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Question: Ease of Manipulating Formulae in Maple

Question:Ease of Manipulating Formulae in Maple

lplex 20 Maple
syntax inequality map
March 23 2020
1


 

I am interested in how easy it is to work with formulae in the Maple language.  For example, you can easily add two equations together with '+'.

 

> 

e1:=x^2+1=2*x;

x^2+1 = 2*x

 (1)
> 

e2:=x^3+x=5;

x^3+x = 5

 (2)
> 

e1+e2;

x^3+x^2+x+1 = 2*x+5

 (3)

 

I was pleased when the following example added (x+1) to both sides of an equation,

 

> 

e3:=x+1;

x+1

 (4)
> 

e1+e3;

x^2+x+2 = 3*x+1

 (5)

Some other algebraic operations work.

> 

e1-e3;

x^2-x = x-1

 (6)
> 

e1*e3;

(x+1)*(x^2+1) = 2*(x+1)*x

 (7)
> 

e1/e3;

(x^2+1)/(x+1) = 2*x/(x+1)

 (8)
> 

e1^(1/2);

(x^2+1)^(1/2) = 2^(1/2)*x^(1/2)

 (9)

 

Build-in functions do not work, though, but there is a simple solution.

> 

exp(e1);

Error, invalid input: exp expects its 1st argument, x, to be of type algebraic, but received x^2+1 = 2*x

  
> 

exp(rhs(e1))=exp(lhs(e1));

exp(2*x) = exp(x^2+1)

 (10)
> 

map(exp,e1);

exp(x^2+1) = exp(2*x)

 (11)

 

The methods also apply to inequality formulae.  I'm not as pleased about how it does '*' and '/' for inequalities.  You can get more control using rhs and lhs functions.  Here are some examples:  

> 

e4:=x^3<5*(x+1);

x^3 < 5*x+5

 (12)
> 

e4+e3;

x^3+x < 6*x+5

 (13)
> 

e4-e3;

x^3-x < 4*x+5

 (14)
> 

e4*e3;

(x^3 < 5*x+5)*(x+1)

 (15)
> 

e4/e3;

(x^3 < 5*x+5)*(1/(x+1))

 (16)
> 

eval(%,x=4);

64/5 < 5

 (17)
> 

evalb(%);

false

 (18)
> 

(16)/x^2;

((x^3 < 5*x+5)*(1/(x+1)))/x^2

 (19)
> 

simplify(%);

((x^3 < 5*x+5)*(1/(x+1)))/x^2

 (20)
> 

lhs(e4)/e3/x^2 < rhs(e4)/e3/x^2;

x/(x+1) < (5*x+5)/((x+1)*x^2)

 (21)
> 

simplify(%);

x/(x+1) < 5/x^2

 (22)
> 

 


 

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