{@admin, if it makes good sense, please create a domain for all things Symbolically Maths+Logics (Symbolic Solutions? [your choice] ) and move this topic there - - thank you} @rfateman @certik @carette What is your perspective on the relative benefit and concomitant cost to providing a low-level in…

[image] oscarbenjamin: Personally I think that automatic evaluation is the major mistake made in sympy (and many other CAS). Currently in Symbolics.jl (0.10.0) any numeric type (the default symbol) automatically transforms x - x to 0. If I understand right, @oscarbenjamin and @carette are bot…

I was warning that x-x is tricky. It’s actually fairly safe to transform it to 0*x. For one, that’s type-safe, in the sense that x is still around, so you know the result’s type properly. (Polymorphic 0 is a major pain.) If your numeric types include infinities, then this is required. If your numer…

[image] carette: I was warning that x−xx-x is tricky. It’s actually fairly safe to transform it to 0∗x0*x . For one, that’s type-safe, in the sense that xx is still around, so you know the result’s type properly. (Polymorphic 00 is a major pain.) It’s zero(x) or zero(T) in Julia

Okay I see why the Nemo and Flint timings are so similar: Nemo just uses Flint for the calculation. This is what I meant by speed ultimately being determined by the lower-level libraries. [image] jzr: If I understand right, @oscarbenjamin and @carette are both saying it should stay as x - x unt…

[image] ChrisRackauckas: It’s zero(x) or zero(T) in Julia This doesn’t work if x is an array — zero(x) * x will throw if x is not a square matrix. In the context of rings it is fine, of course, though it still won’t be equivalent to x-x for square matrices that may contain non-finite values. …

julia> using Symbolics julia> Term(sqrt,[2]) sqrt(2) I don’t get why you’d work harder than that. You can build any expression to be lazily like that, or use @register on others. [image] stevengj: This doesn’t work if x is an array — zero(x) * x will throw if x is not a square matrix. In the c…

[image] ChrisRackauckas: I don’t get why you’d work harder than that. You can build any expression to be lazily like that, or use @register on others. I think you’re right, I was mistaken. Term(-, [x,x]) produces x - x which seems like what’s desired. Why doesn’t x - x produce the same result…

[image] ChrisRackauckas: In which case trying to get 0 * x as they posted is an X-Y problem: just writing it as zero(x) is more direct and means what they actually meant using Base Julia functionality. 0 * x is not the same as zero(x) if x is not finite (NaN or ±Inf). That’s why x - x can …

As the originator of this thread, it is my hope and request that we ( that means you Julians :slight_smile: ) return to being about “CAS Best Practices”. That there are different considerations held by CAS experts is helpful information. Let it be, so we move forward. Thank you all for participati…

If you want it exact, don’t ask for the Float64 result? julia> ex = Term(sqrt,[big(2)]) sqrt(2) julia> eval(toexpr(ex)) 1.414213562373095048801688724209698078569671875376948073176679737990732478462102 It just follows Julia’s semantics. [image] stevengj: 0 * x is not the same as zero(x) if x …

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