How can I verify the equality of two more complicated objects

Posted on 2006-10-29 04:52 By Karel Srot (

78)

Categories:

How do I ...? with Maple

Hello,
can you help me with my problem?

If I want to verify two objects like this

> a:=exp(I*x)=0;
> b:=cos(x)+I*sin(x)=0;

I can use the command

> verify(a, b, 'relation(testeq)');

But how can I verify equality of more complicated objects, for example

> a:={exp(I*x)=0, x^2-x};
> b:={cos(x)+I*sin(x)=0, x*(x-1)};

The command

> verify(a, b, 'set(testeq)');

is (of course) not enough. Is there a way how to do it? How to compare the objects recursively? Mayby the solution is to write my owv verification object, but I don't know how to do it. Is it possible to define a procedure and use it in such way?

> verify(a, b, 'myproc')

If it is so, how should the procedure look like, so it could be used for verification.

Thank you very much for your help.

Karel Srot

verify

Comment on 2006-10-29 07:01 from Mariner ( Maple Rating 4

562)

It seems that verify needs some spoon-feeding. For example:

a:={exp(I*x)=0, x^2-x}:
b:={cos(x)+I*sin(x)=0, x*(x-1)}:
verify(a, b, 'set(testeq)');
false

restart;
a:={exp(I*x)=0, x^2-x}:
b:={convert(cos(x)+I*sin(x),exp)=0, expand(x*(x-1))}:
verify(a, b,verify(a, b, 'set'));
true

Hope this helps.

J. Tarr

Maybe I described my problem

Comment on 2006-10-29 15:19 from Karel Srot (

78)

Maybe I described my problem imprecisely. I want to test objects in more general way. I post a new blog post where my problem is better described. Now I can't see the post im my blog posts (why?), but I will give here the link when I will be able to do that.

The link to my blog post is http://www.mapleprimes.com/blog/karel-srot/testing-objects-for-equivalence. I hope there is my problem described better.

Verification

Comment on 2006-10-30 04:20 from alec ( Maple Rating 4

1608)

In this particular example, the verification can be done as

a:={exp(I*x)=0, x^2-x}:
b:={cos(x)+I*sin(x)=0, x*(x-1)}:
verify(a,b,set({testeq,relation(testeq)}));

                                 true

A new verification procedure can be added as in the following example,

VerifyTools:-AddVerification(example=proc(x,y) evalb(x=y^2) or evalb(y=x^2) end);

verify(1,3,example);
                                false
verify(2,4,example);
                                 true

A series of examples of verification procedures can be found through

kernelopts(opaquemodules=false):
interface(verboseproc=2):
print(VerifyTools:-VerifyTab);

I posted a command for nested verification in my blog, Nested Verification. Using it, the verification in the first example in this comment can be done as

verify(a,b,nested(testeq));

                                 true

__________
Alec Mihailovs
http://mihailovs.com/Alec/