Spacing of math symbols to the left of a letter and between two letters

Question

I am a little annoyed with the inconsistency of the spacing of some math symbols like + and - when they appear to the left of a letter (or symbol) and when they appear between two letters (or symbols), as shown in the picture. Is there a reason for these spacing to be different? Is there any way to make them always equal without me having to do it manually every time they appear in the text?

Thanks.

Answer 1

Fully automatic, thanks to LuaTeX.

\documentclass{article}
\usepackage{amsmath}
\usepackage{luacode}
\begin{luacode*}

local muglue_subtype
do
    for num, name in pairs(node.subtypes(node.id("glue"))) do
        if name == "muglue" then
            muglue_subtype = num
            break
        end
    end
end
assert(muglue_subtype, "No such subtype!")

function table.contains(haystack, needle)
    for _, straw in next, haystack do
        if straw == needle then
            return true
        end
    end
    return false
end

local glue_fields = { "width", "stretch", "stretch_order", "shrink", "shrink_order" }

local function binordspacing(head,style,penalties)
    local cur = head
    local match = 0
    while cur do
        local subtype = node.subtypes(cur.id)[cur.subtype]
        if match == 0 and table.contains({"op", "bin", "rel", "open", "punct"}, subtype) then
            match = 1
        elseif match == 1 and subtype == "bin" then
            match = 2
        elseif match == 2 and subtype == "ord" then
            local binordspacing = tex.getmath("binordspacing", style)
            local n = node.new("glue", muglue_subtype)
            for _, field in ipairs(glue_fields) do
                n[field] = binordspacing[field]
            end
            head = node.insert_before(head, cur, n)
            match = 0
        else
            match = 0
        end
        cur = cur.next
    end
    return true
end

luatexbase.add_to_callback("pre_mlist_to_hlist_filter", binordspacing, "binordspacing")

\end{luacode*}
\begin{document}
\begin{equation*}
    \alpha = -p(-w_1-v_0) - g(w_1)
\end{equation*}

\begin{center}
    $\alpha = -p(-w_1-v_0) - g(w_1)$
\end{center}
\end{document}

Ahhh, my eyes!

---

In the comments you mentioned that you'd also like to have space between the opening parenthesis and the minus (oh god, why?) so I came up with a more configurable approach. This allows you to insert random spacing in places where TeX would not consider that (for good reasons).

\documentclass{article}
\usepackage{amsmath}
\usepackage{luacode}
\begin{luacode*}

local muglue_subtype
do
    for num, name in pairs(node.subtypes(node.id("glue"))) do
        if name == "muglue" then
            muglue_subtype = num
            break
        end
    end
end
assert(muglue_subtype, "No such subtype!")

local glue = glue or {}
function glue.copy(src)
    local glue_fields = { "width", "stretch", "stretch_order", "shrink", "shrink_order" }
    local g = node.new("glue", muglue_subtype)
    for _, field in ipairs(glue_fields) do
        g[field] = src[field]
    end
    return g
end

local knuth_table = {
    ord   = { ord = "0"  , op = "1"  , bin = "(2)", rel = "(3)", open = "0"  , close = "0"  , punct = "0"  , inner = "(1)" },
    op    = { ord = "1"  , op = "1"  , bin = "*"  , rel = "(3)", open = "0"  , close = "0"  , punct = "0"  , inner = "(1)" },
    bin   = { ord = "(2)", op = "(2)", bin = "*"  , rel = "*"  , open = "(2)", close = "*"  , punct = "*"  , inner = "(2)" },
    rel   = { ord = "(3)", op = "(3)", bin = "*"  , rel = "0"  , open = "(3)", close = "0"  , punct = "0"  , inner = "(3)" },
    open  = { ord = "0"  , op = "0"  , bin = "*"  , rel = "0"  , open = "0"  , close = "0"  , punct = "0"  , inner = "0  " },
    close = { ord = "0"  , op = "1"  , bin = "(2)", rel = "(3)", open = "0"  , close = "0"  , punct = "0"  , inner = "(1)" },
    punct = { ord = "(1)", op = "(1)", bin = "*"  , rel = "(1)", open = "(1)", close = "(1)", punct = "(1)", inner = "(1)" },
    inner = { ord = "(1)", op = "1"  , bin = "(2)", rel = "(3)", open = "(1)", close = "0"  , punct = "(1)", inner = "(1)" }
}

local function subtype(n)
    if not n then
        return nil
    end
    return node.subtypes(n.id)[n.subtype]
end

local function traverse(head, style)
    for n in node.traverse(head) do
        if n.id == node.id("sub_mlist") then
            traverse(n.list, style)
        else
            if subtype(n) == "bin" then
                local undefined = false
                -- look at the previous
                local prevtype = subtype(n.prev)
                if knuth_table[prevtype] and knuth_table[prevtype].bin == "*" then
                    undefined = true
                    local g = glue.copy(tex.getmath(prevtype .. "binspacing", style))
                    head = node.insert_before(head, n, g)
                end
                -- look at the next
                local nexttype = subtype(n.next)
                if undefined or knuth_table.bin[nexttype] == "*" then
                    local g = glue.copy(tex.getmath("bin" .. nexttype .. "spacing", style))
                    head = node.insert_after(head, n, g)
                end
                undefined = false
            end
        end
    end
end

local function binordspacing(head,style,penalties)
    traverse(head, style)
    return true
end

luatexbase.add_to_callback("pre_mlist_to_hlist_filter", binordspacing, "binordspacing")

\end{luacode*}

% Add further abominations to this list
\Umathopenbinspacing\displaystyle=\thinmuskip
\Umathopenbinspacing\textstyle=\thinmuskip
\Umathbinordspacing\displaystyle=\thinmuskip
\Umathbinordspacing\textstyle=\thinmuskip

\begin{document}
\begin{equation*}
    \alpha = -p(-w_1-v_0) - g(w_1)
\end{equation*}

\begin{center}
    $\alpha = -p(-w_1-v_0) - g(w_1)$
\end{center}
\end{document}

Answer 2

You ask,

Is there a reason for these spacing[s] to be different?

Indeed there is! What you've (re-)discovered is the difference between - (and + too) being employed as either a unary or a binary operator.

If the spacing were the same for both types of operators, you would probably get annoyed that it is the same.

In essence, what you're observing is the result of centuries of fine math typography, which has established that making the spacing around unary and binary operators the same is not optimal.

Here are some practical examples of the application of spacing rules for unary and binary operators.

\documentclass{article}
\begin{document}      
\obeylines % just for this example               
``$-$'' and ``$+$'' treated as unary operators:
$\dots,-3,-2,-1,0,+1,+2,+3,\dots$
$-1 \ne +1$
\bigskip
``$-$'' and ``$+$'' treated as binary operators:
$\dots,{}-3,{}-2,{}-1,0,{}+1,{}+2,{}+3,\dots$ --- looks awful!
$1+1=2$ \quad $2-2=0$
\bigskip
Mixed use:
$-1=5-6$ \quad $-5+6=+1$
\end{document}

Answer 3

Welcome! This is actually a feature and not a bug. The first minus is a sign while the second one is a binary operator. If you want the larger spacing, you can add a {}.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
 \alpha&=-p(-w_1-v0)-g(w_1)\\
 \alpha&={}-p(-w_1-v0)-g(w_1)\\
\end{align*}
\end{document}

But to me it seems more reasonable to treat signs different from operators.