Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,321
questions
1
vote
0answers
29 views
Specify border conditions correctly when Piecewise in DSolve, unexpected answer
I want help figuring out how to set the correct border condition for this differential equation that includes a Piecewise statement with a discontinuity at the ...
5
votes
1answer
76 views
DSolve inconsistently able to evaluate expression
I am trying to use DSolve to evaluate a coupled system of ODEs as follows
DSolve[{Y0[X] + Y0''[X] == 0, Y1[X] + Y1''[X] == X Y0[X]}, {Y0[X], Y1[X]}, X]
However, ...
2
votes
1answer
40 views
1
vote
1answer
60 views
Symbolic Vector calculus
Can mathematica perform symbolic vector calculus? Say I want to find
$$\mathbf{v} = \mathbf{a} \exp(\mathbf{b}\cdot\mathbf{x})$$
$$\nabla \cdot \mathbf{v} = \mathbf{b}\cdot \mathbf{v}$$
If I try
...
0
votes
1answer
90 views
With Intel Xeon(R) E5-2667 v4 and 250GB RAM: still automatically quitting kernel when doing symbolic integrations
[![Here is the configuration for my calculation. Guess it can't be affected by this.][1]][1]
I was in trouble when solving the algebraic equations for q1 and q2.
\begin{equation}\label{eq:18}
\begin{...
0
votes
0answers
37 views
Symbolic 3x3 Jacobian matrix not being computed as expected
First question I have ever typed in a stackexchange forum so I hope you'll forgive me if i make rookie mistakes.
I'm try to compute the symbolic expression of a 3x3 Jacobian of a vector
...
-4
votes
1answer
132 views
How to write a really complicated formula into mathematica and do symbolic computation?
I want write the following formula $a$ into mathematica and do symbolic computation like $a^2$. $a$ is defined as follows:
\begin{multline*}
a=\sum_{t=0}^{T-1}f_1^2(t)+11\sum_{t=0}^{T-1}f_2^2(t)+\\
\...
0
votes
4answers
96 views
Integration challenge
For positive real $a \leq \pi$ and $b \leq \pi$
$\int_{-a/2}^{a/2} \frac{\sin{(b/2)}}{\sqrt{1+\cos^2 (b/2)\tan^2 (\phi )}} \; d \phi = 2 \arcsin \left[ \sin (a/2) \sin (b/2) \right] $
as can be ...
3
votes
1answer
206 views
RootReduce and Simplify for an algebraic expression
The American Invitational Mathematics Exam (AIME) 2006 asked contestants to reduce this expression:
$$\sqrt{104 \sqrt{6} + 468 \sqrt{10} + 144 \sqrt{15} + 2006}$$
The answer is $13 \sqrt{2} + 4 \sqrt{...
1
vote
0answers
37 views
Vectan.m in Mathematica12 - returns VPValue instead of VP (same with SP etc) [closed]
for years I was using Vectan.m to do analytical vector calculations. There seem to be a problem in Mathematica 12 (on Mac). All loads well, but then instead of VP[a,b] it returns VPValue[a, b]:
<&...
1
vote
1answer
90 views
Problem with Analytical Integration with Constant
Could you help me out on how to integrate this long equation with constant as it is indefinite integral so I assumed I could not use numerical integration (eg: Simpsons's 3/8 Rule or Trapezoidal Rule) ...
1
vote
1answer
59 views
GeneratedParameters in Integrate
I defined a function of two variables, let's say
u[x_, y_] := 4 x^4 + 6 x y - 24 x^2 y^2 + 4 y^4
I want to partial integrate (with respect to y) the partial derivative of u with respect to x obtaining ...
3
votes
1answer
74 views
Pattern matching problems involving FullForm and Plus and Times
I am trying to match an expression that will be a sum of more than one terms, with the last one being a product. For example, the objecta+b+x*y. I am using the ...
3
votes
1answer
40 views
Type formation rules for 1-position expressions
I made a summary of the rules for formation of types for simple 1-position expressions, as I understand them.
Here it is in textual form:
A symbol, say, α, is a discrete entity, represented by a ...
0
votes
0answers
25 views
Why does explicit Dirichlet Transform of Liouville Lambda not evaluate?
I have four expressions for the Dirichlet Transform of the Liouville-Lambda function, but one form does not evaluate, any ideas why and what could be done?
3
votes
2answers
67 views
How to symbolically evaluate expression within If[]?
I have a function, say f, that needs to take one of two symbolic forms depending on the value of its inputs. This function is part of a very large expression, and I'...
3
votes
0answers
62 views
2D Poisson equation with Piecewise RHS - symbolic solution?
I'm trying to solve the following 2D Poisson equation symbolically:
$$
-\nabla^2 u(x,y) =
\begin{cases}
1-\text{sech}\left(\frac{w}{2 d}\right) \cosh \left(\frac{x}{d}\right)
& -w/2 \leq ...
2
votes
1answer
52 views
Recursive computation of symbolic series
I don't have experience in Mathematica and I would like to use the ability it has to do symbolic computations to find the terms of a series of functions recursively. The terms I want to find are given ...
1
vote
0answers
54 views
Alternatives to NumericQ that allow symbols to be considered numeric
I am writing a program in which I am using NumericQ. I am trying to allow symbols to also be considered Numeric, so I have been using NumericQ[a]=True for all of ...
0
votes
1answer
47 views
Reduce coefficients from constraints in a set of equations
Total beginner here. I am chaining 4 quadratic equations $f_i(x)$ at 4 knots $k_i$ (where $0 < k_i < 1$ and $k_{i+1} > k_i$) on a wrapped unit interval (i.e. $0 \leq x \leq 1$):
$$ f_i(x) = ...
1
vote
2answers
109 views
Mathematica's evaluation of nested summations
As suggested there, here is a copy of the question I've posted on Math.Stackexchange.
Suppose we want to count the number of instructions executed by the following Python code:
...
4
votes
3answers
462 views
Useless result of Integrate
Considering a Fourier sine series, I calculate
int = Integrate[Log[1 + Sin[x]]*Sin[i*x], {x, 0, Pi}, Assumptions -> i ∈ PositiveIntegers]
...
1
vote
1answer
36 views
Changing expression using a new variable definition
If I have an expression that looks like the following:
$$ \frac{i \sqrt{\frac{\sigma _2}{\sigma _1}} \left(-\sigma _2 q_1(t){}^2+\sigma _1 q_2(t){}^2+\left(\omega _2-\omega _1\right) q_2(t) q_1(t)\...
0
votes
1answer
84 views
How to derive all KKT points of a parametric optimization problem
Suppose we have a symbolic optimization problem where all parameters and decision variables are nonnegative like the following problem. I would be thankful to know if there is any method to find all (...
0
votes
0answers
31 views
Getting the coefficients of an expression with Solve
I have a very lengthy expression (600+ terms) with derivatives of several functions, which I want to write in a compact way. I would like to get the coefficients of terms I know exist in this ...
0
votes
1answer
73 views
Symbolic partial differentiation of a Lagrangian function including a summation
I'm using Mathematica to double-check that I correctly derived first order conditions for the models I'm researching. Before I get started, I wanted to actually teach myself how to use Mathematica, ...
0
votes
2answers
178 views
Is it possible to calculate the desired area analytically?
I have the three two-variable curves $f,g,h$ with $0\leq x\leq \frac {\pi}{2} $ and $0 \leq y \leq \pi$
I use ContourPlot as
...
2
votes
0answers
28 views
Removing function arguments from expressions with derivatives
( This question is basically the opposite of this one: Variable dependency...easy one )
I would like to be able to output expressions in Mathematica that look more like pen-and-paper math. In ...
0
votes
0answers
18 views
Partially activate a derivative
Is there a way to make an inactive derivative do some amount of simplification? For instance, say I have
Inactive[D][{{f,g},{u,v}},x]
I would like ...
0
votes
1answer
49 views
How to simplify for a ratio of two variables
Say I have an equation like
$$2 z \ln[\frac{a v_{2}^{2}}{b_{2}}]+(v_{1}-2v_{2}) - z \ln[\frac{a v_{1}^{2}}{b_{1}}]\geq0$$
...
4
votes
1answer
78 views
Substitute known function's derivative
Suppose I know that the time derivative of $x(t)$ is $\dot{x}(t)=-x(t)$. I consider the function $V(x)=x^2$ and I want to compute the time derivative of $V$ along the trajectories of $x$, namely $\dot{...
1
vote
2answers
87 views
How to work symbolically with a compiled function?
I have a compiled function f to be used as a piece of a much larger calculation. I would like to expand out a function that calls ...
0
votes
1answer
62 views
Partial derivatives of this function
I have a function $y(x)$ which is the solution of the initial value problem -
$y = \frac{1-y}{A} - \frac{y.|r(x)+m(x)|^2}{B}$ with an initial condition $y_0=1$.
I solved for $y(x)$ using the following ...
2
votes
0answers
68 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
82 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
106 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
1answer
70 views
Why does the integration of this symbolic matrix slow down after compilation?
There's a symbolic matrix as the following. Why does the integration of the symbolic matrix slow down after compilation? How to eliminate the error information in red? Thanks.
Note: The sample matrix ...
4
votes
1answer
138 views
How to speed up the calculation process of a symbolic matrix?
There are a symbolic matrix and a real number list. I'm going to replace the symbols of the matrix with all the elements of the list, and then to get the Eigenvalues...
4
votes
2answers
673 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
...
1
vote
1answer
47 views
How to generate assumptions automatically for definite integrals？
In Mathematica, a trick to speed up the process of definite integrals is by adding assumptions. For example, the following codes run faster if we add such assumptions:
...
5
votes
2answers
184 views
Factorising blinear forms with Mathematica
Say I have some symbolic output that looks like the following:
expr = A a1 b1 + B a1 b2 + C a2 b1 + D a2 b2
I would like to factorise this in the following way:
...
5
votes
3answers
327 views
How do you find information regarding the derivative?
I have been struggling with an issue that I believe has a simple way to solve.
Given that I have extracted a term of a partial differential equation:
f(1,2,0) [x,y,z]. In this case, it is similar to ...
0
votes
0answers
52 views
Can mathematica solve this analysis difficult problem ? "Functional" equation
Given two continuous functions $G,H: \mathbb R^+ \rightarrow \mathbb R$ such that $\frac{G}{H}$ is positive and strictly increasing, I am looking for two continuous functions $f_0, f_1 :[0,1] \...
5
votes
1answer
203 views
DSolve - incorrect solution to PDE
Bug introduced in 12.2, persisting through 12.3.1.
I'm trying to solve a simple Schrödinger equation in external field:
...
0
votes
1answer
49 views
Solving coupled ODE symbolically for the parameters
I'm trying to solve the following system:
$$ \dot{x_1} = -i w_1 x_1+ i s_1 x_2 $$
$$ \dot{x_2} = -i w_2 x_2- i s_2 x_1 $$
For $X(t)_{1,2}$,
where $x_{1,2} = X(t)_{1,2}\cdot e^{ip(t)_{1,2}}$
I know ...
2
votes
0answers
42 views
Derivative of unknown functions and constants [closed]
I'm trying to do symbolic differentiation with Mathematica for expressions with unkown functions and constans.
For example the following expression:
$$\text{expr} = \omega_1 Q_1^2 Q_2 + \frac{Q_1^3}{\...
0
votes
0answers
39 views
Identity operator of unspecified dimensions
I would like to create a function which can can take a symbolic square matrix $m$ and returns
$m \otimes I$. Where $I$ is the idenity operator of same dimensions as $m$. The actual function I am ...
0
votes
3answers
105 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 ...
0
votes
2answers
118 views
DSolve to obtain a tanh solution
We are given a simple ODE with BCs:
$\xi^2 \frac{df^2}{dx^2} + f - f^3 = 0$
$f(x=0) = 0$
$\\f(x\to\infty) = 1$
On paper this is quite easy to solve. One can obtain the solution
$f(x) = \operatorname{...
1
vote
1answer
133 views
how to define unit vectors in mathematica
I'm struggling a little bit trying to understand how to address this problem, I would like to do this in mathematica: is just that I don't know how to do the dot product between $\mathbf{J}$ and $\...
