very large real antisymmetric matrix. Then from Matrix Cookbook, we know the ...
2
votes
1answer
84 views
Converting an equation to the form $ax+by=c$
I have a linear equation that comes as a result of applying orthogonality on a non-homogeneous boundary condition with two unknowns $C_1$ and $C_2$. Can someone help me to express this equation in the ...
4
votes
1answer
136 views
Simplifying the final coefficient expression of the solution to a Laplacian
I have been trying to solve a boundary value problem analytically which involves a three-dimensional temperature Laplacian over a parallelepiped. In the final step of my solution, using the two non-...
2
votes
1answer
96 views
Solving a system of polynomial equations - can I be sure that the number of solutions, and the solutions are correct?
I need to solve a system of two polynomials with integer coefficients in two variables, $\{Q_1(w,z)=0,\,Q_2(w,z)=0\}$, and want to compute all real solutions. I'm able to run ...
1
vote
1answer
64 views
Counting real roots of bivariate polynomial
For a proof, I'm working with a polynomial $p(x,m)$ and I need to show that: For any $m\in (0,6)$, $p_m(x)\equiv p(x,m)$ has a unique real root in $(0,1/2)$. I find that this is true by using Reduce ...
0
votes
0answers
51 views
How implement Dual Quaternion algebra in Mathematica?
How can we manipulate and operate with dual quaternionic variables in Mathematica? Since a dual quaternion can be expressed like this
$\hat q = a + \epsilon b $
where $a,b \in \mathbb{H}$, or ...
3
votes
1answer
108 views
How to express this radical in terms of Golden Ratio?
(1/3)*Sqrt[(1/11)*(-3 - 2*Sqrt[5] + 3*Sqrt[178 + 82*Sqrt[5]])]
$$
r=\frac{1}{3} \sqrt{-2 \sqrt{5}+3 \sqrt{82
\sqrt{5}+178} \over 11}
$$
I need to express this ...
1
vote
1answer
44 views
Define trace-like function (e.g. cyclically invariant) involving operators without built-in meaning
I am interested in defining a function, say $\mathrm{Tra}$, that imply operators without build-in meaning, say it involves products with the $\cdot$ (Esc . Esc), ...
0
votes
1answer
42 views
Derive arbitrary steps between two expressions
Can someone show me the syntax to find the algebraic transformations between:
$\sqrt{1+(\frac{dy}{dx})^2}dx$
and
$\sqrt{dx^2+dy^2}$
And more generally, how to get the algebraic derivation between ...
0
votes
1answer
67 views
1
vote
3answers
72 views
Mathematica inverting algebraic output order
This is a somewhat silly requirement, but would help a lot in my workflow. Whenever I output an algebraic expression which contains a number, mathematica always orders the number first whenever ...
3
votes
1answer
49 views
Replacing an indexed term
Consider the expression:
s[i_, n_] := Sum[(e[c[j]] + e[z[j]])*(l[i, j] + m[i, j]), {j, 1, n}]
I'm trying to replace e[c[3]] by c[3] and have attempted
...
0
votes
0answers
32 views
Expanding complex expression and replacing variables in the result
When I'm finished expanding my expression I would like the result to be expressed again in terms of the original variables (like α, S1, T1, T2). I've tried replace, ...
1
vote
1answer
62 views
Collecting terms from an indexed sum
How can I get Mathematica to collect terms from an indexed sum? My application is somewhat convoluted, but this minimum code captures the idea:
...
3
votes
2answers
115 views
Matrix vector multiplication of trigonometric functions [closed]
My problem is to show the expressions in the photo (from this book) are equivalent using Mathematica. The code below is not giving the desired results. What I have so far should reduce to the column ...
1
vote
1answer
55 views
Similar power merge
How can I tell Mathematica to write
{x^z1*y^(-a1 - z1 - z4)*z^(-a1 - z1 - z4)}
as (x/y)^(z1)(yz)^(-z4)
I mean combining terms with similar power?
3
votes
1answer
108 views
Simplifying algebraically
Is there a way to derive an simplified expression from other equations. Or create an alternate form such that the main equation takes other equations and manipulates the main function.
Here is what I ...
0
votes
2answers
68 views
Releasing multiple nested Hold in a single expression simultaneously
Trivia:
I need to take a coefficient list of a long list of complicated expressions of the form $\prod c_{ij} \left( p_{i,j}(x_1,x_2) \right)^n$ where $n$ is positive integer, and $i,j$ label ...
0
votes
0answers
38 views
How do I substitute an expression into another?
I'm trying to substitute equation (1) to equation (2) in a way that mathematica chooses the best and simpliest form of a result.
To clarify the problem and make it less generic, here is the specifics ...
1
vote
1answer
66 views
How to do a long division over a multivariate polynomial in Mathematica
Does anyone know how to do a long division of a multivariate polynomial over another multivariate polynomial to effectively find the remainder, hopefully with fewest terms and/or lowest degree, in ...
1
vote
1answer
53 views
1
vote
2answers
29 views
How do I get the maximum the maximum degree of a polynomial? [duplicate]
For example applied to y^2*x^3 + z^2+1 it should give 5 due to the y^2*x^3component.
1
vote
2answers
74 views
Collect for nonlinear terms
Is there a way to expand Collect, so that it does not only separate equations by polynomial order, but by general nonlinear functions?
For example
...
3
votes
2answers
193 views
Defining a*b=-b*a
I am fairly new to using Mathematica and was wondering if it's possible to define something along the lines of:
$a*b=-b*a$
a sort of antisymmetry or skew symmetry if you will. I would like to do ...
2
votes
1answer
83 views
Finding Dual Plane Curve Using Eliminate
I want to find the dual curve of the projective plane curve
$$F(x,y,z)=(x^2+y^2+z^2)x+t(x^3+y^3+z^3)=0$$
where $[x,y,z]$ is homogeneous coordinate in proejective 2-space $\mathbb P^2$. The dual ...
1
vote
1answer
53 views
cancel out the common terms and factor out the common terms and extract the coefficients
the following code fail to multiply each equation by dt, since dt does not seem to do any jobs. it remains as a common factor, I would like it to cancel out the 1/dt term and also multiply the rest of ...
3
votes
2answers
214 views
Denoting large recurring parts of an equation by a variable
Suppose I have formula like the following:
(1 - x) (1 - y) + ((1 - x) (1 - y))/(z + 2)
Obviously, (1 - x) (1 - y) is found a couple of places in the formula.
...
3
votes
1answer
48 views
How do I verify if an equation is correctly re-arranged?
Let's say for pen and paper re-arrangement of some equation, sometimes getting a single step wrong and then wasting time on subsequent steps can be a large time sink.
My goal is to be able to verify ...
1
vote
1answer
29 views
Multiplying two expressions with a specific function, efficiently
Paraphrasing, the problem I am trying to solve is the following. I am given two "matrix valued" sums
...
2
votes
0answers
63 views
how to find derivative of an equation of matrices with element-wise multiplication or division
For an equation like this:
$$ M= \left(\begin{array}{c} A\:x-B \otimes y\end{array}\right) \oslash C $$
where $\otimes$ is an element-wise multiplication and $\oslash$ is an element-wise division.
...
1
vote
0answers
22 views
Manipulating a system of equalities into particular form
newbie here just trying to learn the Mathematica syntax.
I have a list of equations, some of them definitions, others relationships, as follows:
...
1
vote
1answer
65 views
Leibniz rule with unknown orders of imput
I'm trying to find a simple way to define
a bilinear and Leibniz functional/map "$B(\cdot,\cdot)$", that eats two functions $f(x),f(y)$ or products theirof and produces the following,
$$
B(f(...
