Questions tagged [symbolic-computation]

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2
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1answer
145 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}(...
3
votes
2answers
59 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
102 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
33 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
281 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, ...
0
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1answer
100 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
177 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
votes
1answer
92 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
vote
1answer
233 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
238 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
161 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
83 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
723 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^...
4
votes
2answers
3k 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
702 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
178 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
459 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
454 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
votes
1answer
759 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 ...
8
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5answers
2k 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
votes
1answer
895 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
1k 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
276 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
98 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
votes
2answers
614 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
389 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
145 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
563 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
votes
1answer
113 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
879 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 ...
35
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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? ...