Simplifying construstion of symbolic numbers

[bowenszhu]

Following the discussion in

• Discourse: Symbolic sqrt(2) and sin(pi)
• Discourse: Basic question on Julia symbolic. How to keep exp(1) as is and not convert it to a floating point number?
• Allow use of algebraic expressions in method coefficients with Symbolics.jl ranocha/BSeries.jl#96
• Promotion with rationals when constructing arrays #849

As of Symbolics v5.1.0 and SymbolicUtils v1.0.3, it is complicated to create a symbolic number that doesn't include a variable.

For example, to create a symbolic $\sqrt 3$, one needs to call

sqrt3 = Symbolics.wrap(Symbolics.Term(sqrt, [3]))

Here, users have to be aware of the Term data structure, in which the field arguments is a Vector instead of just a scalar number.

• The struct definition of Term
• The constructors of Term

And a BasicSymbolic shall be wrapped in a Num in order to properly use promotion rules.

Symbolics.jl/src/wrapper-types.jl

Lines 48 to 52 in 426eb80

	function wrap(x)
	T = SymbolicUtils.symtype(x)
	Symbolics.has_symwrapper(T) ?
	Symbolics.wrapper_type(T)(x) : x
	end

Symbolics.jl/src/num.jl

Lines 1 to 3 in 426eb80

	@symbolic_wrap struct Num <: Real
	val
	end

Symbolics.jl/src/num.jl

Lines 98 to 99 in 426eb80

	Base.promote_rule(::Type{<:Number}, ::Type{<:Num}) = Num
	Base.promote_rule(::Type{<:Symbolic{<:Number}}, ::Type{<:Num}) = Num

We should hide these internal details to make it simpler for end users.

In SymPy and SymEngine, we can do it as follows, which are very straightforward.

using SymPy; Sympy.sqrt(Sym(3))

using SymEngine; sqrt(Basic(3))

[orebas]

What is the current way to just convert a number (and indeed, the number 0) into a symbolic that can be stored in a vector with other symbolic expressions? I tried (Symbolics.Term(Symbolics.identity, [Real(Float64(result))]) ) but this gives an error when I try to store it in an array, the error is

ERROR: LoadError: MethodError: Cannot `convert` an object of type
  SymbolicUtils.BasicSymbolic{Float64} to an object of type
  SymbolicUtils.BasicSymbolic{Real}