One can believe whatever one pleases (hmm) but the convention in algebra and logic is to use the term "term" exactly this ways, and I think this way "does type check" because we use notions of algebra (with one "real analysis metaphor") in this task (i.e. polynomial, differential).
I think you refer to some programming language specifications -- but these usually don't use notions of polynomial, differential or equation so it does not type check, iswim!
There's another subtle issue as the term "polynomial" sometimes stands for both syntactical and semantical object (particular expression AND particular function); in general you do differentiate functions, not expressions, but then the funny thing about polynomials is you can differentiate them purely syntactically; then you do some jumps between language and metalanguage and it doesn't seem to do harm in general but oh that's so dirty; but why do I even write it? if you were curious you'd be already reading some abstract algebra or model theory (highly recommended topics btw).

ok, I can't help this: "mathematical operators" is a funny pleonasm, perhaps to distinguish them from "geographical operators"? ;)

I know what you mean, usually that's "arithmetical operators"; these names again seem to be byproduct of the way we write BNF for expressions in programming languages; some operations are called arithmetical as they rely on ALU hardware implementation or traditionally did, so symbols for them are "arithmetical operators" to distinguish from say some compilation-time ones like casting or pointers or constructors sometimes... it's just not a very fortunate overlap of vocabulary I guess.

It doesn't really matter, it's important the description of this task is no longer offensive :)
You know so many people these days are offended with some use of words or another, and I never had any fun in this so decided to fight for my right to be offended by confusing terms with predicates.

Hugs'n'kisses,
the serverly offended snappy comrade drcz

Hi,
racket version is missing #lang racket header!

Hi, racket version is initialized with (require going), should be (provide going), otherwise the tests don't work.

No, it would not :) Polynomials are functions of n>0 variables over a ring. Rings only have two actions, traditionally called (and written as) addition and multiplication. Exponents are only shorter notation for repeated multiplication of an element by itself, therefore you can only have 0 or more of these, where "multiplied 0 times by itself" is interpreted as the unit of multiplication. For single-variable polynomial the (existence and number of) roots are connected to the highest "exponent" of the variable (called the degree of a polynomial) -- most notably for algebraically closed fields (which are special cases of rings) you have fundamental theorem of algebra. How would it translate for negative powers? A negative number of roots?

such an expression with negative exponents is no longer a polynomial, is it? :)

current definition of churchToInt doesn't work; why not just (church)=>church((x)=>x+1,0) ?

To be precise, you mean Church numerals, not numbers; traditionally by numbers we mean these "abstract entities" that numerals represent; so we have e.g. Ramsey numbers, Graham's numbers, prime numbers, perfect numbers etc; and for representations we have Roman numerals, von Neuman numerals, Church numerals, Peano numerals etc.
Map is not the teritory (and the joke is there's no teritory really, just maps all the way down ;)).

tests for haskell do not work because (a) test scripts contains tabs, (b) haskell by default warns about these and (c) these warnings are treated as errors. the tabs are on every line with "RPN.calc". could you please fix this? we can't submit the solution :)