# How do you format a polynomial output so the coefficients and variables aren't combined into a fraction?

Suppose a computation gives the polynomial as its output. I'd like to know how to format the output similarly to the input line of the screenshot below.

Mathematica's output likes to combine fractions, and when the expressions are much more involved and symbolic, this makes it more difficult to read off.

Thanks in advance!

• Commented Aug 29, 2020 at 10:44

## 2 Answers

Mma has its internal rules concerning the order of the terms in expressions. It is possible, but very difficult to override this order. Generally, it is not recommended.

Nevertheless, I often use such transformations on the very last stage of my calculations in order to bring the expression to the form most comfortable to look at. This may be important to reduce errors and simplify work.

Here is your expression:

expr = 5/32*x + 7/11*x^5


You might do something like this

expr /. a_*x^n_. :> HoldForm[a]*HoldForm[x^n]/. HoldForm[x^1] :> HoldForm[x]


Try.

Do not forget that after this action it is impossible to make any further operations unless you remove the HoldForm by applying ReleaseHold[%]to the result.

Have fun!

• Awesome, thanks!! This was very helpful getting me on the right track. The actual application was multivariate but a function based on your initial idea got the job done. I'll add an answer with the function in case it's helpful, or there are suggestions. I'm new-ish to using stack exchange, so let me know if that is/isn't in line with usual procedure. Commented Aug 30, 2020 at 16:34
• That's perfectly OK. Commented Aug 30, 2020 at 17:56
• This gives an undesirable result when 7 is replaced by -7. Then + remains and it is followed by a negative sign and then the fraction. Is there a fix for this problem? Commented May 14, 2023 at 3:14
• @wdacda In this case one should slightly change the code. For example,like this: rule1 = a_*x^n_. :>If[a >= 0, HoldForm[a]*HoldForm[x^n], -HoldForm[Evaluate[Abs[a]]]* HoldForm[x^n]]; rule2 = HoldForm[x_^1] :> HoldForm[x] . Then 5/32*x - 7/11*x^5/.rule1/.rule2 yields the desired answer. Have fun! Commented May 14, 2023 at 16:57

As per @Alexei's suggestion to use HoldForm, here's a function that formats a polynomial the way I was looking for. In this case it's for hard-coded 3 variables, but could probably be straightforwardly extended to use the length of var to do so automatically:

formatPolynomial[poly_, vars_ : {p, q, pdq}] := Module[{ dim, coeffs, output },
dim = Max[Cases[CoefficientRules[poly, vars], v_?VectorQ :> Total[v], 2]] + 1;
coeffs = CoefficientList[poly, vars, {dim, dim, dim}];
output = Sum[coeffs[[i, j, k]] Subscript[tmp, i - 1, j - 1, k - 1], {i, 1,
dim, 1}, {j, 1, dim, 1}, {k, 1, dim, 1}];
output = output /. {a_ Subscript[tmp, n_, m_, l_] :> HoldForm[a] Subscript[tmp, n, m,l]} /. {Subscript[tmp, n_, m_, l_] :> vars[[1]]^n vars[[2]]^m vars[[3]]^l} /. {a_ HoldForm[b_] :> HoldForm[({b} // MatrixForm)] a};
output
]


This gives output so the coefficients of individual monomials (which I'm looking for) are easily identifiable:

• Perhaps formatPolynomial[poly_, v_] := Expand @ Collect[poly, v, HoldForm] is simpler? Commented Aug 30, 2020 at 16:50
• Whoa, that's much simpler!!! I didn't realize Collect could take a third argument like that. Would you like to post a new answer with this so I can accept it? Commented Aug 31, 2020 at 1:20
• This is great, with a but: How do I get ordered powers. For example Expand@Collect[3/8 - (15 x^2)/4 + (35 x^4)/8, x, HoldForm] gives x^2 (-15/4) +3/8 + x^4 (35/8) Commented May 14, 2023 at 4:05