Missing + overload when trying to create a point with symbolic coefficients

[micahscopes]

So I wanted to make a symbolic sphere using Reduce.jl symbols. I started off by making a point like this:

using Grassmann, Reduce;

X = :x*v1 + :y*v2 + :z*v3
pt = ↑(X)

But I get an error:

MethodError: no method matching +(::Float64, ::Expr)
Closest candidates are:
  +(::Any, ::Any, !Matched::Any, !Matched::Any...) at operators.jl:529
  +(::Float64, !Matched::Float64) at float.jl:401
  +(::AbstractFloat, !Matched::Bool) at bool.jl:106
  ...

Stacktrace:
 [1] +(::Float64, ::Float64, ::Expr, ::Expr, ::Expr) at ./operators.jl:529
 [2] ∑(::Float64, ::Float64, ::Expr, ::Vararg{Expr,N} where N) at /home/micah/.julia/packages/AbstractTensors/4KbT3/src/AbstractTensors.jl:280
 [3] macro expansion at /home/micah/.julia/packages/Grassmann/EjCrQ/src/products.jl:0 [inlined]
 [4] *(::Chain{⟨∞∅+++⟩,1,Any,5}, ::Chain{⟨∞∅+++⟩,1,Any,5}) at /home/micah/.julia/packages/Grassmann/EjCrQ/src/products.jl:856
 [5] ^(::Chain{⟨∞∅+++⟩,1,Any,5}, ::Int64) at /home/micah/.julia/packages/Grassmann/EjCrQ/src/algebra.jl:615
 [6] macro expansion at ./none:0 [inlined]
 [7] literal_pow at ./none:0 [inlined]
 [8] ↑(::Chain{⟨∞∅+++⟩,1,Any,5}) at /home/micah/.julia/packages/Grassmann/EjCrQ/src/Grassmann.jl:124
 [9] top-level scope at In[6]:2

I can get around this by first defining:

using Base;
Base.:+(a::Float64, b::Expr) = a*v+b;

It fixes the problem, for now, but seems a little too hacky to make a PR worthy solution. I tried:

using Base;
Base.:+(a::Number, b::Expr) = a*v+b;

and got:

MethodError: +(::Simplex{⟨∞∅+++⟩,0,v,Float64}, ::Expr) is ambiguous. Candidates:
  +(a::T, b::Union{Expr, Symbol, #s71, #s70} where #s70<:Complex where #s71<:Real) where T<:TensorGraded in Grassmann at /home/micah/.julia/packages/Grassmann/EjCrQ/src/algebra.jl:706
  +(a::Number, b::Expr) in Main at In[7]:2
Possible fix, define
  +(::T, ::Expr) where T<:TensorGraded

Stacktrace:
 [1] +(::Float64, ::Expr) at ./In[7]:2
 [2] +(::Float64, ::Float64, ::Expr, ::Expr, ::Expr) at ./operators.jl:529
 [3] ∑(::Float64, ::Float64, ::Expr, ::Vararg{Expr,N} where N) at /home/micah/.julia/packages/AbstractTensors/4KbT3/src/AbstractTensors.jl:280
 [4] macro expansion at /home/micah/.julia/packages/Grassmann/EjCrQ/src/products.jl:0 [inlined]
 [5] *(::Chain{⟨∞∅+++⟩,1,Any,5}, ::Chain{⟨∞∅+++⟩,1,Any,5}) at /home/micah/.julia/packages/Grassmann/EjCrQ/src/products.jl:856
 [6] ^(::Chain{⟨∞∅+++⟩,1,Any,5}, ::Int64) at /home/micah/.julia/packages/Grassmann/EjCrQ/src/algebra.jl:615
 [7] macro expansion at ./none:0 [inlined]
 [8] literal_pow at ./none:0 [inlined]
 [9] ↑(::Chain{⟨∞∅+++⟩,1,Any,5}) at /home/micah/.julia/packages/Grassmann/EjCrQ/src/Grassmann.jl:124
 [10] top-level scope at In[7]:3

By this point I got kinda lost trying to define

Possible fix, define
  +(::T, ::Expr) where T<:TensorGraded

[chakravala]

It's recommended to have using Reduce, Grassmann instead of using Grassmann, Reduce due to performance reasons. It is in fact faster to load Reduce before Grassmann.

The issue should now be resolved for your use case, although it's not a completely general fix.