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Martin Sleziak

06:21

Approach0 documentation: approach0.xyz/docs

I am not entirely sure about how to use qvar and in what situations it can help me.

in Martin Sleziak's room, Aug 28 at 12:07, by Wei Zhong

@MartinSleziak Yes, $x+y$ will find $a+b$ too, IMHO this is the very basic requirement for a math-aware search engine. Actually, approach0 will look into expression structure and symbolic alpha-equivalence too. But for now, $x_1$ will not get $x$ because approach0 consider them not structurally identical, but you can use wildcard to match $x_1$ just by entering a question mark "?" or \qvar{x} in a math formula. As for your example, enter $\frac \qvar{x} \qvar{y} $ is enough to match it.

From approach0.xyz/guide/#advanced-usage "In raw query, you can use \qvar{} to name wildcards which represent different expressions. For instance: $\qvar{x} = \ln (1 + X_t^2) + \qvar{y}$."

question Do I understand correctly that \qvar will force the expression to be different variable.

Let me try to explain on example.

If I search for $\gcd(a,a)=a$, then results such as $\gcd(n,n)=n$ will be among top hits, but this will also match $\gcd(s,t)=u$.

If I add qvar to each a, then each of the three variables has to be different. So $\gcd(s,t)=u$ is still a match, but $\gcd(n,n)=n$ is not.

Did I understand that correctly?

However, originally I came here to ask about a different problem.

question When the variable has to be the same and when not?

For example, if I search for $\gcd(ab,c)=\gcd(a,c)\gcd(b,c)$ then both $\gcd(xy,z)=\gcd(x,z)\gcd(y,z)$ and $\gcd(ab,c)=\gcd(d,e)\gcd(f,g)$ will match this. But the first one has much higher score. (Simply because $a$ is always replaced by the same expression, the same for $b$ and $c$.)

Now what if I have two formulas, like in $\gcd(ab,c)=\gcd(a,c)\gcd(b,c)$, $\gcd(a,b)=1$. Will Approach0 understand that $a$ from the same formula is the same as $a$ from the second one?

Judging by the results returned, it seems that it probably does. At least the top questions returned by those two queries are almost exactly the same questions, which is exactly what I would expect.

So I do not have to add anything special, Approach0 will automatically treat all occurrences of the same letter as representing the same variable. Is that correct?

8 hours later…

Wei Zhong

14:53

@MartinSleziak Not force, but to rank wildcard symbols higher if they are different symbols.

@MartinSleziak Absolutely right.

Wei Zhong

15:14

@MartinSleziak This is a good question, unfortunately, approach0 symbolic scoring function (MNC algorithm) does not connect between two key words. It only applies to a single keyword and get a symbolic similarity score between query keyword. In fact, the number of tokens that can be passed to this MNC function is limited (maximum 64), this is for efficiency reason also.

Wei Zhong

15:37

@MartinSleziak Within one expression, yes, MNC algorithm will take alpha-equivalence into consideration and rank expression higher if they have similar set of "bound variables".

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