computer science

TomSym

TomSym is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand TomSym rather than just read about it. In short: The TomSym MATLAB symbolic modeling engine is a platform for modeling applied optimization and optimal control problems. Description TomSym is complete modeling environment in Matlab with support for most built-in mathematical operators in Matlab.

Key takeaways

TomSym belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect TomSym to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of TomSym from memory before moving on to harder problems.

Reference excerpt

The TomSym MATLAB symbolic modeling engine is a platform for modeling applied optimization and optimal control problems.

Description TomSym is complete modeling environment in Matlab with support for most built-in mathematical operators in Matlab. It is a combined modeling, compilation and interface to the TOMLAB solvers. The matrix derivative of a matrix function is a fourth rank tensor - that is, a matrix each of whose entries is a matrix. Rather than using four-dimensional matrices to represent this, TomSym continues to work in two dimensions. This makes it possible to take advantage of the very efficient handling of sparse matrices in Matlab, which is not available for higher-dimensional matrices. TomSym has a variety of functions, among them:

Ability to transform expressions and generate analytical first and second order derivatives, including sparsity patterns. Interfaced and compatible with MAD, i.e. MAD can be used when symbolic modeling is not suitable. Numerical differentiation can be used to parts of the model. Functionality for plotting and computing a variety of information for the solution to the problem. Support for if, then, else statements. Ability to analyze p-coded Matlab files. Automated code simplification for generated models, for example. Multiplication by 1 or the identity matrix is eliminated: 1*A = A Addition/subtraction of 0 is eliminated: 0+A = A All-same matrices are reduced to scalars: [3;3;3]+x = 3+x Scalars are moved to the left in addition/subtraction: A-y = -y+A Inverse operations cancel: sqrt(x)^2 = x

Modeling The TomSym symbolic source transformation makes it possible to define any the set of decision variables (both continuous and integer) and any type of constraint as well as scalars and constant parameters.

Linear programming An example linear programming problem would look like this:

Mixed-integer nonlinear programming A MINLP problem is defined just like a linear programming problem. This example also shows how to convert the model into a general TOMLAB problem.

Multi-index modeling tomSym makes it possible to build models with two or more variable indices in MATLAB. The following example creates a variable 'flow' with four indices. The variable is then used to create a constraint over two of the indices and to sum the multiplication with a two-dimensional matrix.

Automatic and numerical differentiation For functions that cannot be interpreted by tomSym it is possible to use either automatic differentiation or numerical differentiation. In the following example a simple problem is solved using the two methods.

References

External links TomSym Home Page.

Worked examples

Example 1 — a first encounter with TomSym

Start with the simplest possible case. Write down what TomSym claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to TomSym before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about TomSym ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of TomSym

In research: TomSym appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses TomSym in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: TomSym is common in secondary-school and first-year university syllabi. It links to neighbouring topics Mathematical optimization software, Numerical software, so understanding it makes those chapters shorter.
In everyday life: Look for TomSym outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “TomSym” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study TomSym in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what TomSym means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain TomSym out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is TomSym in simple terms?

The TomSym MATLAB symbolic modeling engine is a platform for modeling applied optimization and optimal control problems. Description TomSym is complete modeling environment in Matlab with support for most built-in mathematical operators in Matlab.

Why does TomSym matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study TomSym?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on TomSym.