Questions tagged [symbolic]

For questions about symbolic computation, as opposed to numerical computations.

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3
votes
3answers
158 views

Why such a big difference between results of Integrate and NIntegrate?

Studying an interesting article of Daniel Lichtblau, I consider a variation of an example from it, calculating an improper integral ...
0
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2answers
32 views

Fast fourier coefficients for a long sum

I have a very long expression involving a sum of exponentials, say: Sum[(RandomReal[] + RandomReal[] a) Exp[2 I ii x Pi], {ii, -10, 10}] I want the fastest way to ...
0
votes
0answers
27 views

Standard way to define a linear operator?

Say I want to define some simple linear operator. I can do this by f[c_?NumericQ x_] := c f[x] f[x_ + y_] := f[x] + f[y] Or let's define a bi-linear operator ...
0
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1answer
27 views

Simplifying cross product expressions II

This is related to Simplifying cross product expressions Consider the following: ...
0
votes
1answer
25 views

exclude terms from expansion

Suppose I define F1[R + a] = F1[R] + a D[F1[R],R] F2[R + 2 a] = F2[R] + 2 a D[F2[R],R] and I want to expand the square of their sum keeping only first order terms ...
2
votes
1answer
90 views

Simplifying cross product expressions

Suppose I want to calculate: Cross[A1 + B1, A2 - B2] + Cross[A1 - B1, A2 + B2] which is equal to 2 A1xA2 - 2 B1xB2 Using ...
0
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1answer
48 views

Surd factors do not auto cancel each other out

Simplify[Sqrt[Pr] - (Sqrt[Pr/Ra])*Sqrt[Ra]] The above command should give me 0 as the simplified outcome, but it keeps ...
0
votes
0answers
41 views

How to find eigenvalues of 8x8 matrix?

I am new to Mathematica, and was trying to find the eigenvalues of an 8x8 matrix using Mathematica. I have fairly simplifies the matrix A into a mathematical expression and I know the final ...
1
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1answer
47 views

How to define distributivity of CenterDot on bras and kets

I am working on a code for a coupled quantum harmonic oscillator and found myself in a hiccup when trying to evaluate the inner product of linear combinations of bras and kets. I have initially ...
0
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0answers
23 views

Replacement of functions bound by sums and integrals in NCAlgebra

I want to use the NCAlgebra package to do some simplification on non commutative expressions involving integrals. For example, one such expression would be $$ I=\left(\int f(x)g(x) dx\right) * h $$ ...
3
votes
1answer
77 views

How to get True for X^2>= 0? [closed]

How to get true when introducing the expression $x^2 \geq 0$ in mathematica ? how do I specify that x is real ? GreaterEqual[x^2, 0, Element[x, Reals]]
2
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2answers
92 views

Does a positive real solution exist to this problem?

I wrote the following code for getting the solution. I am not sure if the code I wrote is correct. The problem is further intensified by the fact that I don't know if a solution exists to this problem ...
0
votes
0answers
37 views

Cancel common factors in symbolic product

Suppose I have the following function G[n_, k_] := Product[g[n + i]/g[i], {i, 0, k}] where $n,k$ are assumed to be natural numbers and $g$ is a nonzero symbolic ...
1
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1answer
33 views

Difficulty in evaluating the constants of simultaneous equations

How to find the constants A1, A2, B1, B2 using linear solve or null space function in Mathematica. ...
0
votes
1answer
91 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 ...
3
votes
1answer
104 views

Solve system of trigonometric polynomials

I am trying to solve a real system of trigonometric polynomials, which contain 7 symbols {b[1],b[2],b[3],b[4],a[2],a[3],a[4]} between 7 equations: ...
0
votes
1answer
79 views

Finding the exact symbolic formula for a function defined recursively

Let me introduce the problem. I have the following functions; The first one is defined recursively $h(i,j):=\frac{i-1}{j+1}h(i+2,j-2)$ and $h(i,0)=1$ where $i$ and $j$ are even integers, greater than $...
0
votes
2answers
109 views

Incorrect results of differentiation

Let us consider the derivative D[Floor[x]*Sin[Pi*x]^2, x] // Simplify ...
0
votes
1answer
97 views

Why are the results of integrations of a DiracDelta related integrand and its approximations strikingly different?

Let us consider a double integral, treating it as a functional which corresponds a number to a function, ...
0
votes
2answers
101 views

Solving a non-linear system of equations symbolically [closed]

How would I solve this systems of non-linear equations symbolically: $$ \mu N -\frac{\beta S I}{N} - \nu S = 0 \qquad (1)$$ $$\frac{\beta S I}{N} -\gamma I - \nu I = 0 \qquad (2)$$ $$\gamma I - \nu R =...
1
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0answers
34 views

Four dimensional symbolic integration using HalfSpace

Consider the regions $r1 and $r2 defined as follows, ...
0
votes
2answers
57 views

Error in Integration of special functions using mathematica 12.0

When I try to integrate the following, Integrate[-GegenbauerC[22,-1/2,x]/(1+k*x),{x,-1,1}] where -1<k<1 and k!=0, Mathematica gives different results if I ...
2
votes
0answers
45 views

Piecewise PDE Over 3 Regions with Continuity Boundary Conditions

I am using Wolfram Language for the first time for my research and could really use some help! I am trying to find the analytical solution of a PDE which has piecewise constants and a piecewise input. ...
7
votes
0answers
132 views

Series with ArcTan gives wrong symbolic answer in Wolfram Language

Bug introduced after 9, persisting through 12.2. Recently, I have found a very bad problem with Wolfram Language. It gives the wrong answer for a quite simple expression! When calculating ...
0
votes
0answers
36 views

Looking to plot a recursive function with two variables

I have a function that I would like to plot, with Z on the y-axis and N on the x-axis over values from about 0-100 for each: $\qquad M=A^{2/3} a_s+\frac{Z^2 a_c}{\sqrt[3]{A}}+\frac{a_a (N-Z)^2}{4 A}-A ...
0
votes
1answer
46 views

How can I solve a linear equation with many input variables symbolically without taking forever

Background: I have a linear equation whereas T2 and T3 are transformation matrices, Rp is ...
4
votes
3answers
133 views

ApplySides Integrate to equations in differential one-form

Related to this Can we abuse notation and write equations in differential one-form? Is it possible to ApplySides a form of ...
0
votes
1answer
52 views

Symbolic Real Positive Definite Matrix

I'd like to define a symbolic real positive definite matrix. For the 2 x 2 example, I thought I could define four real variables using ...
2
votes
0answers
61 views

How can I simplify a symbolic tensor expression?

My question is about simplifying tensor expressions. If I have $(a+b)\otimes (c+d)$ The function TensorExpand gives $a\otimes c + a\otimes d + b\otimes c + b\otimes ...
5
votes
4answers
314 views

Calculating commutators in quantum mechanics symbolically with the help of Mathematica

Say I have a hamiltonian $H=p_x^2+p_y^2+x^2+y^2+x^4+y^4$, and I want to calculate the commutator $\left[A,B\right] \equiv AB-BA$ of arbitrary operators $\mathcal{O}=x^ap_x^by^cp_y^d$, where $a,b,c,d\...
1
vote
1answer
67 views

Graphing Heat Equation

I was able to solve the heat equation, but am unsure of how to graph the partial sums of the solution. The problem: a.) Solve the heat equation subject to ...
1
vote
1answer
63 views

Solving a Heat Equation

I'm new to Mathematica and am a little lost as to how to code this heat equation: u(0, t) = 0, u(L, t)=0, t>0 u(x, 0)= 1, 0<x<L/2 = 0, L/2<x<L How would I go about solving this?
4
votes
3answers
63 views

Algebraic solution from system of symbolic equations for single variable

I have a mathematical system like K_1 = c*h/d K_2 = b*h/c K_3 = a*h/b C = a+b+c+d h+d = W/h + b + 2a Constants: K_1, K_2, K_3, C, W Solve for: h, a,b,c,d Is it ...
1
vote
0answers
35 views

Differential operator in Mathematica

I am fairly new to Mathematica and I wanted to know if I can define the following operator $E:=(x^2\sqrt{1-K(x^2+y^2+z^2}+y^2+z^2)\gamma^{1}\partial_{1}+(y^2\sqrt{1-K(x^2+y^2+z^2}+x^2+z^2)\gamma^{2}\...
0
votes
2answers
96 views

How to extend this integration to all the reals?

Doing an exercise on calculus with 12.2 on Windows 10 Pro, I obtain a = Integrate[Sqrt[1 + Sin[t]], {t, 0, x}, Assumptions -> x \[Element] Reals] ...
0
votes
1answer
64 views

DSolve doesn't respond

So I am trying to use DSolve to solve the following system of equations: ...
2
votes
1answer
78 views

Can Limit take limits of unknown functions?

For example, when I input this f[0] = 0; Limit[f[x], x -> 0] , it does not output 0. Is there a way to get it to output <...
1
vote
0answers
40 views

Symbolically solving linear program [closed]

I have been surprised that Mathematica cannot solve a linear program. Specifically, I have tried to solve the following problem: ...
0
votes
0answers
56 views

Solving partial differential equation

I am new to mathematica and I want to solve the following pde. I have two boundary conditions and one initial condition. I have tried the following code but the output is not the solution and it's ...
7
votes
1answer
244 views

Problems with DSolve and NDSolve for Dirichlet problem on an annulus

To solve the Dirichlet problem on an annulus, I do the following in 12.2 on Windows 10 Pro ...
1
vote
1answer
68 views

Symbolic Integration with trigonometric functions

I have this trigonometric integral which takes forever to evaluate $\int dx \frac{4 \left(\cos \left(p_1 x\right)-\frac{\sin \left(p_1 x\right)}{p_1 x}\right) \left(\cos \left(p_2 x\right)-\frac{\...
1
vote
0answers
39 views

Take overall minus sign in front in dot product with symbolic variables

I have the following as the output of a calculation a.b+(-a).b and I would like Mathematica to evaluate this to zero. Is there a way to specify that for my ...
1
vote
1answer
52 views

DSolve a partial differential equation with two boundary conditions

While trying to solve: $$ z \frac{\partial}{\partial z} (z G(s,z))=z \cosh (s) \frac{\partial}{\partial z} G(s,z)-\frac{1}{2} \sinh (s) \frac{\partial}{\partial s} G(s,z) $$ using DSolve it gives a ...
0
votes
0answers
50 views

Equations with Tensor product and Ket in Mathematica:

I tried to express this equation in Mathematica: I defined necessary things: ...
1
vote
1answer
57 views

Understand a result of FullSimplify

FullSimplify[((Sqrt[5] - 1)/(2*2^(1/4)))*Sqrt[Sqrt[2]*5^(1/4) - Sqrt[Sqrt[5] - 1]]] returns ...
1
vote
1answer
141 views

How can I solve a system of PDEs with constraints but having unknown boundary conditions

I have a 1st order system of two PDEs with two independent variables and two dependent variables. ...
0
votes
0answers
53 views

Solve method in Mathematica, symbolically solving method

I am looking for a way to solve this equation symbolically with Mathematica. ...
1
vote
1answer
76 views

How to get Mathematica to return more accurate symbolic eigenvectors

This code: Eigenvectors[{{Cos[t], Sin[t]}, {Sin[t], -Cos[t]}}] returns this output: ...
0
votes
1answer
79 views

speed up symbolic summation

I have the following summation L=24; sind=Range[-Pi,Pi,2*Pi/L]; Sum[f, {x, sind}, {y, sind}, {x1, sind}, {y1, sind}, {x2, sind}, {y2, sind}] where ...
4
votes
3answers
163 views

Initial-boundary value problem of 2nd order linear PDE with variable coefficient

Today I was studying partial differential equations and I tried to check if my solution was correct, I thought Mathematica code would be easy, but it wasn't. Here is my problem: Solve $u_{xx}-2tu-u_t=...

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