Questions tagged [algebraic-manipulation]
The art of manipulating an algebraic expression into the desired form.
555
questions
0
votes
0answers
24 views
Easy way to extract coefficients of functions in an ODE/PDE?
Suppose I have an ODE like
$$ \epsilon y''(x) + xy'(x) + \epsilon^2 y(x)=0$$
or a PDE like
$$ \dfrac{{\cal U}}{{\cal T}}\dfrac{\partial u}{\partial t}+\dfrac{{\cal U}^{2}}{{\cal L}}u\dfrac{\partial u}{...
5
votes
3answers
151 views
Verify that given expr is a general solution to a given ODE
As in the title, for example:
eq = y''[x] + 4 y[x] == 7;
sol = DSolveValue[{eq}, y[x], x]
7/4 + C[1] Cos[2 x] + C[2] Sin[2 x]
...
2
votes
0answers
71 views
How to sum the KroneckerDelta[] in equation?
How to sum the KroneckerDeltas in following equation?
k, p1, ...
1
vote
2answers
53 views
How to efficiently simplify using PowerExpand
I am tying to simplify the following expression using Simplify, FullSimplify, Expand and <...
0
votes
0answers
28 views
Simplifying Expressions in a Different Way
Let's say I have the following code,
f[x_]:=(b-x)/(b-a)
(b-a)*f[x]^2
Is there a way to get Mathematica to output (b-x)*f[x] ...
0
votes
1answer
61 views
Taking absolute square of the following term
I have this equation and I wanted to find the absolute square of this term in Mathematica
$$ H_1 = \left | 1 + j\; \left(\frac{ 2 \pi}{1-e^\lambda}\right) \right|^2 $$
I did this in mathematica
<...
2
votes
1answer
70 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
94 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
28 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
85 views
numerical values of coefficients
Consider the following output:
x= (Sqrt[3/(2 (1 + Sqrt[11]/4))] b[0, Ļ/3] - (1 + Sqrt[7/3]) b[(2 Ļ)/3, (2 Ļ)/3])/(4 Sqrt[2] 7^(1/4) Sqrt[1 + Sqrt[7]/4])
If i do <...
1
vote
1answer
61 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
118 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
57 views
2
votes
2answers
57 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
81 views
1
vote
1answer
70 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
48 views
TensorExpand, TensorProduct and Distribution over Scalars
Consider:
TensorExpand[( b1 x )\[TensorProduct] (b1 x + b2),
Assumptions -> x ā Reals]
(*x^2 b1\[TensorProduct]b1 + x b1\[TensorProduct]b2*)
This works as ...
1
vote
1answer
86 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
77 views
Simple Question: How to simplify what is inside the Sin function like below?
I have this code of Mathematica
(1/(2 (fj - fk) Ļ))
Cos[(fj - fk) Ļ T + (fj - fk) Ļ (T + Ī“t)] Sin[(fj -
fk) Ļ T - (fj - fk) Ļ (T + Ī“t)]
There are a few ...
0
votes
2answers
49 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
35 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
39 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
66 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
114 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.
$$
\...
3
votes
2answers
251 views
How to write a positive function as sum of positive terms only
A multivariate polynomial function can be written in a certain form (x^m (1-x)^n y^k + ... ) if the function is Positive in the whole domain and contains a finite ...
5
votes
4answers
315 views
How to generate all combination of multiplication of multiple variables (raised to some powers)
I want to generate all the possible combinations (commutative) of a few variables but also raised to some fixed powers.
Lets take the following example:
I have three variables ...
1
vote
2answers
91 views
How to simplify an equation corresponding to an ellipsoid? [duplicate]
The equation
29/36 - x/2 + x^2/4 + y/9 + y^2/36 - (4 z)/9 + z^2/9 == 1
is equivalent to
...
0
votes
2answers
82 views
Inverse function and Integral: How to simplify this DSolve output?
I'm trying to DSolve these equations with each other:
...
0
votes
1answer
53 views
How to compute the factors in Bezout's Identity
If I have two polynomials $p(x),q(x)$, PolynomialGCD[p,q,x] can give me their greatest common divisor. But how to compute the polynomials $a(x),b(x)$ such that $d(x)...
0
votes
1answer
51 views
How do you convert an ordinary equation into a parametric equation? [duplicate]
It's a 3D linear equation
{P1: 2x-y-3z+2=0,P1: x+2y-z-6=0}
Are there any methods that can convert this linear equation to its parametric form.
Ps:the parametric form is {x=7t, y=-t+14/5, z=5t}
1
vote
1answer
52 views
How to use Collect to group negative terms?
For example, I have: $-d^2-k^{d+1}+d k^d+d+k-1$.
I want to get: $-\left(d^2+k^{d+1}+1\right)+d k^d+d+k$.
0
votes
1answer
72 views
Solving a coupled system of ODEs
I have two coupled ODEs for $T(x)$ and $t(x)$:
$$\frac{d^2 T}{d x^2}-\beta (T-t)+K=0 \tag 1$$
$$\frac{d t}{dx}-\alpha(T-t)=0 \tag 2$$
$\alpha, \beta$ and $K$ are constants $>0$. Also, it is known ...
2
votes
1answer
59 views
How to get the result in terms of a previously defined expression?
Say I have a vector
X[n_] := Table[Subscript[x, i], {i, 1, n}]
and a matrix of connections:
...
4
votes
2answers
78 views
Trouble verifying a solution to a differential equation
I am reading a physics book which has discussed one approach towards solving the differential equation
$$
\frac{d^2 x(t)}{dt^2} = Cx(t)
$$
as follows:
Using Mathematica to solve the equation. I tried ...
2
votes
1answer
101 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
31 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 ...
6
votes
1answer
153 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
85 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
141 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
121 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
67 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 ...
1
vote
0answers
57 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
116 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
48 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
68 views
1
vote
3answers
74 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
51 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
34 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 Ī±, S1, T1, T2). I've tried replace, ...
