Questions tagged [symbolic-computation]

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2
votes
0answers
71 views

Algorithm for computing inner products multiple times

I am taking a computational linear algebra course and i got stuck during a homework problem concerning the computation of inner products. I am supposed to compute the inner product:$$\mathrm{a}_{\...
0
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0answers
25 views

Negative binomial expansion of general symbolic polynomial

Using Sympy, I would like to compute the negative binomial expansion of a general symbolic polynomial, e.g., $(x_1 + x_2 + x_3 + 4 x_4)^{-1}$. I understand that I can go by recursively partitioning ...
0
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0answers
11 views

Sufficient conditions to ensure divergence of a sequence in Maxima

I am using Maxima to check whether a given sequence is diverging to $+\infty$. I know that this problem is undecidable and we note that Maxima is throwing an error: ...
2
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1answer
187 views

Lambdifying a symbolic matrix in Julia

If I have a symbolic matrix defined as T below, is there any way to lambdify this as function of variables, say σ..., and return ...
0
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1answer
39 views

Problems with first and second complement

What I know 1=negative,0=positive Example 1. 27-13=14 Example 2. -39+92=53 For example 1. 27 to binary is 11011 13 to binary is 1101 So 1101 change to two complement will ...
12
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4answers
775 views

Example where autodiff works but symbolic differentiation will not?

According to the survey paper on autodiff (linked) Autodiff works on inputs that cannot be specified in closed form but can be described by a sequence of code, each component of which is ...
1
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0answers
26 views

Multibody Systems modeling disadvantages [closed]

Multibody Systems modeling is a very systematic approach usually results in large sparse Jacbian matrix. I am working to model a system consisting of 11 bodies and 63 constraint equations as soon as i ...
1
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2answers
53 views

Numerical integral with symbolic integral in exponent

Many times in fourier approximation we come across integrals such as $$\int_0^1 e^{-\gamma\int_0^xu_0(\eta)d\eta}dx$$ where $\gamma$ is a constant and the data for $u_0$ is provided as a discretely ...
2
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1answer
362 views

Forward and backward integration — cause of errors

I write a test program to integrate foward on $[0,T_f]$ and then backward on $[T_f,0]$ from the endpoint of the forward integration an Hamiltonian system: $$ \dot q(t) = \frac{\partial H}{\partial p}(...
5
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3answers
103 views

Finding exact rational solution to linear integer equations in Matlab

I have a linear system of equations $$Ax=b$$ where $A$ is an $N\times N$ matrix with integer values, and $b$ is a $N\times 1$ vector with integer values. Due to prior knowledge, I know that I am ...
5
votes
1answer
145 views

Nullspace calculation of large matrix with rational numbers without round-off errors (exact)

I need to calculate a basis of the nullspace of large (up to a thousand columns and rows) matrices. For my application, it is very important that no round-off errors occur during the computation, so I ...
1
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0answers
36 views

Maple: patmatch does not identify patterns inside diff() operator

I understand that the function applyrule uses patmatch to identify patterns and apply transformations accordingly. Suppose, I ...
3
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2answers
435 views

Developping PDE with Python symbolically and numericaly

I feel like publishing some previous works from my PhD thesis. I was using Mathematica to build a system of 2N partial differential equations for 2N functions by symbolic spatial Taylor expansion, ...
1
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1answer
140 views

Solving systems of nonlinear ODEs in epidemiology

I have a 9 systems of nonlinear ODEs to solve. I want to determine the endemic equilibrium points. How do I go about it? I tried manual calculation but it becomes cumbersome. Can software be used ...
1
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1answer
249 views

Any FOSS MATLAB/Octave toolbox for high-speed variable precision arithmetic?

I need to use variable precision arithmetic in MATLAB for an expensive set of computation. The vpa function provided by the symbolic math toolbox is very slow. I found a non-free alternative toolbox ...
2
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1answer
98 views

Symbolic convex analysis toolkit for Maple

I'm looking for the SCAT (Symbolic convex analysis toolkit) for Maple written by Hamilton and Borwein. I have seen some references in the specialized literature than mention some urls. However, the ...
1
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1answer
290 views

Matlab symbolic differentiation of Legendre polynomials

Consider $f(x)= \sum\limits_{n=0}^N a_n p_n (x)$, where $p_n$ are the Legendre polynomials. If one wants to differentiate $f'$ symbolically, i.e. to compute $$f'(x) = \sum\limits_{n=0}^{N-1} b_n p_n (...
4
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2answers
257 views

Alternatives to Mathematica

looking to introduce a mathematics program in my work, I would have 2 uses: In a classroom (high school level), providing good visualisation of physics ideas, and making my lecture more interactive. ...
1
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0answers
189 views

Lambdify error when sympy array contains number

This example is a dummy example, but it describes exactly whats goes on in my problem. As a result from some sympy calculation and manipulation i got two arrays ...
2
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1answer
87 views

Performing computations over the set of constructable numbers

The set of constructable numbers is commonly defined in one of two ways: the set of finite numbers reachable from the rational numbers through a finite sequence of addition/subtraction, ...
1
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1answer
966 views

How to solve the problem without using symbolic computation

I have the following simple nonlinear equations with two unknowns only: $$\left\{ \begin{array}{c} \int_1^2{\dfrac{ e^{{a_1} x+{a_2} x^3}}{1+x^2}} \, dx=1 \\[13pt] \int_1^2{ x^2 e^{{a_1} x+{a_2} x^...
5
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2answers
4k views

Symbolic computation vs. numerical computation

I am curious as to what the current status is for symbolic computation, and future outlooks as well. Here are some questions I would like to pose : What is the current outlook for symbolic ...
10
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3answers
934 views

Benchmarks for Gröbner bases and polynomial system solution

In the recent question Solving system of 7 nonlinear algebraic equations symbolically, Brian Borchers experimentally confirmed that Maple can solve a polynomial system that Matlab/Mupad cannot handle. ...
2
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0answers
224 views

How to construct a subring of a polynomial ring in Magma

This is a question about the computer algebra system Magma. I have been looking for a place to ask this type of question on the SE network and scicomp.SE was suggested to me; hopefully it finds a home ...
1
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0answers
536 views

General algorithm to solve systems of symbolic equations

I want to simplify (solve) a system of linear + nonlinear symbolic equations as much as possible. the equations are of random orders, without differentiation. is there a general & well-known ...
0
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1answer
615 views

MATLAB: Backslash operator using symbolic variables with an overdetermined system

I have an overdetermined system (too many equations), expressed as Ax=b, in MATLAB. When I try to solve it using A\b, I receive the error: ...
2
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1answer
784 views

Saving symbolic function to increase efficiency in Matlab

I have a lengthy expression which is calculated using symbolic differentiation of a rather complicated function. I now intend to call this resulting (symbolic function) in a for loop many times, and ...
9
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6answers
3k views

Seeking a free symbolic regression software

Now that Formulize / Eureqa started charging $2500 a year for using it and having crippled the trial version, does anyone know of any replacements that can do similar things like find an equation ...
2
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1answer
1k views

Symbolic Computations with Block Matrices in Maple

Due to the derivation of an algorithm I tried to use Maple (9.5) to calculate some block matrix expression. Unfortunately Maple seems to ignore the assumption I set on the variable. Lets consider the ...
0
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3answers
2k views

Looking for ways to speed up the numeric evaluation of a symbolic expression in Matlab

{Summary: I have a symbolic expression DCritnF expressed in terms of two variables x1 and x2. I need to find it's numeric value and I used combination of double and subs as given below. ...
0
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2answers
284 views

Systems of nonlinear equations

Consider the nonlinear system of equations $$ (1) \quad qk^2a_1^2E^2+wna_0a_1AE+pnka_0^2a_1E+rn^2a_0^2A^2-rn^2a_0^3A^2+qk^2a_0a_1ABE-qk^2na_0^2E^2=0, $$ $$ (2) \quad nwa_1^2AE+nwa_0a_1AB+2pnka_0a_1^...
2
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0answers
108 views

CAS to perform “simple” tensor operations in index notation

Heres a couple of questions, 1) Does a CAS exist that can manipulate Cartesian based tensors and produce a simplified output that is hopefully in index notation? 2) If not, is there some indirect ...
5
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3answers
862 views

How can I teach Maxima to use units?

I want to do engineering and scientific calculations im Maxima/wxmaxima. I do not want to manually check every time if my units make sense, how can I achieve this? I'm looking at Maxima because it's ...
10
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5answers
435 views

How to deal with complexity in numerical code, for example, when dealing with large Jacobian matrices?

I am solving a non-linear system of coupled equations, and have calculated the Jacobian of the discretised system. The result is really complicated, below are (only!) the first 3 columns of a $3\times ...
3
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1answer
68 views

Minimizing expression DAGs

Say I have an expression involving adds, subtractions, and multiplications. I know that it is safe to assume commutativity, associativity, distributivity, etc., and would like to automatically ...
1
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0answers
152 views

What libraries are available for solving problems at the college physics level? [closed]

Are there any libraries available for solving problems at the level of college physics? In particular, I'm interested in libraries for general purpose programming languages that can calculate results ...
1
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1answer
581 views

How easy is it to combine symbolic and numeric computation in Matlab?

CS Beta people: I have been doing some multiple integrals with a combination of symbolic and numerical integration (because symbolic answers have not always been possible). I have been using ...
4
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1answer
116 views

Simple substitutions using symbolic computing in MATLAB

Suppose I have the following MATLAB code. syms a b c1 c2 c1 = a + b + pi*b c2 = a + b + 0.5*b Then c1 gets evaluated to ...
9
votes
5answers
2k views

Symbolic solution of a system of 7 nonlinear equations

I've got a system of ordinary differential equations - 7 equations, and ~30 parameters governing their behavior as part of a mathematical model of disease transmission. I'd like to find the steady ...
17
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8answers
1k views

Is there any open-source or easy-to-access software that can simplify algebraic expressions like $x^{2}+2x+3, x=\sqrt{2}t-1$?

I always calculate things by hand, but now my comrades are getting nasty and making a lot of repetitive exercises involving just plugging things in like the expression above. I am particularly ...
12
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2answers
902 views

Automatic generation of integration points and weights for triangles and tetrahedra

Usually one would consult a paper or book to find integration points and weights for unit triangle and tetrahedra. I am looking for a method to automatically compute such points and weights. The ...
36
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6answers
2k views

Symbolic software packages for Matrix expressions?

We know that $\mathbf A$ is symmetric and positive-definite. We know that $\mathbf B$ is orthogonal: Question: is $\mathbf B \cdot\mathbf A \cdot\mathbf B^\top$ symmetric and positive-definite? ...