# Questions tagged [symbolic-computation]

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### 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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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### 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 ...
290 views

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 ...
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. ...
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 ...
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 ...
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: ...
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 ...
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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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? ...