Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Bra–ket notation wikipedia , lookup
History of the function concept wikipedia , lookup
Approximations of π wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Principia Mathematica wikipedia , lookup
Positional notation wikipedia , lookup
Chapter 5: MuPAD Objects I Numbers, Identifiers, Expressions MATLAB for Scientist and Engineers Using Symbolic Toolbox You are going to See that MuPAD handles objects Get to know MuPAD numbers, identifiers and expression types Use these objects for various purposes 2 Domain Types Every MuPAD object belongs to some data type, called the domain type. Domain Types MuPAD Kernel: DOM_INT, DOM_RAT, etc. MuPAD Language: Dom::Matrix(R), etc User Defined Types Identifying Domain Types 3 Fundamental Domain Types 4 Fundamental Domain Types (cont.) 5 Operands: op and nops A MuPAD object can be decomposed into operands. Functions for accessing operands. Accessing sub-operands 6 Operands: Example Accessing specific operands 7 Operands: Nested Lists Object: Operands and sub-operands 8 Exercise The following call of solve returns a set: Extract the value of the solution for y and assign it to the identifier y. Solution: 9 Numbers Number Data Types Accessing Components 10 Numbers (cont.) Integral Quotient and Remainder Number? Not a Number! 11 Functions & Operators for Numbers 12 Exercise Compute the decimal expansions of and 163 3 with a precision of 10 and 100 digits, e respectively. What is the 234th digit after the decimal point of ? 13 Exercise After you execute x:= 10^50/3.0, only the first DIGITS decimal digits of x are guaranteed to be correct. a. Truncating the fractional part via trunc is therefore questionable. What does MuPAD do? b. What is returned for x after increasing DIGITS? 14 Identifiers Identifiers are names such as x or f that may represent variables and unknowns. DOM_IDENT 15 _assign and assign The operator := is a short form of the system function _assign. assign: sets or lists of equations are transformed into assignments: 16 Identifier Concatenation Concatenation operator “.” 17 Exercise Read the help page for solve. Solve the system of equations x1 + x2 = 1, x2 + x3 = 1, . . . , x19 + x20 = 1, x20 = π in the unknowns x1, x2, . . . , x20. Read the help page for assign and assign the values of the solution to the unknowns. 18 Symbolic Expressions An object containing symbolic terms Number of Operands Top Level Operator 19 Expression Tree Graphical Representation of Expression op(f,0) = + op(f,[1,0]) 0 op(f,2) op(f,[1,1,0]) sin * x g x 0.3 op(f,[1,3]) ? 1/5 y op(f,[1,2,1,2]) 20 21 22 System Functions vs. Operators They are equivalent Variable number of arguments Operators are converted into system functions internally. 23 Sequence and Range $ and .. Sequence Operator Range Operator Used with other operators 1 2 3 ... 100 1 2 3...10 24 Mapping a Function Applies a function to all operands of a MuPAD object. Function Concatenation Operator Use Back-ticks for Operator Symbols 25 Operator Priorities Higher priority operators apply first Example 26 Key Takeaways Now, you are able to use op() and nops() to access operands of MuPAD objects, draw an expression tree for an expression, tell how to use the following system functions and operators. dom_type _mult . $ delete .. op map assign _sum nops 27 Notes 28