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Course: CIS 120, Fall 2009
School: UPenn
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dispatch Dynamic again Static members Extra office hours this week Extra office hours this week Brent: Wednesday, Moore 100A it is, 5-7PM Alexey: Thursday 5-7, location TBA No office hours for Brent on Friday 9/23/09 2 Sample Exams Posted on class web site 9/23/09 3 HW2 9/23/09 4 Inheritance of fields public class Item { protected Container container; protected String description; ... } public...

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dispatch Dynamic again Static members Extra office hours this week Extra office hours this week Brent: Wednesday, Moore 100A it is, 5-7PM Alexey: Thursday 5-7, location TBA No office hours for Brent on Friday 9/23/09 2 Sample Exams Posted on class web site 9/23/09 3 HW2 9/23/09 4 Inheritance of fields public class Item { protected Container container; protected String description; ... } public class Character extends Item { ... } Since Character extends Item, every Character will automatically inherit the fields container and description no need for Character to declare its own container or description! 9/23/09 5 CONSTRUCTORS AGAIN 9/23/09 6 Constructors and Overloading Constructors can be overloaded: A class can have many constructors, differing in the number and/or types of parameters Well come back to the topic of overloading later, but heres a little example... 9/23/09 7 public class Rectangle { private Point lowerLeft; private double width, height; public Rectangle(Point lowerLeft, double width, double height) { this.lowerLeft = lowerLeft; this.width = width; this.height = height; } public Rectangle(double width, double height) { this.lowerLeft = new Point(0,0); this.width = width; this.height = height; } public double getX() { ... } public double getY() { ... } public void move(double dx, double dy) { ... } } 9/23/09 8 ... Point p = new Point(0,0); Rectangle r1 = new Rectangle(p,1,1); Rectangle r2 = new Rectangle(2,2); 9/23/09 9 Constructors and Inheritance Constructors are not inherited But one constructor can invoke another... A constructor can use either this or super in its first line (only), to invoke another constructor in the same class definition (this) or its superclass (super) Otherwise, an implicit call to super() is inserted at the beginning 9/23/09 10 public class Rectangle { private Point lowerLeft; private double width, height; public Rectangle(Point lowerLeft, double width, double height) { this.lowerLeft = lowerLeft; this.width = width; this.height = height; } public Rectangle(double width, double height) { this(new Point(0,0), width, height); } public double getX() { ... } public double getY() { ... } public void move(double dx, double dy) { ... } } 9/23/09 11 public class Square extends Rectangle { public Square(Point lowerLeft, double side) { // Call superclass constructor with sides equal super(lowerLeft, side, side); } public Square(Point lowerLeft) { // Call constructor above with default side length this(lowerLeft, 1); } } 9/23/09 12 ... Point p = new Point(0,0); Rectangle r1 = new Square(p,2); Rectangle r2 = new Square(p); ... r1.move(3,0); ... System.out.println(r2.getX()); ... What gets printed? Why? 9/23/09 13 stack heap Rectangle r1 Rectangle r2 Square Point lowerLeft double width double height Square Point lowerLeft double width double height Point double x double y 0 0 14 2 2 1 1 9/23/09 public class ColoredSquare extends Square { String color; public ColoredSquare(Point lowerLeft, double side, String color) { // Call superclass constructor with sides equal super(lowerLeft, side, side); this.color = color; } } 9/23/09 15 INHERITANCE AND DYNAMIC DISPATCH 9/23/09 16 Dynamic Dispatch Standard method call in Java Determine which method to invoke based on dynamic type of object To trace b.m() b: A must model heap: Overriding replaces methods in subclasses, so knowing the dynamic type is crucial 17 9/23/09 public class A { int a; public A() { a = 5; } public void m () { a = a + 1; } } public class B extends A { int b; public B() { b = 3; } public void m () { super.m(); b = b + 1; } } ... A x = new A(); B y = new B(); What does the memory configuration look like at the end? What happens if we do y.m()? 9/23/09 18 public class C { int c; public C() { c = 2; } public void p() { this.q(); } public void q() { c = 3; } } public class D extends C { int d; public D() { c = c+1; d = 3; } public void q() { d = 5; super.q(); } } D y = new D(); ... y.p(); ... What does the memory configuration look like at the end? What are the values of the instance variables? 9/23/09 19 STATIC MEMBERS 9/23/09 20 Different roles for classes Models for object creation and behavior for new class creation instance variables: object data methods: object functionality Templates Extend abstract and concrete classes Containers for functionality and data that does not need multiple instances (static methods and data) 21 9/23/09 Classes as containers Container for a set of related static methods and variables To access static members of class C variable: C.var method: C.meth(...) 9/23/09 22 Example: the Math class Defines common mathematical constants and functions Math.PI 3.141592653589793 Math.sin(Math.PI/2) Math.log(Math.E) Math.pow(2,3) 1.0 1.0 8.0 Math.pow(2, 0.5) 1.4142135623730951 Math.sqrt(3*3 4*4) 9/23/09 5.0 23 What + goes into a class Dynamic: different for different instances Variables: separate values Methods: computation that depends on instance variables, this Static: independent of class instance Variables: shared value for all instances Methods: same computation 9/23/09 24 Quiz interface A { public int m(); } class B0 implements A { public int m() { return 0; } } class B1 implements A { public int m() { return 1; } } A a0 = new B0(); A a1 = new B1(); 9/23/09 1. 2. 3. 4. What are the static (compile time) types of a0 and a1? What are the dynamic (run time) types of a0 and a1? What is the result of a0.m()? What is the result of a1.m()? 25 Static vs. Dynamic The keyword static has many meanings in Java. static type, static data, static method, static nested class... Static information can be determined just by looking at the text of the program Dynamic information requires reasoning about the runtime memory configuration Roughly: 9/23/09 26 Static fields and methods Information and behavior that is common to all instances of a class public class Ticket { private static int issued; public static int getIssued(){ return Ticket.issued; } private int number; public Ticket() { this.number = Ticket.issued; Ticket.issued++; } public int getNumber() { return this.number; } } static dynamic 9/23/09 27 Issuing tickets The static variable issued tracks the total number of Ticket objects The instance (dynamic) variable number stores the number of a particular Ticket object Ticket t1 = new Ticket(); t1.getNumber() 0 Ticket t2 = new Ticket(); t2.getNumber() 1 Ticket.getIssued() 2 9/23/09 28 Memory model t1: t2: Class Ticket Ticket int number : 1 int issued : 2; Ticket int number : 0 Location of issued known statically Activation record for getIssued has no reference to this. 9/23/09 29 How to refer to things Class C, o instance of C static dynamic variable dv o.dv dv this.dv what from anywhere static methods of C dynamic methods of C 9/23/09 variable sv C.sv o.sv sv C.sv sv C.sv this.sv method sm C.sm() o.sm() sm() C.sm() sm() C.sm() this.sm() method dm o.dm() dm() this.dm() 30 Access Control public private package (package private) protected Why control access? public class Point implements Displaceable { public double x, y; public Point(double anX, double aY) { x = anX; y = aY; check(); } public double getX() { return x; } public double getY() { return y; } public void move(double dx, double dy) { x += dx; y += dy; check(); } public void check() { if (x < 0.0) { x = 0.0; } if (y < 0.0) { y = 0.0; } } } 9/23/09 32 Why control access? public class Point implements Displaceable { private double x, y; public Point(double anX, double aY) { x = anX; y = aY; check(); } public double getX() { return x; } public double getY() { return y; } public void move(double dx, double dy) { x += dx; y += dy; check(); } public void check() { if (x < 0.0) { x = 0.0; } if (y < 0.0) { y = 0.0; } } } 9/23/09 33 Package access package cis120.lecture10; package declaration public class Counter { int count; public void setCount(int val) { make visible in if (val >= 0) other packages count = val; } public int getCount() { return count; } } 9/23/09 34 Top-level access Classes may have either public or package access. package cis120.lecture10; public class A { . } class B { } Package access 9/23/09 35 Package Groups of classes that work together Named similarly to Unix directories (but with . instead of /) java.nio java.nio.channels java.nio.channels.spi The Java API is organized into a large number of packages Packages are also useful for your own Java programs 9/23/09 36 Referring to package members Explicitly java.io.Reader r = new java.io.FileReader("myfile"); Importing classes from the package import java.io.Reader; import java.io.FileReader; Reader r = new FileReader("myfile"); Importing the whole package import java.io.*; Reader r = new FileReader("myfile"); 9/23/09 37 Package hierarchy java.io.Reader Reader class in java.io java.util.regex.* All classes in java.util.regex java.util.* 9/23/09 All classes in java.util 38 Creating our own packages 1. 2. 3. 4. Build a corresponding directory hierarchy Point Java to the root of the directory hierarchy Add package declarations Make public the names we want to see from anywhere 9/23/09 39 The directory hierarchy /lectures root of the hierarchy /lectures/cis120 /lectures/cis120/lecture10 /lectures/cis120/lecture10/Counter.java /lectures/cis120/lecture10/Counter.class /lectures/cis120/lecture10/Ticket.java /lectures/cis120/lecture10/Ticket.class The Java classpath tells Java where the roots of your class hierarchies are DrJava knows how to set the classpath to find the classes you create and compiled in it 40 9/23/09
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Waterloo - MATH - 136
Math 136Assignment 10 Solutions1. By checking whether columns of P are eigenvectors of A, determine whether P diagonalizes A. If so, determine P 1 , and check that P 1 AP is diagonal. a) A = 42 13 ,P= . 5 3 1 1Solution: Check whether the columns of P a
Waterloo - MATH - 136
Math 136Assignment 9 Solutions1. Calculate the determinant of the following matrices. 0 1 1 0 3 0 0 2 a) A = 0 1 2 1 50 0 7 Solution: Expand along the fourth row: 0 3 det A = 0 5 1 1 00 12 00 0 1 1 0 1 1 0 1 1 1 1 2 (5)(2) = 3 1 2 1 5 0 0 2 = (3)(7) 12
Waterloo - MATH - 136
Math 136Assignment 8 Solutions1. For each of the following matrices, nd the inverse, or show that the matrix is not invertible. 1 1 2 a) A = 3 1 5. 223 Solution: To determine if A is 1 1 3 1 22 Since the RREF 1 1 0 1 b) B = 2 2 10 invertible we write 21
Waterloo - MATH - 136
Math 136Assignment 7 Solutions1. Show the each of the following sets form a basis for the subspace that they span, and determine the coordinates of x and y with respect to the basis. a) cfw_(1, 1, 0, 1, 0), (1, 0, 2, 1, 1), (0, 0, 1, 1, 3); x = (2, 2, 5
Waterloo - MATH - 136
Math 136Assignment 6 Solutions1. Determine, with proof, which of the following are subspaces of the given vector space. Find a basis for each subspace. Solution: A is the solution space of a homogeneous system of linear equations 2x1 + x3 = 0, x1 + x2 x
Waterloo - MATH - 136
Math 136Assignment 5Due: Wednesday, Feb 24th1. Let A = a) 2A B1 2 1 10 0 5 1 2 ,B= ,C= . Determine the following 3 2 1 0 2 3 1 1 2 2 4 2 10 0 1 4 2 = 6 4 2 0 2 3 6 6 1 1 6 1 1 = 1 1 . 2 2 1 1 24 1 = 18 2 1 2 18 . 42Solution: 2A B = b) A(B T + C T )
Waterloo - MATH - 136
Math 136Assignment 4 Solutions 3 2 1 2 1 0 1 0 1 0 , C = 1 . 1. Let A = ,B= 2 1 2 13 3 2 Solution: a) AB = 2 1 4 . 4 1 8Determine the following products or state that they are undened.b) BA is undened since B has 3 columns but A has only 2 rows. c) AC
Waterloo - MATH - 136
Math 136Assignment 3 Solutions1. For each of the following systems of linear equations: i) Write the augmented matrix. ii) Row-reduce the augmented matrix into row echelon form. iii) Find the general solution of the system or explain why the system is i
Waterloo - MATH - 136
Math 136 1. DetermineAssignment 2 Solutionsa) proj(2,1,1) (3, 2, 1) and perp(2,1,1) (3, 2, 1). Solution: (3, 2, 1) (2, 1, 1) 9 (2, 1, 1) = (2, 1, 1) = (3, 3/2, 3/2) (2, 1, 1) 2 6 perp(2,1,1) (3, 2, 1) = (3, 2, 1) proj(2,1,1) (3, 2, 1) = (3, 2, 1) (3, 3/
Waterloo - MATH - 136
Math 136Assignment 1 Solutions1. Compute each of the following. a) (1, 3, 4) + (1, 1, 2) Solution: (1, 3, 4) + (1, 1, 2) = (0, 4, 6). b) 3(1, 1, 2) 2(2, 0, 3).Solution: 3(1, 1, 2) 2(2, 0, 3) = (3, 3, 6) + (4, 0, 6) = (7, 3, 12). Solution: The distance
Waterloo - MATH - 136
Math 136Assignment 10Not To Be Handed In1. By checking whether columns of P are eigenvectors of A, determine whether P diagonalizes A. If so, determine P 1 , and check that P 1 AP is diagonal. a) A = b) A = 42 13 ,P= . 5 3 1 1 13 11 ,P= . 31 1 12. Let
Waterloo - MATH - 136
Waterloo - MATH - 136
Math 136Assignment 8Due: Wednesday, Mar 24th1. For each of the following matrices, nd the inverse, or show that the matrix is not invertible. 1 1 0 2 1 1 2 0 1 1 0 3 1 5. b) B = a) A = 2 2 3 5. 223 1 0 13 2 1 1 1 . Find B 1 and use it to solve B x = d,
Waterloo - MATH - 136
Math 136Assignment 7Due: Wednesday, Mar 10th1. Show the each of the following sets form a basis for the subspace that they span, and determine the coordinates of x and y with respect to the basis. a) cfw_(1, 1, 0, 1, 0), (1, 0, 2, 1, 1), (0, 0, 1, 1, 3
Waterloo - MATH - 136
Waterloo - MATH - 136
Math 136Assignment 5Due: Wednesday, Feb 24th1. Let A = a) 2A B1 2 1 10 0 5 1 2 ,B= ,C= . Determine the following 3 2 1 0 2 3 1 1 2 b) A(B T + C T ) c) BAT + CAT2. Prove that if x M (3, 2) and a, b R are scalars, then (a + b)x = ax + bx. 3. Determine
Waterloo - MATH - 136
Math 136Assignment 4Due: Wednesday, Feb 3rd 3 2 1 2 1 0 1 0 1 0 , C = 1 . 1. Let A = ,B= 2 1 2 13 3 2 a) AB b) BA c) AC d) B T CDetermine the following products or state that they are undened. e) C T C f) BAT2. If AB is a 2 4 matrix, then what size a
Waterloo - MATH - 136
Waterloo - MATH - 136
Waterloo - MATH - 136
Math 136Assignment 1Due: Wednesday, Jan 13th1. Compute each of the following. a) (1, 3, 4) + (1, 1, 2) b) 3(1, 1, 2) 2(2, 0, 3).2. Determine the distance between P (2, 1, 1) and Q(1, 1, 1). 3. Determine which of the following pairs of vectors is ortho
Waterloo - MATH - 136
Math 136Sample Term Test 1NOTES: - Questions 4d, 5, 6 on this test cover material that will not be covered on our term test 1. - Students had 90 minutes to write this test, where you will have 110 minutes. 1. Short Answer Problems a) List the 3 elementa
Waterloo - MATH - 136
Math 136Term Test 1 AnswersNOTE: - Only answers are provided here (and some proofs). On the test you must provide full and complete solutions to receive full marks. 1. Short Answer Problems a) List the 3 elementary row operations. Solution: 1. Multiply
Waterloo - MATH - 136
Math 136Sample Term Test 1 - 2NOTES: - Questions 7, 10b on this test cover material that will not be covered on our term test 1. 1. Short Answer Problems a) List the 3 elementary row operations. b) What can you say about the consistency and the number o
Waterloo - MATH - 136
Math 136Sample Term Test 1 - 2NOTE: - Only answers are provided here (and some proofs). On the test you must provide full and complete solutions to receive full marks. 1. Short Answer Problems a) List the 3 elementary row operations. Solution: 1. Multip
Waterloo - MATH - 136
Math 136Sample Term Test 2 # 1NOTES: - In addition to these questions you should also do questions 4d, 5, 6 from sample term test 1 # 1. 1. Short Answer Problems a) What is the denition of the row space and column space of a matrix A. b) What is the den
Waterloo - MATH - 136
Math 136Sample Term Test 2 # 1 AnswersNOTE: - Only answers are provided here (and some proofs). On the test you must provide full and complete solutions to receive full marks. 1. Short Answer Problems a) What is the denition of the row space and column
Waterloo - MATH - 136
Math 136Sample Term Test 2 # 2NOTES: - In addition to these questions you should also do questions 7, 10 b from sample term test 1 # 2. 1. Short Answer Problems a) Let S = cfw_v1 , . . . , vn be a non-empty subset of a vector space V . Dene the stateme
Waterloo - MATH - 136
Math 136Sample Term Test 2 # 2 AnswersNOTE: - Only answers are provided here (and some proofs). On the test you must provide full and complete solutions to receive full marks. 1. Short Answer Problems a) Let S = cfw_v1 , . . . , vn be a non-empty subse
Waterloo - MATH - 136
Math 136 1. Short Answer ProblemsTerm Test 1 Solutions[2] a) Calculate proj(1,1,2) (1, 2, 2). Solution: proj(1,1,2) (1, 2, 2) =(1,2,2)(1,1,2) (1, 1, 2) (1,1,2) 2= 5 (1, 1, 2). 6[1] b) If n = a b, then what is a n?Solution: Since a b gives an vector
Waterloo - MATH - 136
Math 136Term Test 2 InformationMonday, Mar 15th, 7:00 - 8:50 pmMaterial Covered: Sections 3-1, 3-2, 3-3, 3-4, 4-1, 4-2, 4-3, 4-4. You need to know: - All denitions and statements of theorems and lemmas. - How to prove a subset of a vector space is or i
Waterloo - MATH - 136
Math 136 1. Short Answer ProblemsTerm Test 2 Solutions[1] a) What is the denition of a basis B of a vector space V ? Solution: A basis is a linearly independent spanning set. [1] b) What is the denition of the dimension of a vector space V ? Solution: T
Waterloo - MATH - 136
Math 136Final Exam InformationWednesday, April 14, 2010 9:00 AM - 11:30 AM PAC 1,2,3,4,5,6,7,8,11,12Material Covered: Entire Course. Information: - Although the test covers the entire course, there is an emphasis on material after term test 2. - You ne
Waterloo - MATH - 136
Math 136 - Final Exam Winter 2009NOTE: The questions on this exam does not exactly reect which questions will be on this terms exam. That is, some questions asked on this exam may not be asked on our exam and there may be some questions on our exam not a
Waterloo - MATH - 136
NOTE: These are only answers to the problems and not full solutions! On the nal exam you will be expected to show all steps used to obtain your answer. 1. Short Answer Problems a) det A = 3 (2) = 5 so A1 = 1 0 0 b) L1 = 0 1 0 , 0 01 3 2 . 11 10 0 1 0 0 L2
Waterloo - MATH - 136
Math 136 - Final Exam Spring 2009NOTE: The questions on this exam does not exactly reect which questions will be on this terms exam. That is, some questions asked on this exam may not be asked on our exam and there may be some questions on our exam not a
Waterloo - MATH - 136
1. a) If the rank is 4 and there are 4 linear equations, then there is a leading 1 in each row of the coecient matrix and hence the system is consistent for all b. The number of parameters in the general solution is 5-4=1. b) v = 1(x2 + 1) + 2(x2 + 2x) +
Waterloo - MATH - 136
Math 136Tutorial 1 Problems1: Let x = (3, 5, 1) and y = (2, 1, 1). Calculate 2x 3y , (x + y ) x and determine if x and y are orthogonal. 2: Verify the Cauchy-Schwarz inequality and the triangle inequality if x = (2, 6, 3) and y = (3, 4, 5). 3: Find an e
Waterloo - MATH - 136
Math 136Tutorial 2 Problems1: Determine proj(1,0,1) (6, 2, 6) and perp(1,0,1) (6, 2, 6). 2: Find the distance from the point P (0, 2, 1) to the plane 2x1 x3 = 5. 3: Calculate the area of the parallelogram determined by (2, 3) and (5, 2) in two dierent w
Waterloo - MATH - 136
Math 136Tutorial 3 Problems 1 0 1 1: Consider S = 2 , 1 , 1 . Determine which of the following are in the span 4 1 1 of S . Write each vector in the span as a linear combination of the vectors in S . 2 a) a = 7. 5 1 19 . b) b = 17 c) Is span S = R3 ? Is
Waterloo - MATH - 136
Math 136Tutorial 4 Problems 12 3 1 3 1: Let A = 3 1, B = ,C= . 1 1 4 21 a) AB b) CB c) C T AT .Calculate the following or state that they dont exist:2: Let S = cfw_(1, 1, 1), (0, 1, 1), (2, 1, 1), (1, 2, 3).a) Write the system of linear equations we
Waterloo - MATH - 136
Math 136Tutorial 5 Problems1: a) Let S : R2 R2 be a stretch by a factor of 5 in the x2 -direction. What is the standard matrix of S . b) Calculate the standard matrix of the composition of S followed by a rotation through angle . 3 c) Calculate the stan
Waterloo - MATH - 136
Math 136Tutorial 6 Problems1: Determine, with proof, which of the following are subspaces of R4 . a) The solution space of a homogeneous system with 3 equations in 4 unknowns. b) W = x1 x2 M (2, 2) | x1 + x2 + x3 + x4 = 1 . x3 x4c) S = cfw_p(x) P2 | p(
Waterloo - MATH - 136
Math 136Tutorial 7 Problems1: a) Verify that B = cfw_(1, 0, 1), (1, 1, 2), (1, 1, 1) is a basis for R3 . 1 2, what is v ? b) If [v ]B = 3 2: Find a basis and determine the dimension ofc) Determine the coordinates of x = (1, 1, 1) and y = (4, 2, 7) with
Waterloo - MATH - 136
Math 136Tutorial 8 Problems 1 2 1 3 5 7 1. 1: Find the inverses of A = and B = 3 2 2 1 2 1 2: Let A = 13 . Write A and A1 as a product of elementary matrices. 2 4 2 5 5 2 , and use it to solve Ax = . 1 0 2 133 7 3 5 3: Find an LU-factorization of A = 6
Waterloo - MATH - 136
Math 136Tutorial 9 Problems1: Find the determinant of the following matrices: 123 4 1 2 1 1 1 1 2 1 2 2 2 3 , b) B = a) A = 2 1 2 1 2 1 01 1 1 3 1 3 6 3 1 2: Use Cramers rule to solve x1 5x2 2x3 = 2 2x1 + 3x3 = 3 4x1 + x2 x3 = 1 3: Prove that det A1 =1
Waterloo - AFM - 101
Waterloo - AFM - 101
Waterloo - AFM - 101
Waterloo - AFM - 101
Waterloo - AFM - 101
Waterloo - AFM - 101
Waterloo - AFM - 101
Waterloo - AFM - 101
Waterloo - AFM - 101
Waterloo - AFM - 101
Waterloo - AFM - 101
Keller Graduate School of Management - ACCT - AC557
EXERCISE 12-1 (1520 minutes) (a) (b) 10, 13, 15, 16, 17, 19, 23 1. Long-term investments in the balance sheet. 2. Property, plant, and equipment in the balance sheet. 3. Research and development expense in the income statement. 4. Current asset (prepaid r
Keller Graduate School of Management - ACCT - ACC557
EXERCISE 13-1 (1015 minutes)(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) Current liability. Current liability. Current liability or long-term liability depending on term of warranty. Current liability. Footnote disclosure (assume not p
Keller Graduate School of Management - ACCT - ACC557
EXERCISE 13-1 (1015 minutes)(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) Current liability. Current liability. Current liability or long-term liability depending on term of warranty. Current liability. Footnote disclosure (assume not p
Keller Graduate School of Management - ACCT - ACC552
EXERCISE 13-4 (2025 minutes) SANTANA COMPANY Partial Balance Sheet December 31, 2010 Current liabilities: Notes payable (Note 1). Long-term debt: Notes payable expected to be refinanced in 2011 (Note 1). $4,000,000*3,000,000Note 1. Under a financing agr