Problem with substitute and powers

Question

Hello!

When i try to make a substitution in the following expression:

ex:=-a**2 - b**2 - 2 a b;
substitute(_,$b->-a$);

I get 2aa, which is obviously wrong. However, if i run the following commands:

ex:=-a**2 - b**2 - 2 a b;
expand_power(_);
substitute(_,$b->-a$);

I get 0, as should be. What is the problem with the first example?

Answer 1

Hi Bruno.

Let me first appologise if my answer is not what you expect, but I'm not a cadabra developer... so I might be wrong about the internal functionalities of the software.

It seems that the algorithm substitute search for an expression (like a "string" in programing) and replace it by a new one... without further manipulations.

If the above is right, then in the first of your code blocks:

ex:=-a**2 - b**2 - 2 a b;
substitute(_,$b->-a$);

the substitution would return

-a**2 + a**2 + 2 a a

which is wrong because the minus sign was not modified by the **2 (square) operation!

My Suggestion

Given the describes behaviour you have to be extra careful in substituting if your expression contains powers.

You could define a function to substitute properly:

def my_subs(ex, rl):
    expand_power(ex)
    substitute(ex, rl)
    collect_factors(ex)
    return ex

Then,

foo := - a**2 - b**2 - 2 a b;
rul := b -> - a;
my_subs(foo, rul);

will return the expected zero.

Cheers, Dox.

Comments

Thank you for your answer!

Answer 2

This is a bug in handling of \pow{...} nodes, thanks for pointing it out. A fix will appear shortly.

Comments

Thank you Kasper. We shall wait for the next release!

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Thank you for your answer!

Answer 3

This is fixed in 2.4.5 which is now on github. If anyone needs a binary package for a system other than Ubuntu 22.04 (which is already available from the download page), let me know.

Comments

Great! Thank you K.