Information Technology Reference
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solving problems about alternating current in physics, program for solving problems in
inorganic chemistry, program for solving algebraic problems, etc. In this section, we
introduce some applications and examples about solutions of problems produced by
computer programs.
The system that supports studying knowledge and solving analytic geometry problems.
The system consists of three components: the interface, the knowledge base, the
knowledge processing modules or the inference engine. The program has menus for
users searching knowledge they need and they can access knowledge base. Besides,
there are windows for inputting problems. Users are supported a simple language for
specifying problems. There are also windows in which the program shows solutions of
problems and figures.
The program for studying and solving problems in plane geometry. It can solve
problems in general forms. Users only declare hypothesis and goal of problems base
on a simple language but strong enough for specifying problems. The hypothesis can
consist of objects, relations between objects or between attributes. It can also contain
formulas, determination properties of some attributes or their values. The goal can be
to compute an attribute, to determine an object, a relation or a formula. After
specifying a problem, users can request the program to solve it automatically or to
give instructions that help them to solve it themselves. The program also gives a
human readable solution, which is easy to read and agree with the way of thinking
and writing by students and teachers. The second function of the program is "Search
for Knowledge". This function helps users to find out necessary knowledge quickly.
They can search for concepts, definitions, properties, related theorems or formulas,
and problem patterns.
Examples below illustrate the functions of a system for solving problems of analytic
geometry, a system for solving problems in plane geometry, and a system for solving
algebraic problems. The systems were implemented using C#, JAVA and MAPLE. Each
example presents the problem in natural language, specifies the problem in specification
language to input into the system, and a solution produced from the system.
Example 5.1 : Let d be the line with the equation 3x + 4y - 12 = 0. P and Q are intersection
points of d and the axes Ox, Oy.
a.
Find the midpoint of PQ
b.
Find the projection of O on the line d.
Specification of the problem:
Objects = {[d,line], [P,point], [Q,point]}.
Hypothesis = { d.f = (3*x+4*y-12 = 0), Ox.f = (y = 0), O = [0, 0], P = INTERSECT(Ox, d),
Q = INTERSECT (Oy, d), H = PROJECTION(O, d), Oy . f = (x = 0) }.
Goal = { MIDPOINT(P, Q), H }.
Solution found by the system:
Step 1: {d.f = (3*x+4*y-12 = 0), Ox.f = (y = 0), Oy.f = (x = 0)} {d.f, Ox.f , Oy.f }.
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