变换规则和定义

1、变换规则和定义第1页，共18页，2022年，5月20日，5点27分，星期二2November 18, 2004Start Learning Step by Step1. 应用变换规则expr /. rules在表达式上应用一次规则expr /. rules在表达式上重复应用规则直道结果不再改变应用变换规则expr /. lhs - rhs在表达式上应用某个变换规则expr /. lhs1 - rhs1, lhs2-rhs, .在表达式上依次应用一系列规则应用一组变换规则expr /. rules1, rules2, .应用一组规则得到一个数组一次或重复应用规则第2页，共18页，2022年，5月

2、20日，5点27分，星期二3November 18, 2004Start Learning Step by Step1. 应用变换规则（续）Applying rules to whole expressionsexpr /. rulesapply rules to all subparts of exprReplace expr, rulesapply rules to the whole of expr onlyReplace expr, rules, levspecapply rules to parts of expr on levels specified by levspecAppl

3、ying rules in one way or all possible waysReplace expr, rulesapply rules in one way onlyReplaceList expr, rulesapply rules in all possible ways第3页，共18页，2022年，5月20日，5点27分，星期二4November 18, 2004Start Learning Step by Step2. 对规则的操作Creating and using dispatch tablesDispatch rulescreate a representation o

4、f a list of rules that includes dispatch tablesexpr /. drulesapply rules that include dispatch tables第4页，共18页，2022年，5月20日，5点27分，星期二5November 18, 2004Start Learning Step by Step3. 定义Manual and automatic application of transformation rulesexpr /. lhs - rhsapply a transformation rule to a specific expr

5、essionlhs = rhsassign a value which defines a transformation rule to be used whenever possibleRemoving assignmentsx =.remove the value assigned to the object xClear x, y, .clear all the values of x, y, .第5页，共18页，2022年，5月20日，5点27分，星期二6November 18, 2004Start Learning Step by Step4. 赋值的一些特殊形式Modifying

6、values of variablesi+increment the value of i by 1i-decrement i+ipre-increment i-ipre-decrement ii += diadd di to the value of ii -= disubtract di from ix *= cmultiply x by cx /= cdivide x by c第6页，共18页，2022年，5月20日，5点27分，星期二7November 18, 2004Start Learning Step by Step4. 赋值的一些特殊形式( 续 )Assigning value

7、s to several variables at a timex = y = valueassign the same value to both x and yx, y = value1, value2assign different values to x and y x, y = y, xinterchange the values of x and yAssignments for modifying listsPrependTo v, elemprepend elem to the value of vAppendTo v, elemappend elemv = v, elemma

8、ke a nested list contaning elem第7页，共18页，2022年，5月20日，5点27分，星期二8November 18, 2004Start Learning Step by Step5. 索引的定义Manipulating indexed variablesai = valueadd or overwrite a valueaiaccess a valueai =.remove a value?ashow all defined valuesClearaclear all defined valuesTableai,i,1,n or Arraya, nconver

9、t to an explicit List第8页，共18页，2022年，5月20日，5点27分，星期二9November 18, 2004Start Learning Step by Step6. 函数的定义fx = valuedefinition for a specific expression xfx_ = valuedefinition for any expression, referred to as xThe difference between defining an indexed variable and a function第9页，共18页，2022年，5月20日，5点2

10、7分，星期二10November 18, 2004Start Learning Step by Step7. 定义的次序Treatment of definitions in MathematicaMathematica tries to put specific definitions before more general definitions第10页，共18页，2022年，5月20日，5点27分，星期二11November 18, 2004Start Learning Step by Step8. 即时和延时的定义lhs = rhs(immediate assignment)rhs i

11、s evaluated when the assignment is madelhs := rhs(delayed assignment)rhs is evaluated each time the value of lhs is requestedThe two types of assignments in MathematicaInterpretations of assignments with the = and := operatorslhs = rhsrhs is intended to be the final value of lhs( e.g., fx_=1-x2)lhs

12、:= rhsrhs gives a command or program to be executed whenever you ask for the value of lhs( e.g., fx_:=Expand1-x2)Defining functions for evaluating expressionsfx_ = exprdefine a function which gives the value expr for any particular value of x第11页，共18页，2022年，5月20日，5点27分，星期二12November 18, 2004Start Le

13、arning Step by Step8. 即时和延时的定义( 续 )lhs - rhsrhs is evaluated when the rule is givenlhs : rhsrhs is evaluated when the rule is usedTwo types of transformation rules in Mathematica第12页，共18页，2022年，5月20日，5点27分，星期二13November 18, 2004Start Learning Step by Step9. 记住已知值的函数fx_ := fx = rhsdefine a function w

14、hich remembers values that it findsDefining a function that remembers values it finds第13页，共18页，2022年，5月20日，5点27分，星期二14November 18, 2004Start Learning Step by Step10. 定义联系不同的符号Associating definitions with different symbolsfargs := rhsdefine a downvalue for ffgargs, . := rhsdefine an upvalue for gShor

15、ter ways to define upvaluesfg = value or fgargs = valuemake assignments to be associated with g, rather than ffg:=value or fgargs := valuemake delayed assignments associated with gfarg1, arg2, . = valuemake assignments associated with the heads of all the argi第14页，共18页，2022年，5月20日，5点27分，星期二15Novembe

16、r 18, 2004Start Learning Step by Step10. 定义联系不同的符号( 续 )Possible positions for symbols in definitionsf. := rhsdownvalue for ff/:fg.:=rhsdownvalue for fg/:f.,g,.:=rhsupvalue for gg/:f.,g.,.:=rhsupvalue for g第15页，共18页，2022年，5月20日，5点27分，星期二16November 18, 2004Start Learning Step by Step11. 定义数值值Defining

17、ordinary and numerical valuesexpr = valuedefine a value to be used whenever possibleNexpr = valuedefine a value to be used for numerical approximationDefining numerical valuesthat depend on numerical precisionNexpr = valuedefine a numerical value to be used when defalut numerical precision is requestedNexpr,n=valuedefine a numerical value to be used when n-digit precision is requested第16页，共18页，2022年，5月20日，5点27分，星期二17November 18, 2004Start Learning Step by Step12. 修改内置函数Protection for functionsUnprotectfremove protectionProtectfadd protection第17页，共18页，2022年，5月20日，5点27分，星期二18N