% Description: This file contains a long list of examples demonstrating the abilities of % the translator. Most of these examples come straight from the MathML spec. They % are part of those used during the development of the interface and should all % be correctly translated into OpenMath. % % Version 17 April 2000 % % Author: Luis Alvarez Sobreviela % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % These examples attempt to test the following aspects: % % - Types of arguments % - Containers % + sets % + vectors % + intervals % + matrices % - Sums, products % - Calculus % - Lambda expressions % - Limits % - Quantifiers % - Set functions % - MathML1 Relational operators % - Statistics % - Functions on Matrices % - Various general expressions % - Complex expressions % Expressing different types of numbers mml2om();

6 3

6 3 mml2om();

6 3

6 3 mml2om();

6

10 6 % Containers. mml2om();

b 2 c

2 mml2om();

b 2 c

2 mml2om();

b a c

mml2om();

b a c

mml2om();

b a c

mml2om();

b 2 c

2 mml2om();

123 x

1 2 3 % Must make sure these elements translate % to the correct OpenMath symbols. % The MathML interval maps to different % OPenMath symbols. mml2om();

b 2

2 mml2om();

b 2

2 mml2om();

b 2

2 mml2om();

b 2

2 % Matrices mml2om();

010001100

0 1 0 0 0 1 1 0 0 mml2om();

010001100

0 1 0 0 0 1 1 0 0 % The following operators need to be carefully % monitored because OpenMath has different % representations for such elements. % sums, products mml2om();

x a b x y

mml2om();

x a b f x

mml2om();

x a b f x

% Calculus mml2om();

x a b f x

mml2om();

x x 2

2 mml2om();

x x

mml2om();

x f x

mml2om();

x 2 f x

mml2om();

x 3 f x

mml2om();

x 01 x 2

0 1 2 mml2om();

x 1 ∞ x

1 mml2om();

x a b x

mml2om();

x 2 f x

% Lambda expressions mml2om();

x x

% Limits mml2om();

x 0 x

0 mml2om();

x x a x

mml2om();

V V 0 S a V

0 mml2om();

x 0 x

0 mml2om();

x x a x

% Quantifiers mml2om();

x y z n n 2 x n y n z n

2 mml2om();

a a a

% Set functions. mml2om();

A B

mml2om();

b 2 c b r 24 c

2 2 4 mml2om();

A B

mml2om();

b 2 c b r 24 c

2 2 4 % MathML1 relational operators. The attributes % are unecessary, and so the parser should ignore % them mml2om();

a A

mml2om();

a A

mml2om();

A B

mml2om();

A B

mml2om();

A B

mml2om();

A B

mml2om();

222

2 2 2 mml2om();

2 A u

2 mml2om();

22

2 2 mml2om();

2 A

2 mml2om();

222

2 2 2 mml2om();

2 A u

2 mml2om();

222

2 2 2 mml2om();

2 A u

2 mml2om();

222

2 2 2 mml2om();

2 A u

2 mml2om();

222

2 2 2 mml2om();

2 A u

2 % Statistics mml2om();

b r 24 c

2 4 mml2om();

b r 24 c

2 4 mml2om();

b r 2 4 c 2 4 % Functions on matrices mml2om(); $315702178$ 3 1 5 7 0 2 1 7 8 mml2om(); $315702178$ 3 1 5 7 0 2 1 7 8 mml2om(); $12341$ 1 1 2 3 4 mml2om(); $123422$ 2 2 1 2 3 4 mml2om(); $a 1 2 s$ 1 2 mml2om(); $1234121223212111$ 1 2 3 4 1 2 1 2 2 3 2 1 2 1 1 1 % A variety of different expressions mml2om(); $x y 37$ 3 7 mml2om(); $a b$ mml2om(); $a b$ mml2om(); $b 2 c$ 2 mml2om(); $b 2 c$ 2 mml2om(); $b 2 c$ 2 mml2om(); $x x 3$ 3 mml2om(); $2 x x x x 2$ 2 2 mml2om(); $x x 3$ 3 mml2om(); $x x 3$ 3 % Complex expressions mml2om(); $x ⅈ 1 x ⅈ 1$ 1 1 mml2om(); $x y x y 2 x y 22 x y 2 x y 2 x y 1$ 2 2 2 2 2 1 mml2om(); $x root_of y x_x_x_x_y x_y x_tag_1 a x y$ mml2om(); $x root_of ⅈ x_y ⅈ x_x_y 1 x_x_x_y 2 x_x_x_y x_tag_2 z y$ 1 2