I am using the Symbolics package and having trouble figuring out how to simplify expressions. Note that \sqrt{3} and 3/\sqrt{3} are equal, but I can’t seem to get that. For example: julia> using Symbolics julia> a = sqrt(Num(3)) sqrt(3) julia> a == 3/a sqrt(3) == (3 / sqrt(3)) # this isn't helpful julia> a - 3/a sqrt(3) + -3 / sqrt(3) julia> iszero(ans) false # this is incorrect

Looks like a bug, isequal(a, 3 / a) should return true or at least realize it can’t do the computation. isequal((3/a)^2, 3) also fails, but isequal(simplify((3/a)^2), 3) succeeds.

julia> a = sqrt(3) 1.7320508075688772 julia> 3/a 1.7320508075688774 Notiice the floating point error in the last digit arising out of dividing a rational by its irrational square root.

I’m not sure Symbolics.jl is really setup for this kind of work but maybe @ChrisRackauckas or @cryptic.ax can comment on that. You can do a similar trick as Symbolics.jl simplify exp(0) to 1 - #2 by langestefan julia> using Symbolics julia> a = sqrt(Num(3)) sqrt(3) julia> rules = RuleSet([@rule(~x / ~s => ~x * ~s / (~s)^2)]) SymbolicUtils.Rewriters.Walk julia> simplify(a - 3/a, rewriter=rules) 0 Which works because this rule is built in: julia> sqrt(Num(3))^2 3

For my project, I’ve swapped out Symbolics for PySym. So I’m set, but I would have thought Symbolics should be able to do this sort of simplification without modifications.

You can use SymJ.jl. It is a Julia version of SymPy and faster than Symbolics.jl . using SymJ julia> a = sqrt(Sym(3)) sqrt(3) julia> a - 3/a 0

Just for reference between isequal and == look at [image] Symbolics Equality General Usage I’m trying to extend some modules to work with Symbolics by getting rid of Bool conditionals and divide by zero checks etc. I’m trying to add some unit tests and I want to test if two symbolic equations are equivalent. When I try and extend Base.:(==) by checking if the components of a composite type structure are == symbolically (I even throw in some simplify calls wrapping the LHS and RHS of the equals) it complains about non-Boolean being used in a Boolean context. What’s the trick to see … Giac.jl doesn’t behave that way. (Just saying :smirking_face:) julia> using Giac julia> a = giac_eval(“sqrt(3)”) or a = sqrt(to_giac(3)) GiacExpr: sqrt(3) julia> a == 3/a true

The link to the SymJ.jl announcement (though not yet registered) by the author @j_verzani, is [image] [ANN] GruntzLimit.jl, RischIntegrate.jl, RUBISymbolicIntegration.jl, SymJ.jl Package Announcements New packages, mostly generated with assistance from Claude. These started as an experiment to see how much work it would be to generalize SymbolicLimits.jl and SymbolicIntegration.jl beyond SymbolicUtils.jl to any symbolic type supporting just the TermInterface.jl contracts. GruntzLimits.jl has better coverage (it is on par with SymPy.jl and Giac.jl) and better performance than SymbolicLimits on SymbolicUtils types and, as the Expr type is supported in TermInterface.jl can be used with or witho…

Yeah this is something Symbolics is not very good at. I think we can handle some of the trivial cases here (e.g. 3 / sqrt(3), 3x^2 * y / sqrt(3)) so I’ll set a bot on the problem. My only concern is if it will have a measurable runtime impact on / which is already pretty slow in SymbolicUtils. Benchmarks will tell. SymJ.jl is pretty cool though, I’d definitely recommend giving it a shot. I’m also setting a bot on comparing some things I’m curious about, mainly design decisions that it has a different opinion on. If it gets registered, I think it might be a good backend for some of the polynomial expansion algorithms that Symbolics isn’t good at.

Also, the two expressions not comparing isequal is not really a bug. Symbolics’ expression canonicalization does leave a lot to be desired, but expressions only compare isequal if their tree structures (and corresponding types/shapes) are identical.

Simplification in Symbolics

General Usage

Ay11 November 8, 2026, 11:34am 8

The link to the SymJ.jl announcement (though not yet registered) by the author @j_verzani, is

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Simplification in Symbolics

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