Symbolic Variables

Algebra is a lot like arithmetic but deals with symbolic variables in addition to numbers. Very often these include x, y, and/or z, especially for unknown quantities, which is often your job to solve for. Earlier letters of the alphabet such d a,b,c... are often used for constants, quantities whose values are determined by assumed conditions before you solve a particular problem. Most Enghsh letters find use somewhere as either variables or constants. Remember that variables are case sensitive, so X designates a different quantity than X. As the number of mathematical symbols in a technical subject proliferate, the English (really Latin) alphabet becomes inadequate to name all the needed variables. So Greek letters have to be used in addition. Here are the 24 letters of the Greek alphabet  

If you ever pledged a fraternity or sorority, they probably made you memorize these Greek letters (but your advantage was probably nullified by too 

FIGURE 3.1 The two sides of an equation must remain balanced just like the Scales of Justice. We will remove her blindfold to help her keep the scales balanced. 

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The definitions of the torsional angles are illustrated in Figure 2.7. To emphasize the symmetry (Cs) of the above conformation, the Z-matrix may also be given in terms of symbolic variables, where variables which aie equivalent by symmetry have identical names. 

The symbolic variables show explicit which parameters are constrained to have the same values, i.e. He and H7 are symmetry equivalent and must therefore have the same distances and angles, and a sign difference in the torsional angle. Although the R4 and R5 (and A3 and A4) parameters have the same values initially, they will be different in the final optimized structure. 

Table number Designated symbol Variable Sampling distribution of... 

Symbol Variable Lower bound Upper bound Starting value... 

The symbolic variables show explicit which parameters are constrained to have the ... 

Separability theorem, 309 SHAKE algorithm, 385 SHAPES force field, 40 Simulated Annealing (SA), global optimization, 342 Simulation methods, 373 Supidfiidiil, iulcs, 3j6 Susceptibility, 237 Symbolic variables, for optimizations, 416 Symmetrical orthogonalization of basis sets, 314 Symmetry adapted functions, 75 Symmetry breaking, of wave functions, 76 ... 

Symbolic variables can also be assigned to names as follows ... 

Symbol Variable Unit Distc Char, value Partial factor Mean/CoV... 

Equation (6.12) comprises all possible relationships that may exist in system instance w. To keep the model simple, we will refer to the problem model Eq. (6.3) as the object model and to the set of relationships as R. A problem model is an abstract representation of a problem domain—a meta-model. Ontological commitments are for developing a data model out of this meta-model. These commitments are interfaces between abstract problem representation and real world data storage. Rearranging the standard definition, we can define a model M as a stmcture (S, /), where S = (T, R) is a global stmcture (standard system definition) and 7 is an interpretation function assigning elements of T to constant symbols (variables) of V. 

Function-symbols (functors) and predicate-symbols start with a lowercase letter. We often write them out followed by a slash and their arity. Examples are aA),//2,p/3. Exceptions are some primitive symbols, such as =/2, function-variable symbols, and predicate-variable symbols start with an uppercase letter. Examples are X, F, P. An anonymous variable is denoted by an underscore Schema-variable symbols and notation-variable symbols consist of a lowercase letter. Examples are ij, k, m, n. The distinction with one-letter constants should always be obvious from context. By abuse of language, we often say variable instead of variable-symbol. 

Some menu commands are instruments used to solve the problems. Thus, we can solve an analytical equation or inequality by the command Symbolic Variable Solve if we previously type the expression in a worksheet and mark the variable to... 

To perform symbolic computations, you must use syms or sym to declare the variables you plan to use to be symbolic variables. First, you have to introduce symbols to the MATLAB environment ... 

NOTE It is assumed that x is defined as symbolic variable, using the syms command. Alternatively, X can be defined as ... 

NOTE The solution Z is 1 x 1 struct that has three symbolic variables yl, y2, and y3. After defining t as a row vector, the MATLAB built in eval function is used to evaluate the symbolic expression of y into numbers as a function f. 

Symbolic variables, for optimizations, 416 Symmetrical orthogonalization of basis sets, 314... 

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